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Vibration-based structural damage detection has been the focus of attention by many researchers over the last few decades. However, most methods proposed for this purpose utilize extracted modal parameters or some indices constructed based on these parameters. A literature review revealed that few papers have employed Frequency Response Functions (FRFs) for detecting structural damage. In this paper, a technique is presented for damage detection which is based on measured FRFs. Proper Orthogonal Decomposition (POD) has been implemented on spatiotemporal responses in each frequency in order to reduce the dimension of the data. This is based on the concept that the forced harmonic response of a linear vibrating system can be fully captured utilizing a single basis vector. A different approach is also presented in this paper in which POD is applied to the frequency domain data. Operational Deflection Shapes (ODSs) have been decomposed using POD to localize the damage. The efficiency of the method is demonstrated through some numerical and experimental case studies.
Flat heat pipes having mesh capillaries were investigated experimentally in this study. An apparatus was designed to test thermal performance of plate type copper water heat pipe having one or two layers of #50 or #80 mesh capillary structures with 5 to 50 W heat input. The working fluid, water, is charged in volumes equivalent to 25%, 33%, or 50% of the internal space. In addition to horizontal orientation, heat pipes were tested with the evaporator section elevated up to 40 degree inclination angle. Temperature distribution of the heat pipe was measured, and the evaporator, adiabatic and condensation resistances were calculated separately. The effects of mesh size, charge volume fraction, and inclination angle on thermal resistance were discussed. In general, the #80 mesh yielded lower thermal resistance than the #50 mesh. Inclination angle has a more significant effect on condenser than evaporator. Analysis of evaporation and condensation in flat heat pipes was conducted and semi-empirical correlations were derived. The present evaporation correlation predicts evaporation resistance between −20% and +30%, and the condensation correlation predicts most condensation resistance data within ±30% for 25% and 33% charge volume fraction.
As inspired by studies of fish schooling in literature, this work investigates hydrodynamic performance of a two-dimensional undulating-foil triad in viscous flows via numerical simulation. The chord of foil oscillates in the form of a streamwise traveling wave. The triad is in triangular formation, i.e., two foils followed by one. A series of triad configuration are computed assuming the same wave speed, amplitude, and frequency of chord traveling wave for each foil. The results show that, to achieve highest thrust efficiency, the two leading foils should separate from each other by 0.4 chord length, perform antiphase undulating motion, and the leading edge of the trailing foil stay 0.2 chord length in front of the trailing edges of the leading foils. An underlining mechanism, vortex pair shedding from the leading foil interacting with boundary-layer vorticity field of the trailing foil, has been identified to explain the efficiency enhancement. This optimal triad configuration is different from that obtained in a previous potential flow analysiss.
In this paper, cyclic damage behavior of cyclically load drop curves and their fatigue initiation life of Sn/3.5 Ag/0.75Cu BGA solder joint specimens under oblique displacement cyclic tests were investigated by the theory of damage — coupled endochronic viscoplasticity.
By linearly unloading with damage elastic modulus and the linearly damage-free behavior of grip system, the damage loops of force-Φ angle oblique displacement of BGA solder joint specimen were converted successfully into damage loops of the representative solder ball under cyclically proportional straining, which can be predicted by the endochronic constitutive equations. These results established the relationship of the BGA oblique displacement amplitudes da(Φ) and the effective inelastic strain amplitudes of solder ball: da (Φ)= . Based on the phenomena of cyclic damage and its fatigue life, a Φ dependent degree of damage in the evolution equation of damage under proportional strain path was proposed to depend positively on and N cycles. Using this parameter in the damage per cycle computed by the endochronic theory, a Φ modified cycles N(Φ)/β(Φ) can be defined and then derive the Φ modified Lee-Coffin-Manson (Φ-LCM) equation for the fatigue initiation life of solder ball:
Finally, a Φ modified Lee's BGA (Φ LBGA) equation for BGA solder joint specimens can be derived:
This equation can predict quite well the life data of Sn/3.5Ag/0.75Cu solder joint specimens under Φ ϵ [0π/2]. As a consequence, a vehicle to study the fatigue initiation life of BGA solder joint specimens is constructed completely by the workable methodology and the theory discussed in the paper.
Though the total stress undrained analysis approach in geotechnical engineering is widely utilized by practicing engineers, it has some intrinsic imperfections that cause the obtained parameters to have unavoidable empirical correlations. In this study, an undrained soft clay model is developed, which overcomes the imperfections of the conventional total stress undrained approach. In addition, the high soil stiffness at small strain and the concept of yield surface are employed to realistically simulate actual soil behavior. The model parameters can be obtainable directly from conventional laboratory tests. The model is validated through different laboratory stress path tests and strength tests in this paper.
The two dimensional punch problem for planar anisotropic elastic half-plane is revisited using the Lekhnitskii's formulation with aid of the Fourier transform and boundary integral equation. Four different conditions of contact problem for the rigid punch are analyzed in this study. From the combination of surface Green's function of half-plane and Hooke's law of anisotropic material, a set of Fredholm integral equations are obtained for mixed boundary value problems. After solving the integral equation according to specified contact condition, the explicit distributions of surface traction under the punch are obtained in closed-form. From the surface traction and Green's function of anisotropic half-plane, the full-field solutions of stresses are constructed. Numerical calculations of surface traction under the rigid punch are presented base on the analysis and are discussed in detail.
A body insonified by a sound field is known to experience a steady force that is called the acoustic radiation force. In this paper, the method of wave function expansion is adopted to study the scattering and the radiation force function caused by a plane normal harmonic acoustic wave incident upon an arbitrarily thick-walled functionally graded cylindrical shell submerged in and filled with compressible ideal fluids. A laminate approximate model and the so-called state space formulation in conjunction with the classical transfer matrix (T-matrix) approach are employed to present an analytical solution based on the two-dimensional exact equations of elasticity. Two typical models, representing the elastic properties of FGM interlayer, are considered. In both models, the mechanical properties of the graded shell are assumed to vary smoothly and continuously with the change of volume concentrations of the constituting materials across the thickness of the shell. In the first model, the simple rule of mixture governs. In the second, an elegant self-consistent micromechanical model which assumes an interconnected skeletal microstructure in the graded region is employed. Particular attention is paid on dynamical response of these models in a wide range of frequency and for different shell wall-thicknesses. In continue, by focusing on the second model, the normalized radiation force function and the form function amplitude are calculated and compared for different shell wall thicknesses and various profile of variations. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.
In this paper, the new concept of theory about Large Unified Symmetries for Hamilton systems are presented. The Large Unified Symmetries and conserved quantities for Hamilton systems are studied by the relation between the three kinds of symmetries and the three kinds of conserved quantities. We worked on the Large Unified Symmetries and conserved quantities by Noether symmetry, Lie symmetry and Mei symmetry, including the definition and criterion of the Large Unified Symmetries and the conserved quantities deduced from them. The Large Unified Symmetries are a intersection set among the Noether symmetries, the Lie symmetries and the Mei symmetries. The theory about Large Unified Symmetries will play an important role in the fields of modern theoretical physics.
This study utilized a U-shape platform device to generate a single cavitation bubble for the detail analysis of the flow field characteristics and the cause of the counter jet during the process of bubble collapse induced by pressure wave. A series of bubble collapse flows induced by pressure waves of different strengths are investigated by positioning the cavitation bubble at different stand-off distances to the solid boundary. It is found that the Kelvin-Helmholtz vortices are formed when the liquid jet induced by the pressure wave penetrates the bubble surface. If the bubble center to the solid boundary is within one to three times the bubble's radius, a stagnation ring will form on the boundary when impacted by the penetrated jet. The liquid inside the stagnation ring is squeezed toward the center of the ring to form a counter jet after the bubble collapses. At the critical position, where the bubble center from the solid boundary is about three times the bubble's radius, the bubble collapse flows will vary. Depending on the strengths of the pressure waves applied, either just the Kelvin-Helmholtz vortices form around the penetrated jet or the penetrated jet impacts the boundary directly to generate the stagnation ring and the counter jet flow. This phenomenon used the particle image velocimetry method can be clearly revealed the flow field variation of the counter jet. If the bubble surface is in contact with the solid boundary, the liquid jet can only splash radially without producing the stagnation ring and the counter jet. The complex phenomenon of cavitation bubble collapse flows are clearly manifested in this study.
In this paper, an evolution equation of cyclically internal damage in the intrinsic damage time scale after the threshold cycles N0 was extended by employing its damage parameters proposed to be dependent of frequency (v) and temperature (T) under cyclic fatigue loading. The resulting damage-coupled endochronic viscoplasticity can drive v and T modified power form equations of cyclic damage and its fatigue initiation life = N1 + N0. Under fatigue tests with T effect and N0 = 0, the power form equation of N1(T)/(Th), named as T-LCM (T modified Lee Coffin-Manson) equation for fatigue initiation life can bederived. The T modified factor (Th) depends on the T dependent material elastic modulus, the cyclicstress-strain response and the damage parameters. Theoretical predictions in the life data ofSn/3.8Ag/0.7Cu solder alloy under cyclic strain test with Tϵ [298,393] K were very well.
Also under fatigue tests with v effect only, the power form equation of /v-LCM (v modified Lee-Coffin-Manson) equation for fatigue initiation life can be derived. The v modified parameter depends on the v dependent cyclic stress-strain response and the damage parameters. Theoreticalpredictions in the life data of 96.5Sn/3.5Ag solder alloy with surface cracking effect i.e. N0 ≠ 0 during cyclicstrain tests with v ϵ [0.001,1] Hz were quite well.
Obviously, the values of power exponents C in the T-LCM and the v-LCM equations can not be determinedsimply by the least square method as in the Coffin-Manson empirical formulae. Also, they must bejustified by constrains imposed in the material parameters defining in the cyclic stress-strain response andthe accumulation behavior of cyclic damage.
The resultant equations derived here and the Δ-LCM equation derived under Δ angle proportional cyclicstrain tests can be combined together to form a T-v-ΔLCM equation for fatigue life studies in the solderalloys using bulk specimens or BGA solider joint specimens.
Welded structures are vulnerable to fracture due to cracks, especially at the welds. To investigate the safety of T-Shape welded structures used in some construction sites, a method is proposed in this paper to evaluate the crack occurrence probabilities of the structures. Three major factors that affect the crack occurrence are taken into consideration. They are residual stress, diffusible hydrogen content and chemical composition of the weld metal. In the analysis, finite element analysis is performed to find the residual stress distribution of the structures. The uncertainties of diffusible hydrogen content and chemical composition are treated as random variables. The critical cooling time is found and utilized for evaluating the crack occurrence probability of the welded structure. Numerical results indicate that T-shape welded joints lead to higher residual stresses and higher crack occurrence probabilities in comparison with the traditional butt joints. Therefore, more attention should be paid to this kind of welded joints when they are used.
In this study a double two-inlet Y-type microchannel with two up-down symmetrical obstacles was applied. This was done because the positions of the obstacles in the flow channel, arranged in an up- down symmetrical fashion, could provide a higher mixing efficiency. As for the optimal layout of obstacles inthe microchannel, the positions of the two up-down symmetrical obstacles were set as the location of obstacle A/D = 0.198, the length of obstacle K/D = 0.453, the horizontal spacing between the two obstacles T/D = 0, and the flow channel width between the two obstacles Y/D = 0.080, This was because it could generate theflow mixing efficiency with 0.984 and at a lower Reynolds number, Re 4.7. These observations willcontribute to the improvement of a Y-type micromixer design.
The study had indicated that the computational performances of the characteristics method with the time-line cubic spline interpolation are related to the endpoint constraint, especially for large Courant number in which the foot of the characteristic trajectory is located near the endpoint. The first derivative endpoint constraint with higher-order central difference approximation provides better simulation results among various endpoint constraints, but it still induces some degree of numerical error. In this study, by locating the foot of the characteristic trajectory away from the endpoint, the temporal reachout technique is proposed to avoid the effect of endpoint constraint on the time-line cubic spline interpolation. Modeling the transport of a Gaussian concentration distribution in a uniform flow with constant diffusion coefficient and the viscous Burgers equation is used to examine the temporal reachout technique. The outcomes show that the temporal reachout technique yields much better simulation results than the first derivative endpoint constraint with higher-order central difference approximation. The effect of endpoint constraint on the time-line cubic spline interpolation can be greatly diminished by the use of the temporal reachout technique.
In this technical note, a compound path integral solution (CPIS) method is utilized to calculate the response exceedance probabilities of a nonlinear compliant offshore structure subjected to slow drift wave force excitations. The structure's slow drift response exceedance probabilities have also been calculated by using the original PIS method for comparison purpose. It is found that the efficiency of the CPIS method for predicting the structure's slow drift response exceedance probabilities is higher than that of the original PIS method.
In this work, a method for increasing the storage capability of a solar thermal energy system has been discussed. The system includes two tanks with the flexibility in choosing the best storage medium on the basis of the solar collector's outlet temperature. The results show that using such a hybrid storage system, the storable energy can be increased. Comparing the results with those for simple common storage systems, the extent of improvement was calculated.
For verification of the results, a small pilot system was assembled. The test apparatus operated during 2008-2009 cold months and the parameters were recorded. Comparison of the theoretical and experimental results showed a good agreement.