Skip to main content Accessibility help
×
Hostname: page-component-77c89778f8-gvh9x Total loading time: 0 Render date: 2024-07-24T21:13:15.008Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  05 June 2012

Maurice Petyt
Affiliation:
University of Southampton
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Oden, J. T. 1967 Mechanics of Elastic StructuresNew YorkMcGraw-HillGoogle Scholar
Cowper, G. R. 1966 The shear coefficient in Timoshenko's beam theoryJ. Appl. Mech. Trans. ASME 88 335CrossRefGoogle Scholar
Kreysziz, E. 1972 Advanced Engineering MathematicsNew YorkWileyGoogle Scholar
Courant, R.Hilbert, D. 1953 Methods of Mathematical PhysicsNew YorkInterscienceGoogle Scholar
Kanotorovich, L. V.Krylov, V. I. 1958 Approximate Methods of Higher AnalysisGroningenNoordhoffGoogle Scholar
Mikhlin, S. G. 1964 Variational Methods in Mathematical PhysicsNew YorkMacmillanGoogle Scholar
Mikhlin, S. G. 1965 The Problem of the Minimum of a Quadratic FunctionalSan FranciscoHolden-DayGoogle Scholar
Bishop, R. E. D.Gladwell, G. M. L.Michaelson, S. 1965 The Matrix Analysis of VibrationCambridgeCambridge University PressGoogle Scholar
Dym, C. L.Shames, I. H. 1973 Solid Mechanics: A Variational ApproachNew YorkMcGraw-HillGoogle Scholar
Warburton, G. B. 1976 The Dynamical Behaviour of StructuresOxfordPergamonGoogle Scholar
Oden, J. T. 1972 Finite Elements of Nonlinear ContinuaNew YorkMcGraw-HillGoogle Scholar
Przemieniecki, J. S. 1968 Theory of Matrix Structural AnalysisNew YorkMcGraw-HillGoogle Scholar
Timoshenko, S.Goodier, J. N. 1970 Theory of ElasticityNew YorkMcGraw-HillGoogle Scholar
Love, A. E. H. 1944 Mathematical Theory of ElasticityNew YorkDoverGoogle Scholar
Courant, R. 1943 Variational methods for the solution of problems of equilibrium and vibrationsBull. Amer. Math. Soc 49 1CrossRefGoogle Scholar
Leckie, F. A.Lindberg, G. M. 1963 The effect of lumped parameters on beam frequenciesAeronaut. Quart 14 224CrossRefGoogle Scholar
Rudder, F. F. 1970
Oden, J. T. 1967 Mechanics of Elastic StructuresNew YorkMcGraw-HillGoogle Scholar
Yang, T. Y.Sun, C. T. 1973 Axial-flexural vibration of frameworks using finite element approachJ. Acoust. Soc. Amer 53 137CrossRefGoogle Scholar
Gladwell, G. M. L. 1964 The vibration of framesJ. Sound Vibration 1 402CrossRefGoogle Scholar
Carnegie, W.Thomas, J.Dokumaci, E. 1969 An improved method of matrix displacement analysis in vibration problemsAeronaut. Quart 20 321CrossRefGoogle Scholar
Kopal, Z. 1961 Numerical AnalysisLondonChapman and HallGoogle Scholar
Scheid, F. 1968 Numerical AnalysisSchaum's Outline SeriesNew YorkMcGraw-HillGoogle Scholar
Thomas, D. L.Wilson, J. M.Wilson, R. R. 1973 Timoshenko beam finite elementsJ. Sound Vibration 31 315CrossRefGoogle Scholar
Lees, A. W.Thomas, D. L. 1982 Unified Timoshenko beam finite elementJ. Sound Vibration 80 355CrossRefGoogle Scholar
Corn, S.Bouthaddi, N.Piranda, J. 1997 Transverse vibrations of short beams: finite element models obtained by a condensation methodJ. Sound Vibration 201 353CrossRefGoogle Scholar
Huang, T. C. 1961 The effect of rotary inertia and of shear deformation on the frequency and normal mode equations of uniform beams with simple end conditionsJ. Appl. Mech. Trans. ASME 28 579CrossRefGoogle Scholar
Huang, T. C.Kung, C. S. 1963 New tables of eigenfunctions representing normal modes of vibration of Timoshenko beamsDevelopments in Theoretical and Applied MechanicsNew YorkPlenum Press59Google Scholar
Dawe, D. J. 1978 A finite element for the vibration analysis of Timoshenko beamsJ. Sound Vibration 60 11CrossRefGoogle Scholar
Moan, T. 1973 On the local distribution of errors by finite element approximationsTheory and Practice in Finite Element Structural AnalysisYamada, Y.Gallagher, R. H.TokyoUniversity of Tokyo Press43Google Scholar
Hinton, E.Campbell, J. S. 1974 Local and global smoothing of discontinuous finite element functions using a least squares methodInt. J. Num. Meth. Eng 8 461CrossRefGoogle Scholar
Hinton, E.Scott, F. C.Ricketts, R. E. 1975 Least squares stress smoothing for parabolic isoparametric elementsInt. J. Num. Meth. Eng 9 235CrossRefGoogle Scholar
Barlow, J. 1976 Optimal stress locations in finite element modelsInt. J. Num. Meth. Eng 10 243CrossRefGoogle Scholar
Hughes, T. J. R. 1977 A simple and efficient finite element for plate bendingInt. J. Num. Meth. Eng 11 1529CrossRefGoogle Scholar
Bhashyam, G. R.Prathap, G. 1981 The second frequency spectrum of Timoshenko beamsJ. Sound Vibration 76 407CrossRefGoogle Scholar
Vermeulen, A. H.Heppler, G. R. 1998 Predicting and avoiding shear locking in beam vibration problems using the β-spline field approximation methodComp. Methods Appl. Mech. Eng 158 311CrossRefGoogle Scholar
Olson, M. D. 1975 Compatibility of finite elements in structural mechanicsOkehamptonRobinson and AssociatesH1Google Scholar
Vlasov, V. Z. 1961 Thin Walled Elastic BeamsWashington, DCNational Science FoundationGoogle Scholar
Tanaka, M.Bercin, A. N. 1997 Finite element modelling of the coupled bending and torsional free vibration of uniform beams with an arbitrary cross-sectionAppl. Math. Modell 21 339CrossRefGoogle Scholar
Mota Soares, C. A.Barradas Cardoso, J. E. 1979 Finite element dynamic analysis of structures based on the Vlasov beam theoryNumerical Analysis of the Dynamics of Ship Structures, EuromechParisGoogle Scholar
Hu, Y.Jin, X.Chen, B. 1996 A finite element model for the static and dynamic analysis of thin-walled beams with asymmetric cross-sectionsComput. Struct 61 897CrossRefGoogle Scholar
Wang, Q.-F. 1997 Spline finite member element method for vibration of thin-walled members with shear lagJ. Sound Vibration 206 339CrossRefGoogle Scholar
Kim, J. H.Kim, Y. Y. 2000 One-dimensional analysis of thin-walled closed beams having general cross-sectionsInt. J. Num. Math. Eng 49 6533.0.CO;2-I>CrossRefGoogle Scholar
Lindberg, G. M. 1963 Vibration of non-uniform beamsAeronaut. Quart 14 387CrossRefGoogle Scholar
Cleghorn, W. L.Tabarrock, B. 1992 Finite element formulation of a tapered Timoshenko beam for free lateral vibration analysisJ. Sound Vibration 152 461CrossRefGoogle Scholar
Thomas, J.Dokumaci, E. 1974 Simple finite elements for pre-twisted blading vibrationAeronaut. Quart 25 109CrossRefGoogle Scholar
Yardimoglu, B.Yildirim, T. 2004 Finite element model for vibration analysis of pre-twisted Timoshenko beamJ. Sound Vibration 273 741CrossRefGoogle Scholar
Gupta, R. S.Rao, S. S. 1978 Finite element eigenvalue analysis of tapered and twisted Timoshenko beamsJ. Sound Vibration 56 187CrossRefGoogle Scholar
Raveendranath, P.Singh, G.Pradhan, B. 2000 Free vibration of arches using a curved beam element based on a coupled polynomial displacement fieldComput. Struct 78 583CrossRefGoogle Scholar
Litewka, P.Rakowski, J. 2001 Free vibrations of shear-flexible and compressible arches by FEMInt. J. Num. Math. Eng 52 273CrossRefGoogle Scholar
Wu, J.-S.Chiang, L.-K. 2004 A new approach for free vibration analysis of arches with effects of shear deformation and rotary inertia consideredJ. Sound Vibration 277 49CrossRefGoogle Scholar
Rossi, R. R. 1989 In-plane vibrations of circular rings of non-uniform cross-section with account taken of shear and rotatory inertia effectsJ. Sound Vibration 135 443CrossRefGoogle Scholar
Wu, J.-S.Chiang, L.-K. 2004 Free vibration of a circularly curved Timoshenko beam normal to its initial plane using finite curved beam elementsComput. Struct 82 2525CrossRefGoogle Scholar
Kim, N.-I.Seo, K.-J.Kim, M.-Y. 2003 Free vibration and spatial stability of non-symmetric thin-walled curved beams with variable curvaturesInt. J. Solids Structures 40 3107CrossRefGoogle Scholar
Thomas, D. L.Wilson, R. R. 1973 The use of straight beam finite elements for analysis of vibrations of curved beamsJ. Sound Vibration 26 155CrossRefGoogle Scholar
Dunne, P. C. 1968 Complete polynomial displacement fields for finite element methodAeronaut. J 72 245Google Scholar
Irons, B. M.Ergatoudis, J.Zienkiewicz, O. C. 1968 Comment on ‘Complete polynomial displacement fields for finite element method’Aeronaut. J 72 709Google Scholar
Carr, J. B. 1970 The effect of shear flexibility and rotatory inertia on the natural frequencies of uniform beamsAeronaut. Quart 21 79Google Scholar
Barlow, J. 1976 Optimal stress locations in finite element modelsInt. J. Num. Meth. Eng 10 243CrossRefGoogle Scholar
Eisenberg, M. A.Malvern, L. E. 1973 On finite element integration in natural co-ordinatesInt. J. Num. Meth. Eng 7 574CrossRefGoogle Scholar
Bathe, K. J. 1996 Finite Element ProceduresUpper Saddle River, NJPrentice HallGoogle Scholar
Zienkiewicz, O. C.Taylor, R. L. 1989 The Finite Element Method. Vol. 1: Basic Formulation and Linear ProblemsLondonMcGraw-Hill Book CompanyGoogle Scholar
Hellen, T. K. 1976 Numerical Integration considerations in two and three dimensional isoparametric finite elementsThe Mathematics of Finite Elements and Applications IIWhiteman, J. R.LondonAcademic Press511Google Scholar
Krauthammer, T. 1979 Accuracy of the finite element method near a curved boundaryComputers and Structures 10 921CrossRefGoogle Scholar
Cook, R. D.Malkus, D. S.Plesha, M. E.Witt, R. J. 2002 Concepts and Applications of Finite Element AnalysisNew YorkJohn Wiley & SonsGoogle Scholar
Cook, R. D. 1975 Avoidance of parasitic shear in plane elementJ. Struct. Div. Proc. ASCE 101 1239Google Scholar
Clough, R. W.Chopra, A. K. 1966 Earthquake stress analysis in earth damsJ. Eng. Mech. Proc. ASCE 92 197Google Scholar
Hammer, P. C.Marlowe, O. J.Stroud, A. H. 1956 Numerical integration over simplexes and conesMathematical Tables and other Aids to Computation 10 130CrossRefGoogle Scholar
Laursen, M. E.Gellert, M. 1978 Some criteria for numerically integrated matrices and quadrature formulas for trianglesInt. J. Num. Meth. Eng 12 67CrossRefGoogle Scholar
Belytschko, T. 1972 Finite elements for axisymmetric solids under arbitrary loadings with nodes on originAIAA J 10 1532CrossRefGoogle Scholar
Buck, K. E. 1973 Comment on ‘Finite elements for axisymmetric solids under arbitrary loadings with nodes on origin’AIAA J 11 1357CrossRefGoogle Scholar
Belytschko, T. 1973 Buck, K. E.AIAA J 11 1358CrossRef
Deresiewicz, H.Mindlin, R. D. 1955 Axially symmetric flexural vibrations of a circular discJ. Appl. Mech., Trans. ASME 22 86Google Scholar
Gazis, D. C.Mindlin, R. D. 1960 Extensional vibrations and waves in a circular disc and a semi-infinite plateJ. Appl. Mech. Trans. ASME 27 541CrossRefGoogle Scholar
Baker, W. E.Daly, J. M. 1967 Dynamic analysis of continuum bodies by direct stiffness methodShock and Vibration Bull 36 55Google Scholar
Gupta, K. K. 1984 STARS – A general purpose finite element computer program for analysis of engineering structuresNASA Reference Publication1129Google Scholar
Irons, B. M. 1971 Quadrature rules for brick based finite elementsInt. J. Num. Meth. Eng 3 293CrossRefGoogle Scholar
Eisenberg, M. A.Malvern, L. E. 1973 On finite element integration in natural coordinatesInt. J. Num. Meth. Eng 7 574CrossRefGoogle Scholar
Gao, D. P.Petyt, M. 1983 Prediction of frequencies of a practical turbine discISVR MemorandumUniversity of SouthamptonGoogle Scholar
Rao, S. S.Prasad, A. S. 1975 Vibrations of annular plates including the effects of rotary inertia and transverse shear deformationJ. Sound Vibration305CrossRefGoogle Scholar
Bathe, K. J. 1996 Finite Element ProceduresUpper Saddle River, NJPrentice HallGoogle Scholar
Zienkiewicz, O. C.Taylor, R. L. 1989 The Finite Element MethodLondonMcGraw-Hill BookGoogle Scholar
Johnson, S. E.Field, E. I. 1973
To, C. W. S. 1982 Application of the finite element method for the evaluation of velocity response of anvilsJ. Sound Vibration 84 529CrossRefGoogle Scholar
Hellen, T. K. 1976 Numerical integration considerations in two and three dimensional isoparametric finite elementsThe Mathematics of Finite Elements and Applications IIWhiteman, J. R.LondonAcademic Press511Google Scholar
Hellen, T. K. 1972 Effective quadrature rules for quadratic solid isoparametric finite elementsInt. J. Num. Meth. Eng 4 597CrossRefGoogle Scholar
Salama, A. M. 1976 Finite Element Dynamic Analysis of Blade Packets and Bladed Disc AssembliesThesisUniversity of SouthamptonGoogle Scholar
Armenakas, A. E.Gazis, D. C.Herrmann, G. 1969 Free Vibrations of Circular Cylinder ShellsOxfordPergamon PressGoogle Scholar
Adini, A.Clough, R. W. 1961
Melosh, R. J. 1963 Basis for derivation of matrices for the direct stiffness methodAIAA J 1 1631CrossRefGoogle Scholar
Smith, C. V. 1970
Tinawi, R. A. 1972 Anisotropic tapered elements using displacement modelsInt. J. Num. Meth. Eng 4 475CrossRefGoogle Scholar
Lindberg, G. M.Olson, M. D.Tulloch, H. A. 1969
Lindberg, G. M.Olson, M. D. 1970 Convergence studies of eigenvalue solutions using two finite plate bending elementsInt. J. Num. Meth. Eng 2 99CrossRefGoogle Scholar
Reid, R. E. 1965
Gorman, D. J. 1981 An analytical solution for the free vibration analysis of rectangular plates resting on symmetrically distributed point supportsJ. Sound Vibration 79 561CrossRefGoogle Scholar
Petyt, M.Mirza, W. H. 1972 Vibration of column supported floor slabsJ. Sound Vibration 21 355CrossRefGoogle Scholar
Wah, T. 1964 Vibration of stiffened platesAeronaut. Quart 15 285CrossRefGoogle Scholar
Huffington, N. J. 1956 Theoretical determination of rigidity properties of orthogonally stiffened platesJ. Appl. Mech. Trans. ASME 23 15Google Scholar
Bogner, F. K.Fox, R. L.Schmit, L. A. 1966 397
Butlin, G. A.Leckie, F. A. 1966
Rossi, R. E. 1997 A note on a finite element for vibrating thin, orthotropic rectangular platesJ. Sound Vibration 208 864CrossRefGoogle Scholar
Mason, V. 1967 On the use of rectangular finite elementsISVR ReportUniversity of SouthamptonGoogle Scholar
Mason, V. 1968 Rectangular finite elements for analysis of plate vibrationsJ. Sound Vibration 7 437CrossRefGoogle Scholar
Wilson, R. R.Brebbia, C. A. 1971 Dynamic behaviour of steel foundations for turbo-alternatorsJ. Sound Vibration 18 405CrossRefGoogle Scholar
Hughes, T. J. R.Taylor, R. L.Kanoknukulcha, W. 1977 A simple efficient finite element for plate bendingInt. J. Num. Meth. Eng 11 1529CrossRefGoogle Scholar
Pugh, E. D. L.Hinton, E.Zienkiewicz, O. C. 1978 A study of quadrilateral plate bending elements with reduced integrationInt. J. Num. Meth. Eng 12 1059CrossRefGoogle Scholar
Hinton, E.Bicanic, N. 1979 A comparison of Lagrangian and Serendipity Mindlin plate elements for free vibration analysisComputers and Structures 10 483CrossRefGoogle Scholar
Srinivas, S.Joga Rao, C. V.Rao, A. K. 1970 An exact analysis for vibration of simply supported homogeneous and laminated thick rectangular platesJ. Sound Vibration 12 187CrossRefGoogle Scholar
Robinson, J. 1978 Element evaluation – a set of assessment points and standard testsFinite Element Methods in the Commercial EnvironmentRobinson, J.OkehamptonRobinson and Associates218Google Scholar
Tocher, J. L. 1962
Petyt, M. 1967
Petyt, M. 1966
Gustafson, P. N.Stokey, W. F.Zorowski, C. F. 1953 An experimental study of natural vibrations of cantilevered triangular platesJ. Aeronaut. Sci 20 331CrossRefGoogle Scholar
Clough, R. W.Tocher, J. L. 1966
Clough, R. W.Felippa, C. A. 1968 399
Dickinson, S. M.Henshell, R. D. 1969 Clough–Tocher triangular plate bending element in vibrationAIAA J 7 560CrossRefGoogle Scholar
Batoz, J.-L.Bathe, K.-J.Ho, L.-W. 1980 A study of three-node triangular plate bending elementsInt. J. Num. Meth. Eng 15 1771CrossRefGoogle Scholar
Lynn, P. P.Dhillon, B. S. 1971
Deak, A. L.Pian, T. H. H. 1967 Application of the smooth surface interpolation to the finite element analysisAIAA J 5 187CrossRefGoogle Scholar
Birkhoff, G.Garabedian, H. L. 1960 Smooth surface interpolationJ. Math. Phys 39 258CrossRefGoogle Scholar
Veubeke, B. Fraeijs De 1968 A conforming finite element for plate bendingInt. J. Solids Structures 4 95CrossRefGoogle Scholar
Orris, R. M.Petyt, M. 1973 A finite element study of the vibration of trapezoidal platesJ. Sound Vibration 27 325CrossRefGoogle Scholar
Rock, T.Hinton, E. 1974 Free vibration and transient response of thick and thin plates using the finite element methodInt. J. Earthquake Eng. Struct. Dyn 3 51CrossRefGoogle Scholar
Razzaque, A. 1984 On the four noded discrete Kirchhoff shell elementsAccuracy, Reliability and Training in FEM TechnologyRobinson, J.OkehamptonRobinson and Associates473Google Scholar
Soh, A.-K.Ling, C. 2000 An improved discrete Kirchhoff triangular element for bending, vibration and buckling analysisEur. J. Mech. A. Solids 19 891CrossRefGoogle Scholar
Bathe, K.-J. 1996 Finite Element ProceduresUpper Saddle River, NJPrentice HallGoogle Scholar
Hernández, E.Hervella-Nieto, L.Rodriguez, R. 2003 Computation of the vibration modes of plates and shells by low-order MITC quadrilateral finite elementsComput. Struct 81 615CrossRefGoogle Scholar
Janabi, B. S. AlHinton, E. 1987 A study of the free vibrations of square plates with various edge conditionsHinton, E.Numerical Methods and Software for Dynamic Analysis of Plates and ShellsSwanseaPineridge Press167Google Scholar
Leissa, A. W. 1969 Vibration of PlatesWashington DCUS Government Printing OfficeGoogle Scholar
Cowper, G. R.Kosko, E.Lindberg, G. M.Olson, M. D. 1968
Ghazzi, S.Barki, F. A.Safwat, H. M. 1997 Free vibration analysis of penta, hepta-gonal shaped platesComp. Struct 62 395CrossRefGoogle Scholar
Popplewell, N.McDonald, D. 1971 Conforming rectangular and triangular plate bending elementsJ. Sound Vibration 19 333CrossRefGoogle Scholar
Claassen, R. W.Thorne, C. J. 1961 Vibrations of thin rectangular isotropic platesJ. Appl. Mech. Trans ASME 28 304CrossRefGoogle Scholar
Lindberg, G. M. 1967
Plunkett, R. 1963 Natural frequencies of uniform and non-uniform rectangular cantilever platesJ. Mech. Eng. Sci 5 146CrossRefGoogle Scholar
Olson, M. D.Lindberg, G. M. 1970
Yurkovich, R. N.Schmidt, J. H.Zak, A. R. 1971 Dynamic analysis of stiffened panel structuresJ. Aircraft 8 149Google Scholar
McBean, R. P. 1968
Olson, M. D.Hazell, C. R. 1977 Vibration studies on some integral rib-stiffened platesJ. Sound Vibration 50 43CrossRefGoogle Scholar
Petyt, M. 1977 Finite strip analysis of flat skin-stringer structuresJ. Sound Vibration 54 537CrossRefGoogle Scholar
Rao, M. N. BapuGuruswamy, P.Venkateshwara Rao, M.Pavithran, S. 1978 Studies on vibration of some rib-stiffened cantilever platesJ. Sound Vibration 57 389Google Scholar
Ramesh, C. K.Belkune, R. M. 1973 Free vibrations of plate-beam systemsTheory and Practice in Finite Element Structural AnalysisYamada, Y.Gallagher, R. H.TokyoUniversity of Tokyo Press357Google Scholar
Miller, R. E. 1980 Dynamic aspects of the error in eccentric beam modellingInt. J. Num. Meth. Eng 15 1447CrossRefGoogle Scholar
Grandle, R. E.Rucker, C. E. 1971 343
Thornton, E. A. 1972
Wilson, R. R.Brebbia, C. A. 1971 Dynamic behaviour of steel foundations for turbo-alternatorsJ. Sound Vibration 18 405CrossRefGoogle Scholar
Nair, P. S.Rao, M. S. 1984 On vibration of plates with varying stiffener lengthJ. Sound Vibration 95 19CrossRefGoogle Scholar
Rao, M. S.Nair, P. S.Durvasula, S. 1985 On vibration of eccentrically stiffened plates with varying stiffener lengthJ. Sound Vibration 99 568Google Scholar
Mukherjee, A.Mukhopadhyay, M. 1988 Finite element free vibration of eccentrically stiffened platesComp. Struct 30 1303CrossRefGoogle Scholar
Palani, G. S.Iyer, N. R.Appa, T. V. S. R. 1992 An efficient finite element model for static and vibration analysis of eccentrically stiffened plates/shellsComp. Struct 43 651CrossRefGoogle Scholar
Palami, G. S.Iyer, N. R.Appa Rao, T. V. S. R. 1993 An efficient finite element model for static and vibration analysis of plates with arbitrary located eccentric stiffenersJ. Sound Vibration 166 409CrossRefGoogle Scholar
Lee, Y. Y.Ng, C.-F. 1998 Sound insertion loss of stiffened enclosure plates using the finite element method and the classical approachJ. Sound Vibration 217 239CrossRefGoogle Scholar
Popplewell, N. 1971 The vibration of a box-type structure I. Natural frequencies and normal modesJ. Sound Vibration 14 357CrossRefGoogle Scholar
Dickinson, S. M.Warburton, G. B. 1967 Vibration of box-type structuresJ. Mech. Eng. Sci 9 325CrossRefGoogle Scholar
Popplewell, N.Youssef, N. A. N.McDonald, D. 1976 Economical evaluation of the vibration characteristics of rectangular structures with sloping roofsJ. Sound Vibration 44 493CrossRefGoogle Scholar
Huang, T. C.Kung, C. S. 1963 New tables of eigenfunctions representing normal modes of vibration of Timoshenko beamsDevelopments in Theoretical and Applied MechanicsNew YorkPlenum Press59Google Scholar
Lees, A. W.Thomas, D. L.Wilson, R. R. 1976 Analysis of the vibration of box beamsJ. Sound Vibration 45 559CrossRefGoogle Scholar
Schmit, L. A.Bogner, F. K.Fox, R. L. 1968 Finite deflection structural analysis using plate and shell discrete elementsAIAA J 6 781Google Scholar
Hickling, R.Kamal, M. M. 1982 Engine Noise: Excitation, Vibration and RadiationNew YorkPlenum PressCrossRefGoogle Scholar
Lalor, N.Petyt, M. 1982 211
Zienkiewicz, O. C.Taylor, R. L. 1991 The Finite Element Method. Vol. 2: Solid and Fluid Mechanics, Dynamics and Non-linearityLondonMcGraw-Hill Book CompanyGoogle Scholar
Cook, R. D.Malkus, D. S.Plesha, M. E.Witt, R. J. 2002 Concepts and Applications of Finite Element AnalysisNew YorkJohn Wiley & SonsGoogle Scholar
MacNeal, R. H.Harder, R. L. 1988 A refined four-noded membrane element with rotational degrees of freedomComp. Struct 28 75CrossRefGoogle Scholar
Cook, R. D. 1994 Four-node flat shell element: drilling degrees of freedom, membrane-bending coupling, warped geometry, and behaviourComp. Struct 50 549CrossRefGoogle Scholar
Razaqpur, A. G.Aziz, O.Nofal, M. 1990
Ross, C. T. F. 1975 Free vibration of thin shellsJ. Sound Vibration 39 337CrossRefGoogle Scholar
Webster, J. J. 1968 Free vibration of rectangular curved panelsInt. J. Mech. Sci 10 571CrossRefGoogle Scholar
Petyt, M. 1971 Vibration of curved platesJ. Sound Vibration 15 381CrossRefGoogle Scholar
Hernández, E.Hervella-Nieto, L.Rodríguez, R. 2003 Computation of the vibration modes of plates and shells by low-order MITC quadrilateral finite elementsComp. Struct 81 615CrossRefGoogle Scholar
Irie, T.Yamada, G.Kobayashi, Y. 1984 Free vibration of a cantilever folded plateJ. Acoust. Soc. Amer 76 1743CrossRefGoogle Scholar
Wemper, G. 1989 Mechanics and finite elements of shellsASME Appl. Mechanics Rev 42 129CrossRefGoogle Scholar
MacNeal, R. H. 1989 The evolution of lower order plate and shell elements in MSC/NASTRANFinite Elements Anal. Design 5 197CrossRefGoogle Scholar
Noor, A. K. 1990 Bibliography on monographs and surveys on shellsASME Appl. Mech. Rev 43 223CrossRefGoogle Scholar
Gilewski, W.Radwanska, M. 1991 A survey of finite element models for the analysis of moderately thick shellsFinite Elements Anal. Design 9 1CrossRefGoogle Scholar
Bernadou, M. 1996 Finite Element Methods for Thin Shell ProblemsNew YorkJohn Wiley   SonsGoogle Scholar
Bucalem, M. L.Bathe, K. J. 1997 Finite element analysis of shell structuresArch. Comp. Meth. Eng 4 3CrossRefGoogle Scholar
Lim, G. H. 1999 Vibration of plates and shells using finite elements (1996–1997)Finite Elements Anal. Design 31 223CrossRefGoogle Scholar
Mackerle, J. 1999 Finite element vibration analysis of beams, plates and shellsShock and Vibration 6 97CrossRefGoogle Scholar
Yang, H. Y. T.Saigal, S.Masud, A.Kapania, R. K. 2000 A survey of recent shell finite elementsInt. J. Num. Meth. Eng 47 1013.0.CO;2-C>CrossRefGoogle Scholar
Qatu, M. S. 2002 Recent research advances in the dynamic behaviour of shells 1989–2000ASME Appl. Mech. Rev 55 415CrossRefGoogle Scholar
Kraus, H. 1967 Thin Elastic ShellsNew YorkJohn Wiley & SonsGoogle Scholar
Leissa, A. W. 1993 Vibration of ShellsSewickley, PAAcoustical Society of AmericaGoogle Scholar
Warburton, G. B. 1970 Dynamics of shellsSymposium on Structural DynamicsLoughborough UniversityGoogle Scholar
Novozhilov, V. V. 1964 Thin Shell TheoryGroeningenNoordhoffCrossRefGoogle Scholar
Petyt, M.Fleischer, C. C. 1973 367
Webster, J. J. 1968 Free vibration of rectangular curved panelsInt. J. Mech. Sci 10 571CrossRefGoogle Scholar
Olson, M. D.Lindberg, G. M. 1971 Dynamic analysis of shallow shells with a doubly-curved triangular finite elementJ. Sound Vib 19 229CrossRefGoogle Scholar
Zienkiewicz, O. C.Taylor, R. L. 1991 The Finite Element MethodLondonMcGraw-HillGoogle Scholar
Ross, C. T. F. 1984 Finite Element Programs for Axisymmetric Problems in EngineeringChichesterEllis HorwoodGoogle Scholar
Webster, J. J. 1967 Free vibrations of shells of revolution using ring finite elementsInt. J. Mech. Sci 9 559CrossRefGoogle Scholar
Sen, S. K.Gould, P. L. 1974 Free vibration of shells of revolution using FEMASCE J. Eng. Mech. Div 100 283Google Scholar
Fan, S. C.Luah, M. H. 1989 Spline finite element for axisymmetric free vibrations of shells of revolutionJ. Sound Vib 132 61CrossRefGoogle Scholar
Surana, K. S. 1980 Transition finite elements for three-dimensional stress analysisInt. J. Num. Meth. Eng 15 991CrossRefGoogle Scholar
Ahmed, S.Irons, B. M.Zienkiewicz, O. C. 1970 Analysis of thick and thin shell structures by curved finite elementsInt. J. Num. Meth. Eng 2 419CrossRefGoogle Scholar
Zienkiewicz, O. C.Too, J.Taylor, R. L. 1971 Reduced integration technique in general analysis of plates and shellsInt. J. Num. Meth. Eng 3 275CrossRefGoogle Scholar
Weaver, W.Johnston, P. R. 1987 Structural Dynamics by Finite ElementsEnglewood Cliffs, NJPrentice-HallGoogle Scholar
Bathe, K.-J. 1996 Finite Element ProceduresUpper Saddle River, NJPrentice-HallGoogle Scholar
Cook, R. D.Malkus, D. S.Plesha, M. E.Witt, R. J. 2002 Concepts and Applications of Finite Element AnalysisNew YorkJohn WileyGoogle Scholar
Hofmeister, L. D.Evensen, D. A. 1972 Vibration problems using isoparametric shell elementsInt. J. Num. Meth. Eng 5 142CrossRefGoogle Scholar
Olson, M. D.Lindberg, G. M. 1969 Vibration analysis of cantilevered curved plates using a new cylindrical shell finite elementProceedings of the Second Conference on Matrix Methods in Structural Mechanics247Google Scholar
Mota Scares, C. A.Petyt, M. 1978 Finite element dynamic analysis of practical bladed discsJ. Sound Vib 61 561CrossRefGoogle Scholar
Surana, K. S. 1980 Transition finite elements for axisymmetric stress analysisInt. J. Num. Meth. Eng 15 809CrossRefGoogle Scholar
Özakça, M.Hinton, E. 1994 Free vibration analysis and optimisation of axisymmetric plates and shells – 1Comp. Struct 6 1181CrossRefGoogle Scholar
Kunieda, H. 1984 Flexural axisymmetric free vibrations of a spherical dome: exact results and approximate solutionsJ. Sound Vib 92 1CrossRefGoogle Scholar
Reddy, J. N. 2003 Mechanics of Laminated Composite Plates and Shells: Theory and AnalysisBoca Raton, FICRC PressGoogle Scholar
Reddy, J. N. 1985 A review of the literature on finite element modelling of laminated composite platesShock Vib. Dig 17 3CrossRefGoogle Scholar
Noor, A. K.Burton, W. S. 1989 Assessment of shear deformation theories for multi-layered composite platesAppl. Mech. Rev 42 1CrossRefGoogle Scholar
Reddy, J. N. 1989 Refined computational models of composite laminatesInt. J. Num. Meth. Eng 27 361CrossRefGoogle Scholar
Noor, A. K.Burton, W. S. 1990 Assessment of computational models for multilayered anisotropic platesComposite Struct 14 233CrossRefGoogle Scholar
Reddy, J. N. 1990 A review of refined theories of laminated platesShock Vib. Dig 22 3CrossRefGoogle Scholar
Noor, A. K. 1992 Mechanics of anisotropic plates and shells – a new look at an old subjectComput. Struct 44 499CrossRefGoogle Scholar
Reddy, J. N.Robbins, D. H. 1994 Theories and computational models for composite laminatesAppl. Mech. Rev 47 147CrossRefGoogle Scholar
Carrera, E. 2002 Theories and finite elements for multi-layered, anisotropic, composite plates and shellsArch. Comput. Math. Eng 9 87CrossRefGoogle Scholar
Kollar, L. P.Springer, G. P. 2003 Mechanics of Composite StructuresCambridgeCambridge University PressCrossRefGoogle Scholar
Qatu, M. S. 2004 Vibration of Laminated Shells and PlatesKidlingtonElsevierGoogle Scholar
Mei, C.Prasad, C. B. 1989 Effects of large deflection and transverse shear on responses of rectangular symmetrical composite laminates subjected to acoustic excitationJ. Comp. Materials 23 606CrossRefGoogle Scholar
Thornton, E. A. 1977 Free vibrations of unsymmetrically laminated cantilevered composite panelsShock Vibration Bull 47 79Google Scholar
Chow, T. S. 1971 On the propagation of flexural waves in an orthotropic laminated plate and its response to an impulsive loadJ. Comp. Materials 5 306CrossRefGoogle Scholar
Whitney, J. M. 1973 Shear correction factors for orthotropic laminates under static loadJ. Appl. Mech. Trans. ASME 40 302CrossRefGoogle Scholar
Wittrick, W. H. 1987 Analytical three-dimensional elasticity solutions to some plate problems and some observations on Mindlin plate theoryInt. J. Solids Struct 23 441CrossRefGoogle Scholar
Reddy, J. N. 1979 Free vibration of antisymmetric angle-ply laminated plates including transverse shear deformation by the finite element methodJ. Sound Vibration 66 565CrossRefGoogle Scholar
Bert, C. W.Chen, T. L. C. 1978 Effect of shear deformation on vibration of antisymmetric angle-ply laminated rectangular platesInt. J. Solids Struct 14 465CrossRefGoogle Scholar
Reddy, J. N. 1984 A simple higher-order theory for laminated composite platesJ. Appl. Mech. Trans. ASME 51 745CrossRefGoogle Scholar
Reddy, J. N. 1984 A refined nonlinear theory of plates with transverse shear deformationInt. J. Solids Struct 20 881CrossRefGoogle Scholar
Reddy, J. N. 1990 A general non-linear third-order theory of plates with moderate thicknessInt. J. Nonlinear Mech 25 677CrossRefGoogle Scholar
Lee, S.-Y.Wooh, S.-C. 2004 Finite element vibration analysis of composite box structures using the high order plate theoryJ. Sound Vibration 277 801CrossRefGoogle Scholar
Liu, S. 1991 A vibration analysis of composite laminated platesFinite Elements Anal. Design 9 295CrossRefGoogle Scholar
Ghosh, A. K.Dey, S. S. 1994 Free vibration of laminated composite plates – a simple finite element based on higher order theoryComput. Struct 52 397CrossRefGoogle Scholar
Soula, M.Nasri, R.Ghazel, A.Chevalier, Y. 2006 The effects of kinematic model approximations on natural frequencies and modal damping of laminated composite platesJ. Sound Vibration 297 315CrossRefGoogle Scholar
Saravanos, D. A.Heyliger, P. R.Hopkins, D. A. 1997 Layerwise mechanics and finite elements for the dynamic analysis of piezoelectric composite platesInt. J. Solids Struct 34 359CrossRefGoogle Scholar
Saravanos, D. A.Heyliger, P. R. 1999 Mechanics and computational models for laminated piezoelectric beams, plates and shellsAppl. Mech. Rev 52 305CrossRefGoogle Scholar
Benjeddo, A. 2000 Advances in piezoelectric finite element modelling of adaptive structural elementsComput. Struct 76 347CrossRefGoogle Scholar
Qatu, M. S. 2002 Recent research advances in the dynamic behaviour of shells: 1989–2000Appl. Mech. Rev 55 325CrossRefGoogle Scholar
Matsunaga, H. 2002 Assessment of a global higher-order deformation theory for laminated composite and sandwich platesComposite Struct 56 279CrossRefGoogle Scholar
Plantema, F. J. 1966 Sandwich Construction: The Bending and Buckling of Sandwich Beams. Plates and ShellsNew YorkJohn Wiley & SonGoogle Scholar
Allen, H. G. 1969 Analysis and Design of Structural Sandwich PanelsOxfordPergamon PressGoogle Scholar
Shenoi, R. A.Wellicome, J. F. 1993 Composite Materials in Maritime Structures. Vol. 1: Fundamental Aspects. Vol. 2: Practical ConsiderationsCambridgeCambridge University PressGoogle Scholar
Mallikarjura, Kant, T. 1993 A critical review and some results of recently developed refined theories of fibre-reinforced laminated composites and sandwichesComposite Struct 23 293CrossRefGoogle Scholar
Mackerle, J. 2002 Finite element analysis of sandwich structures: a bibliography (1980–2001)Eng. Comput 19 206CrossRefGoogle Scholar
Nayak, A. K.Moy, S. S. J.Shenoi, R. A. 2002 Free vibration analysis of composite sandwich plates based on Reddy's higher-order theoryComposites: Part B 33 505CrossRefGoogle Scholar
Raville, M. E.Ueng, C. E. S. 1967 Determination of natural frequencies of vibration of a sandwich plateExp. Mech 7 490CrossRefGoogle Scholar
Meirovitch, L.Baruh, H. 1983 On the inclusion principle for the hierarchical finite element methodInt. J. Num. Meth. Eng 19 281CrossRefGoogle Scholar
Peano, A. 1976 Hierarchies of conforming finite elements for plane elasticity and plate bendingComput. Math. Appl 2 211CrossRefGoogle Scholar
Zhu, D. C. 1986 Development of hierarchical finite element methods at BIAAProceedings of the International Conference on Computational MechanicsGoogle Scholar
Hayek, S. I. 2001 Advanced Mathematical Methods in Science and EngineeringNew YorkMarcel DekkerGoogle Scholar
Beslin, O.Nicolas, J. 1997 A hierarchical functions set for predicting very high order plate bending modes with any boundary conditionsJ. Sound Vibration 202 633CrossRefGoogle Scholar
Bardell, N. S. 1989 The application of symbolic computing to the hierarchical finite element methodInt. J. Num. Meth. Eng 28 1181CrossRefGoogle Scholar
Bardell, N. S. 1991 Free vibration analysis of a flat plate using the hierarchical finite element methodJ. Sound Vibration 151 263CrossRefGoogle Scholar
Leissa, A. W. 1969 Vibration of PlatesWashington DCUS Government Printing OfficeGoogle Scholar
Bardell, N. S. 1992 The free vibration of skew plates using the hierarchical finite element methodComput. Struct 45 841CrossRefGoogle Scholar
Liew, K. M.Lam, K. Y. 1990 Applications of two-dimensional orthogonal plate functions to flexural vibration of skew platesJ. Sound Vibration 139 241CrossRefGoogle Scholar
Han, W.Petyt, M. 1996 Linear vibration analysis of laminated rectangular plates using the hierarchical finite element method – IComput. Struct 61 705CrossRefGoogle Scholar
Chow, S. T.Liew, K. M.Lam, K. Y. 1992 Transverse vibration of symmetrically laminated rectangular composite plateCompos. Struct 20 213CrossRefGoogle Scholar
Bardell, N. S.Dunsdon, J. M.Langley, R. S. 1995 Compos. Struct 32 237CrossRef
Jensen, D. W.Crawley, E. F. 1984 Frequency determination techniques for cantilevered plates with bending-torsion couplingAIAA J 22 415Google Scholar
Bardell, N. S. 1991
Leissa, A. W. 1993 Vibration of ShellsSewickley, PAAcoustical Society of AmericaGoogle Scholar
West, L. J.Bardell, N. S.Dunsdon, J. M.Loasby, P. M. 1997 217
Leung, A. Y. T.Chan, J. K. W. 1998 J. Sound Vibration 212 179CrossRef
Leung, A. Y. T.Zhu, B.Zheng, J.Yang, H. 2004 J. Sound Vibration 271 67CrossRef
Leung, A. Y. T.Zhu, B. 2004 Transverse vibration of thick polygonal plates using analytically integrated trapezoidal Fourier p-elementComput. Struct 82 109CrossRefGoogle Scholar
Wang, C. M.Reddy, J. N.Lee, K. H. 2000 Shear Deformable Beams and PlatesOxfordElsevierGoogle Scholar
Bardell, N. S.Dunsdon, J. M.Langley, R. S. 1997 Free vibration analysis of coplanar sandwich panelsComput. Struct 38 463CrossRefGoogle Scholar
Raville, M. E.Veng, C. E. S. 1967 Determination of natural frequencies of vibration of a sandwich plateEx. Mech 7 490CrossRefGoogle Scholar
Bardell, N. S.Dunsdon, J. M.Langley, R. S. 1998 Free vibration of thin, isotropic, open, conical panelsJ. Sound Vibration 217 297CrossRefGoogle Scholar
Bardell, N. S.Langley, R. S.Dunsdon, J. M.Aglietti, G. S. 1999 An h-p finite element vibration analysis of open conical sandwich panels and conical sandwich frustaJ. Sound Vibration 226 345CrossRefGoogle Scholar
Wilkins, D. J.Bert, C. W.Egle, D. M. 1970 J. Sound Vibration 13 211CrossRef
Wilkinson, J. H. 1965 The Algebraic Eigenvalue ProblemOxfordClarendon PressGoogle Scholar
Bishop, R. E. D.Gladwell, G. M. L.Michaelson, S. 1965 The Matrix Analysis is of VibrationCambridgeCambridge University PressGoogle Scholar
Gourlay, A. R.Watson, G. A. 1973 Computational Methods for Matrix EigenproblemsChichesterWileyGoogle Scholar
Hughes, T. J. R. 1987 The Finite Element Method: Linear Static and Dynamic Finite Element AnalysisEnglewood Cliffs, NJPrentice HallGoogle Scholar
Kardestuncer, H.Norrie, D. H. 1988 Finite Element HandbookNew YorkMcGraw-HillGoogle Scholar
Sehmi, N. S. 1989 Large Order Structural Eigenanalysis TechniquesChichesterEllis Horwood LtdGoogle Scholar
Jennings, A.McKeown, J. J. 1992 Matrix ComputationChichesterJohn Wiley & SonsGoogle Scholar
Bathe, K. J. 1996 Finite Element ProceduresUpper Saddle River, NJPrentice HallGoogle Scholar
Geradin, M.Rixen, D. 1997 Mechanical Vibrations: Theory and Applications to Structural DynamicsChichesterJohn Wiley & SonsGoogle Scholar
Petyt, M. 1998 Introduction to Finite Element Vibration AnalysisCambridgeCambridge University PressGoogle Scholar
Stewart, G. W. 2001 Matrix Algorithms Vol. II: EigensystemsPhiladelphiaSIAMCrossRefGoogle Scholar
Cook, R. D.Malkus, D. S.Plesha, M. E.Witt, R. J. 2002 Concepts and Applications of Finite Element AnalysisNew YorkJohn Wiley & SonsGoogle Scholar
Gladwell, G. M. L. 1961 Vibrating systems with equal natural frequenciesJ. Mech. Eng. Sci 3 178CrossRefGoogle Scholar
Barth, W.Martin, R. S.Wilkinson, J. H. 1967 Calculation of the eigenvalues of a symmetric tridiagonal matrix by the method of bisectionNumerische Mathematik 9 386CrossRefGoogle Scholar
Peters, G.Wilkinson, J. H. 1969 12 398
Lehoucq, R. B.Sorensen, D. C. 1996 Deflation techniques for an implicitly restarted Arnoldi iterationSIAM J. Matrix Anal. Appl 17 789CrossRefGoogle Scholar
Sleijpen, G. L. G.Vorst, H. A. van der 1996 A Jacobi-Davidson iteration method for linear eigenvalue problemsSIAM J. Matrix Anal. Appl 17 401CrossRefGoogle Scholar
Thomas, D. L. 1979 Dynamics of rotationally periodic structuresInt. J. Num. Meth. Eng 14 81CrossRefGoogle Scholar
Srinivasan, A. V. 1976 Structural Dynamic Aspects of Bladed Disk AssembliesNew YorkThe American Society of Mechanical EngineersGoogle Scholar
Soares, C. A. MotaPetyt, M.Salama, A. M. 1976
Salama, A. M.Petyt, M.Soares, C. A. Mota 1976 45
Leissa, A. W. 1969
Soares, C. A. MotaPetyt, M. 1978 Finite element analysis of practical bladed discsJ. Sound Vibration 61 561CrossRefGoogle Scholar
Nelson, R. L.Thomas, D. L. 1978 Free vibration analysis of cooling towers with column supportsJ. Sound Vibration 57 149CrossRefGoogle Scholar
Guyan, R. J. 1965 Reduction of stiffness and mass matricesAIAA J 3 380CrossRefGoogle Scholar
Irons, B. M. 1965 Structural eigenvalue problems: elimination of unwanted variablesAIAA J 3 961CrossRefGoogle Scholar
Wright, G. C.Miles, G. A. 1971 An economical method for determining the smallest eigenvalues of large linear systemsInt. J. Num. Meth. Eng 3 25CrossRefGoogle Scholar
Geradin, M. 1971 Error bounds for eigenvalue analysis by elimination of variablesJ. Sound Vibration 19 111CrossRefGoogle Scholar
Henshall, R. D.Ong, J. H. 1975 Automatic masters for eigenvalue economizationInt. J. Earthquake Engineering and Structural Dynamics 3 375CrossRefGoogle Scholar
Shah, V. N.Raymund, M. 1982 Analytical selection of masters for the reduced eigenvalue problemInt. J. Num. Meth. Eng 18 89CrossRefGoogle Scholar
Bouhaddi, N. 1992 A method for selecting master DOF in dynamic substructuring using the Guyan condensation methodComput. Struct 45 941CrossRefGoogle Scholar
Anderson, R. G.Irons, B. M.Zienkiewicz, O. C. 1968 Vibration and stability of plates using finite elementsInt. J. Solids Structures 4 1031CrossRefGoogle Scholar
Levy, R. 1971 201
Popplewell, N.Bertels, A. W. M.Arya, B. 1973 A critical appraisal of the elimination techniqueJ. Sound Vibration 31 213CrossRefGoogle Scholar
Thomas, D. L. 1982 Errors in natural frequency calculations using eigenvalue economizationInt. J. Num. Meth. Eng 18 1521CrossRefGoogle Scholar
Lin, R.Xia, Y. 2003 A new eigensolution of structures via dynamic condensationJ. Sound Vibration 266 93CrossRefGoogle Scholar
Qu, Z.-Q. 2004 Model Order Reduction Techniques with Applications in Finite Element AnalysisBerlinSpringerGoogle Scholar
Meirovitch, L. 1980 Computational Methods in Structural DynamicsRijn, The NetherlandsSijthoff & NoordhoffGoogle Scholar
Craig, R. R.Kurdila, A. J. 2006 Fundamentals of Structural DynamicsNew YorkJohn WileyGoogle Scholar
Kubomura, K. 1982 A theory of substructure modal synthesisTrans. AMSE, J. Appl. Mech 49 903CrossRefGoogle Scholar
Craig, R. R. 1987 A review of time-domain and frequency-domain component mode synthesisJ. Modal Anal 2 59Google Scholar
Craig, R. R. 1995 Substructure methods in vibrationTrans. ASME 117 207CrossRefGoogle Scholar
Shyu, W.-H.Ma, Z.-D.Hulbort, G. M. 1997 A new component mode synthesis method: quasi-static mode compensationFinite Elements Anal. Design 24 271CrossRefGoogle Scholar
Tran, D.-M. 2001 Component mode synthesis methods using interface modes: application to structures with cyclic symmetryComput. Struct 79 209CrossRefGoogle Scholar
Craig, R. R.Bampton, M. C. C. 1968 Coupling of substructures for dynamic analysisAIAA J 6 1313Google Scholar
Suarez, L. E.Singh, M. P. 1992 Improved fixed interface method for modal synthesisAIAA J 30 2952CrossRefGoogle Scholar
Craig, R. R.Hale, A. L. 1988 Block-Krylov component synthesis method for structural model reductionAIAA J. Guidance, Control Dynamics 11 562CrossRefGoogle Scholar
Wang, J. H.Chen, H. R. 1990 A substructure modal synthesis method with high computational efficiencyComput. Methods Appl. Mech. Eng 79 203CrossRefGoogle Scholar
Hou, S.-N. 1969 Review of modal synthesis techniques and a new approach. Shock and Vibration Bull 40 25
Jezequel, L.Tchere, S. T. 1991 A procedure for improving component-mode representation in structural dynamic analysisJ. Sound Vibration 144 409CrossRefGoogle Scholar
Bhouhaddi, N.Lombard, J. P. 2000 Improved free-interface substructures representation methodComput. Struct 77 269CrossRefGoogle Scholar
Tournour, M. A.Atalla, N.Chiello, O.Sgard, F. 2001 Validation, performance, convergence and application of free interface component mode synthesisComput. Struct 79 1861CrossRefGoogle Scholar
Haggblad, B.Eriksson, L. 1993 Model reduction methods for dynamic analyses of large structuresComput. Struct 43 735CrossRefGoogle Scholar
Kuang, J. H.Tsuei, Y. G. 1983 A more general method of substructure mode synthesis for dynamic analysisAIAA J 23 618CrossRefGoogle Scholar
Klosterman, A. L. 1976
Ghlaim, K. H.Martin, K. F. 1984 Reduced component modes in damped systemsProc. Int. Conf. on Modal AnalysisSchenectady, NYUnion College683Google Scholar
Ewins, D. J. 2000 Modal Testing: Theory, Practice and ApplicationLetchworthResearch Studies PressGoogle Scholar
Yang, T.Fan, S.-H.Lin, C.-S. 2003 Joint stiffness identification using FRF measurementsComput. Struct 81 2549CrossRefGoogle Scholar
Wang, J. H.Chuang, S. C. 2004 Reducing errors in the identification of structural joint parameters using error functionsJ. Sound Vibration 273 295CrossRefGoogle Scholar
Meritovitch, L. 1967 Analytical Methods in VibrationNew YorkMacmillanGoogle Scholar
Crandall, S. H. 1970 The role of damping in vibration theoryJ. Sound Vibration 11 3CrossRefGoogle Scholar
Beards, C. F. 1983 Structural Vibration AnalysisChichesterEllis HorwoodGoogle Scholar
Rayleigh, Lord 1945 The Theory of SoundNew YorkDoverGoogle Scholar
Adhirkari, S. 2006 Damping modelling using generalized proportional dampingJ. Sound Vibration 293 156CrossRefGoogle Scholar
Jones, D. I. G. 2001 Handbook of Viscoelastic Vibration DampingChichesterJohn Wiley & SonsGoogle Scholar
Sorrentino, S.Fasana, A. 2007 Finite element analysis of vibrating linear systems with fractional derivative viscoelastic modelsJ. Sound Vibration 299 839CrossRefGoogle Scholar
Dovstam, K. 1995 Augmented Hooke's law in frequency domain. A three-dimensional, material damping formulationInt. J. Solids Struct 32 2835CrossRefGoogle Scholar
Snowdon, J. C. 1963 Representation of the mechanical damping possessed by rubberlike materials and structuresJ. Acoust. Soc. Amer 35 821CrossRefGoogle Scholar
Snowdon, J. C. 1968 Vibration and Shock in Damped Mechanical SystemsNew YorkWileyGoogle Scholar
Lazan, B. 1968 Damping of Materials and Members in Structural MechanicsNew YorkPergamonGoogle Scholar
Ungar, E. E. 1973 The status of engineering knowledge concerning the damping of built-up structuresJ. Sound Vibration 26 141CrossRefGoogle Scholar
Bert, C. W. 1973 Material damping: an introductory review of mathematical models, measures and experimental techniquesJ. Sound Vibration 29 129CrossRefGoogle Scholar
Nashif, A. D.Jones, D. I. G.Henderson, J. P. 1985 Vibration DampingNew YorkJohn Wiley & SonsGoogle Scholar
Ewins, D. J. 2000 Modal Testing: Theory, Practice and ApplicationLetchworthResearch Studies PressGoogle Scholar
Caughey, T. K.O’Kelly, M. E. J. 1965 Classical normal modes in damped linear dynamic systemsASME J. Appl. Mech 32 583CrossRefGoogle Scholar
Foss, K. A. 1958 Coordinates which uncouple the equations of motion of damped linear dynamic systemsASME J. Appl. Mech 25 361Google Scholar
Mead, D. J. 1970 The existence of normal modes of linear systems with arbitrary dampingProceedings of the Symposium on Structural DynamicsLoughborough University of TechnologyGoogle Scholar
Geradin, M.Rixen, D. 1997 Mechanical Vibrations: Theory and Applications to Structural DynamicsChichesterJohn Wiley & SonsGoogle Scholar
Kim, M.-C.Lee, I.-W. 1999 A computationally efficient algorithm for the solution of eigenproblems for large structures with non-proportional damping using Lanczos methodInt. J. Earthquake Eng. Struct. Dynamics 28 1573.0.CO;2-2>CrossRefGoogle Scholar
Bowdler, H. J.Martin, R. S.Peters, G.Wilkinson, J. H. 1966 Solution of real and complex systems of linear equationsNumerische Mathematik 8 217CrossRefGoogle Scholar
Bendat, J. S.Piersol, A. G. 1971 Random Data: Analysis and Measurement ProceduresNew YorkWiley-InterscienceGoogle Scholar
Warburton, G. B. 1976 The Dynamical Behaviour of StructuresOxfordPergamon PressGoogle Scholar
Przemieniecki, J. S. 1968 Theory of Matrix Structural AnalysisNew YorkMcGraw-HillGoogle Scholar
Clough, R. W.Penzien, J. 1995 Dynamics of StructuresNew YorkMcGraw-HillGoogle Scholar
Grant, J. E. 1971 Response computation using truncated Taylor seriesJ. Eng. Mech. Proc. ASME 97 295Google Scholar
Levy, S.Wilkinson, J. P. D. 1976 The Component Element Method in DynamicsNew YorkMcGraw-HillGoogle Scholar
Houbolt, J. C. 1950 A recurrence matrix solution for the dynamic response of elastic aircraftJ. Aeronaut. Sci 17 540CrossRefGoogle Scholar
Bathe, K.-J. 1996 Finite Element ProceduresUpper Saddle River, NJPrentice HallGoogle Scholar
Newmark, N. M. 1959 A method of computation for structural dynamicsJ. Eng. Mech. Proc. ASCE 85 67Google Scholar
MacNeal, R. H.McCormick, C W. 1971 The NASTRAN computer program for structural analysisComput. Struct 1 389CrossRefGoogle Scholar
Wilson, E. L.Farhoomand, I.Bathe, K. J. 1973 Nonlinear dynamic analysis of complex structuresInt. J. Earthquake Engineering and Structural Dynamics 1 241CrossRefGoogle Scholar
Hinton, E.Rock, T.Zienkiewicz, O. C. 1976 A note on mass lumping and related processses in the finite element methodInt. J. Earthquake Engineering and Structural Dynamics 4 245CrossRefGoogle Scholar
Archer, G. C.Whalen, T. M. 2005 Development of rotationally consistent diagonal mass matrices for plate and beam elementsComput. Methods Appl. Mech. Eng 194 675CrossRefGoogle Scholar
Hughes, T. J. R. 1987 The Finite Element Method. Linear Static and Dynamic Finite Element AnalysisEnglewood Cliffs, NJPrentice HallGoogle Scholar
Kardestuncer, H.Norrie, D. H. 1988 Finite Element HandbookNew YorkMcGraw-HillGoogle Scholar
Idesman, A.-V.Schmidt, M.Sierakowski, R. L. 2008 A new explicit predictor-multicorrector high-order accurate method for linear elastodynamicsJ. Sound Vibration 310 217CrossRefGoogle Scholar
Wood, W. L. 1990 Practical Time-Stepping SchemesOxfordClarendon PressGoogle Scholar
Robson, J. D. 1963 An Introduction to Random VibrationEdinburghEdinburgh University PressGoogle Scholar
Crandall, S. H.Mark, W. D. 1963 Random Vibration in Mechanical SystemsNew YorkAcademic PressGoogle Scholar
Lin, Y. K.Cai, G. Q. 2004 Probabilistic Structural DynamicsNew YorkMcGraw-HillGoogle Scholar
Bendat, J. S.Piersol, A. G. 2000 Random Data: Analysis and Measurement ProceduresNew YorkJohn WileyGoogle Scholar
Neweland, D. E. 1975 An Introduction to Random Vibrations and Spectral AnalysisLondonLongmanGoogle Scholar
Clough, R. W.Penzien, J. 1993 Dynamics of StructuresNew YorkMcGraw-HillGoogle Scholar
Warburton, G. B. 1976 The Dynamical Behaviour of StructuresOxfordPergamon PressGoogle Scholar
Olson, M. D.Lindberg, G. M. 1970
Olson, M. D. 1972 A consistent finite element method for random response problemsComput. Struct 2 163CrossRefGoogle Scholar
Olson, M. D.Lindberg, G. M. 1970
Olson, M. D.Lindberg, G. M. 1971 Jet noise excitation of an integrally stiffened panelJ. Aircraft 8 847CrossRefGoogle Scholar
Mead, D. J.Pujara, K. K. 1971 Space harmonic analysis of periodically supported beams: response to converted random loadingJ. Sound Vibration 14 525CrossRefGoogle Scholar
Etkin, B. 1972 Dynamics of Atmospheric FlightNew YorkWileyGoogle Scholar
Davis, R. E. 1966 Statistical dependence effect of normal mode responseAIAA J 4 2033CrossRefGoogle Scholar
Harris, C. M.Piersol, A. G. 2001 Shock and Vibration HandbookNew YorkMcGraw-HillGoogle Scholar
Cornwell, R. E.Craig, R. R.Johnson, C. P. 1983 On the application of the mode-acceleration method to structural engineering problemsInt. J. Earthquake Engineering and Structural Dynamics 11 679CrossRefGoogle Scholar
Ewins, D. J. 2000 Modal Testing: Theory, Practice and ApplicationLetchworthResearch PressGoogle Scholar
Hansteen, O. E.Bell, K. 1979 On the accuracy of mode superposition analysis in structural dynamicsInt. J. Earthquake Engineering and Structural Dynamics 7 405CrossRefGoogle Scholar
Bathe, K.-J. 1996 Finite Element ProceduresUpper Saddle River, NJPrentice HallGoogle Scholar
Wilson, E. L.Yuun, M.-Y.Dickens, J. M. 1982 Dynamic analysis by direct superposition of Ritz vectorsInt. J. Earthquake Eng. Struct. Dynamics 10 813CrossRefGoogle Scholar
Craig, R. R. 2002
Arnold, R. R. 1985 Application of Ritz vectors for dynamic analysis of large structuresComput. Struct 21 901CrossRefGoogle Scholar
Butler, T. G. 1982 Using NASTRAN to solve symmetric structures with nonsymmetric loadsTenth NASTRAN Users’ Colloquium, NASA Conference Publication 2249 216Google Scholar
Thomas, D. L. 1979 Dynamics of rotationally periodic structuresInt. J. Num. Meth. Eng 14 81CrossRefGoogle Scholar
Popplewell, N.Bertels, A. W. M.Arya, B. 1973 A critical appraisal of the elimination techniqueJ. Sound Vibration 31 213CrossRefGoogle Scholar
Qu, Z.-Q. 2004 Model Order Reduction Techniques with Applications in Finite Element AnalysisBerlinSpringerGoogle Scholar
Smith, I. M.Griffiths, D. V. 1997 Programming the Finite Element MethodChichesterJohn Wiley & SonsGoogle Scholar
Hinton, E.Owen, D. R. J. 1979 An Introduction to Finite Element ComputationsSwanseaPineridge PressGoogle Scholar
Cook, R. D.Malkus, D. S.Plesha, M. E.Witt, R. J. 2002 Concepts and Applications of Finite Element AnalysisNew YorkJohn Wiley & SonsGoogle Scholar
Hinton, E.Owen, D. R. J. 1984 Finite Element Software for Plates and ShellsSwanseaPineridge PressGoogle Scholar
Hinton, E. 1988 Numerical Methods and Software for Dynamic Analysis of Plates and ShellsSwanseaPineridge PressGoogle Scholar
Rao, S. S. 2005 The Finite Element Method in EngineeringOxfordElsevierGoogle Scholar
Kwon, Y. W.Bang, H. 2000 The Finite Element Method usingBoca Raton FLCRC PressGoogle Scholar
Kielb, R. E.Leissa, A. W. 1985 Vibrations of twisted cantilever plates – a comparison of theoretical resultsInt. J. Num. Meth. Eng 21 1365CrossRefGoogle Scholar
Ewins, D. J.Imregun, M. 1986 State-of-the-art assessment of structural dynamic response analysis methods (DYNAS)Shock and Vibration Bull 56 59Google Scholar
Ewins, D. J.Imregun, M. 1987 A survey to assess structural dynamic response prediction capabilities: DYNASQuality Assurance in FEM TechnologyRobinson, J.OkehamptonRobinson and Associates604Google Scholar
Hughes, T. J. R. 1987 The Finite Element Method: Linear Static and Dynamic Finite Element AnalysisEnglewood CliffsPrentice-HallGoogle Scholar
Irons, B.Ahmad, S. 1980 Techniques of Finite ElementsChichesterEllis HorwoodGoogle Scholar
Petyt, M. 1990 Introduction to Finite Element Vibration AnalysisCambridgeCambridge University PressCrossRefGoogle Scholar
Zienkiewicz, O. C. 1977 The Finite Element MethodLondonMcGraw-HillGoogle Scholar
Wolfe, J. P.Song, C. 1996 Finite Element Modelling of Unbounded MediaChichesterJohn Wiley & SonsGoogle Scholar
1986 A Finite Element PrimerGlasgowNational Engineering Laboratory
1987 Proc. Int. Conf. on Quality Assurance and Standards in Finite Element AnalysisGlasgowNational Engineering Laboratory
Robinson, J. 1987 Quality Assurance in FEM TechnologyOkehamptonRobinson and AssociatesGoogle Scholar
Robinson, J. 1985
Morris, A. J. 1985
Robinson, J. 1979
Robinson, J.Blackham, S. 1981 An evaluation of lower order membranes as contained in the ANSYS and SAP4 FEM systemsFinite Element NewsGoogle Scholar
Robinson, J.Blackham, S. 1981
Hitchings, D.Kamoulakos, A.Davies, G. A. O. 1987
Hitchings, D.Kamoulakos, A.Davies, G. A. O. 1987
Taig, I. C. 1992
Hardy, S. 2001
Robinson, J. 1978 Element evaluation – a set of assessment points and standard testsFinite Element Methods in the Commercial Environment217OkehamptonRobinson and AssociatesGoogle Scholar
Abbassian, F.Dawswell, F.Knowles, N. C. 1987
Rahman, A.Petyt, M. 1995
Friswell, M. J.Mottershead, J. E. 1995 Finite Element Model Updating in Structural DynamicsDordrechtKluwerCrossRefGoogle Scholar
Ewins, D. J. 2000 Modal Testing. Theory, Practice and ApplicationsBaldockResearch Studies PressGoogle Scholar
Braun, S. G.Ewins, D. J.Rao, S. S. 2002 Encyclopedia of VibrationLondonAcademic PressGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Maurice Petyt, University of Southampton
  • Book: Introduction to Finite Element Vibration Analysis
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511761195.022
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Maurice Petyt, University of Southampton
  • Book: Introduction to Finite Element Vibration Analysis
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511761195.022
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Maurice Petyt, University of Southampton
  • Book: Introduction to Finite Element Vibration Analysis
  • Online publication: 05 June 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9780511761195.022
Available formats
×