Skip to main content Accessibility help
×
Home

A Novel Perturbative Iteration Algorithm for Effective and Efficient Solution of Frequency-Dependent Eigenvalue Problems

  • Rongming Lin (a1)

Abstract

Many engineering structures exhibit frequency dependent characteristics and analyses of these structures lead to frequency dependent eigenvalue problems. This paper presents a novel perturbative iteration (PI) algorithm which can be used to effectively and efficiently solve frequency dependent eigenvalue problems of general frequency dependent systems. Mathematical formulations of the proposed method are developed and based on these formulations, a computer algorithm is devised. Extensive numerical case examples are given to demonstrate the practicality of the proposed method. When all modes are included, the method is exact and when only a subset of modes are used, very accurate results are obtained.

Copyright

Corresponding author

Corresponding author. URL:http://research.ntu.edu.sg/expertise/academicprofile/pages/StaffProfile.aspx?ST_EMAILID=MRMLIN, Email: mrmlin@ntu.edu.sg

References

Hide All
[1]He, S. and Singh, R., Estimation of amplitude and frequency dependent parameters of hydraulic engine mount given limited dynamic stiffness measurement, Noise. Control. Eng. J., 53(2) (2005), pp. 271285.
[2]Wang, Q. Y. and Maslen, E. H., Identification of frequency dependent parameters in a flexible rotor system, ASME J. Eng. Gas. Turb. Power., 128(3) (2006), pp. 670676.
[3]Webster, A. and Semke, W., Frequency dependent viscoelastic structural elements for passive broad-band vibration control, J. Vibr. Control., 10(6) (2004), pp. 881895.
[4]Dai, X. J., Lin, J. H., Chen, H. R. and Williams, F. W., Random vibration of composite structures with attached frequency dependent damping layer, Composites. B. Eng., 39(2) (2008), pp. 405413.
[5]Conza, N. E. and Rixen, D. J., Influence of frequency-dependent properties on system identification: simulation study on a human levis model, J. Sound. Vibr., 302(4-5) (2007), pp. 699715.
[6]Mondal, M. and Massoud, Y., Accurate analytical modeling of frequency dependent loop self-inductance, J. Circuit. Sys. Comput., 17(1) (2008), pp. 7793.
[7]Bandran, E. and Ulloa, S. E., Frequency-dependent magnetotransport and particle dynamics in magnetic modulation systems, Phys. Rev. B., 59(4) (1999), pp. 28242832.
[8]Wilkinson, J. H., The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, England, 1972.
[9]Rutishauser, , The Jacobi method for real symmetric matrices, Numer. Math., 9 (1966), pp. 110.
[10]Golub, G. H., H., G. and van Loan, C. F., Matrix Computations, Johns Hopkins University Press, Baltimore, Maryland, 1996.
[11]Moler, C. B. and Stewart, G. W., An algorithm for generalized matrix eigenvalue problems, SIAM J. Numer. Anal., 10(2) (1973), pp. 241256.
[12]Ipsen, I. C. F., Computing an eigenvector with inverse iteration, SIAM Rev., 39 (1997), pp. 254291.
[13]Lanczos, C., An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Res. National. Bureau. Standards., 45 (1950), pp. 255282.
[14]Arnodi, W. E., The principle of minimized iterations in the solution of the matrix eigenvalue problems, Quarter. Appl. Math., 9 (1951), pp. 1729.
[15]Jiaxian, X., An improved method for partial eigensolution of large structures, Comput. Struct., 32 (1989), pp. 10551060.
[16]Bathe, K. J. and Ramaswamy, S., An accelerated subspace iteration method, Comput. Methods. Appl. Mech. Eng., 23(3) (1980), pp. 313331.
[17]Bathe, K. J. and Wilson, E. L., Large eigenvalue problems in dynamic analysis, ASCE, Eng. Mech. Div., 98 (1972), pp. 14711485.
[18]Bathe, K. J. and Wilson, E. L., Solution methods for eigenvalue problems in structural mechanics, Int. J. Numer. Methods. Eng., 6 (1973), pp. 213266.
[19]Borri, M. and Mantegazza, P., Efficient solution of quadratic eigenproblems arising in dynamic analysis of structures, Comput. Methods. Appl. Mech. Eng., 12 (1977), pp. 1931.
[20]Chen, H. C. and Taylor, R. L., Solution of eigenproblems for damped structural systems by Lanczos algorithm, Comput. Struct., 30 (1988), pp. 151161.
[21]Saad, Y., Variations of Arnoldi’s method for computing eigenelements of large unsymmetric matrices, Linear. Algebra. Appl., 34 (1980), pp. 269295.
[22]Zheng, T. S., Liu, W. M. and Cai, Z. B., A general inverse iteration method for solution of quadratic eigenvalue problems in structural dynamic analysis, Comput. Struct., 33(5) (1989), pp. 11391143.
[23]Ewins, D. J., Modal Testing: Theory, Practice and Applications, Research Studies Press, 2000.
[24]Bathe, K. J., Finite Element Procedures, Prentice Hall, 1996.
[25]Lin, R. M. and Lim, M. K., Relationship between improved inverse eigensensitivity and FRF sensitivity methods for analytical model updating, ASME J. Vibr. Acoust., 119(3) (1997), pp. 354363.
[26]Dailey, R. L., Eigenvector derivatives with repeated eigenvalues, AIAA J., 27(4) (1989), pp. 486491.

Keywords

Related content

Powered by UNSILO

A Novel Perturbative Iteration Algorithm for Effective and Efficient Solution of Frequency-Dependent Eigenvalue Problems

  • Rongming Lin (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.