1.

A SEMIANALYTICAL METHOD FOR THE VIBRATION OF AND SOUND RADIATION FROM A TWODIMENTIONAL BEAMSTIFFENED PLATE





Haian Zhou Xiaoming Wang Yulin Mei《Acta Mechanica Solida Sinica》,2011年第3期


A semianalytical method based on space harmonics to investigate the vibration of and sound radiation from an infinite,fluidloaded plate is presented.The plate is reinforced with two sets of orthogonally and equally spaced beam stiffeners,which are assumed to be line forces.The response of the stiffened plate to a convected harmonic pressure in the wavenumber space is obtained by adopting the Green’s function and Fourier transform methods.Using the boundary conditions and space harmonic method,we establish the relationship between the stiffener forces and the vibration displacement of the plate.In this paper,the stiffener forces are expressed in terms of harmonic amplitudes of the plate displacement,which are calculated by using a numerical reduction technique.Finally,the Fourier inverse transform is employed to find expressions of the vibration and sound radiation in physical space.Agreements with existing results prove the validity of this approach and more numerical results are presented to show that this method converges rapidly.

2.

Dynamics of cantilever plates and its hybrid vibration control





Bo Ni Chao Hu《Acta Mechanica Sinica》,2013年第29卷第5期


Applying Lagrange–Germain’s theory of elastic thin plates and Hamiltonian formulation, the dynamics of cantilever plates and the problem of its vibration control are studied, and a general solution is finally given. Based on Hamiltonian and Lagrangian density function, we can obtain the flexural wave equation of the plate and the relationship between the transverse and the longitudinal eigenvalues.Based on eigenfunction expansion, dispersion equations of propagation mode of cantilever plates are deduced. By satisfying the boundary conditions of cantilever plates, the natural frequencies of the cantilever plate structure can be given.Then, analytic solution of the problem in plate structure is obtained. An hybrid wave/mode control approach, which is based on both independent modal space control and wave control methods, is described and adopted to analyze the active vibration control of cantilever plates. The loworder(controlled by modal control) and the highorder(controlled by wave control) frequency response of plates are both improved. The control spillover is avoided and the robustness of the system is also improved. Finally, simulation results are analyzed and discussed.

3.

The wave and vibratory power transmission in a finite Lshaped Mindlin plate with two simply supported opposite edges





ChunChuan Liu · FengMing Li · TingWei Liang · WenHu Huang P.O.Box 137 School of Astronautics Harbin Institute of Technology 150001 Harbin China《Acta Mechanica Sinica》,2011年第27卷第5期


In this paper,wave and vibratory power transmission in a finite Lshaped Mindlin plate with two simply supported opposite edges are investigated using the wave approach.The dynamic responses,active and reactive power flow in the finite plate are calculated by the Mindlin plate theory (MPT) and classic plate theory (CPT).To satisfy the boundary conditions and continuous conditions at the coupled junction of the finite Lshaped plate,the nearfield and farfield waves are entirely contained in the wave approach.The inplane longitudinal and shear waves are also considered.The results indicate that the vibratory power flow based on the MPT is different from that based on the CPT not only at high frequencies but also at low and medium frequencies.The influence of the plate thickness on the vibrational power flow is investigated.From the results it is seen that the shear and rotary inertia correction of the MPT can influence the active and reactive power at the junction of the Lshaped plate not only at high frequencies but also at low and medium frequencies.Furthermore,the effects of structural damping on the active and reactive power flow at the junction are also analyzed.

4.

ELASTICPLASTIC DYNAMIC RESPONSE OF FULLY BACKED SANDWICH PLATES UNDER LOCALIZED IMPULSIVE LOADING 被引次数：1





Hua Liu Wuchao Chen Jialing Yang《Acta Mechanica Solida Sinica》,2010年第23卷第4期


An analytical model is developed to assess the elasticplastic dynamic response of fully backed sandwich plates under localized impulse load.The core is modeled as an elasticperfectly plastic foundation.The top face sheet is treated as an individual plate resting on the foundation.The elasticplastic analysis for the top face sheet is based on a minimum principle in dynamic plasticity associated with the finite difference technique.The effects of spatial and temporal distributions of the impulsive loading on the dynamic response of sandwich plates are discussed.The model can be used to predict the impulseinduced local effect on fully backed sandwich plates.

5.

ELASTIC DYNAMIC ANALYSIS OF MODERATELY THICK PLATE USING MESHLESS LRPIM 被引次数：1





Ping Xia Shuyao Long Hongxue Cui《Acta Mechanica Solida Sinica》,2009年第22卷第2期


A meshless local radial point interpolation method （LRPIM） for solving elastic dynamic problems of moderately thick plates is presented in this paper. The discretized system equation of the plate is obtained using a locally weighted residual method. It uses a radial basis function （RBF） coupled with a polynomial basis function as a trial function,and uses the quartic spline function as a test function of the weighted residual method. The shape function has the properties of the Kronecker delta function,and no additional treatment is done to impose essential boundary conditions. The Newmark method for solving the dynamic problem is adopted in computation. Effects of sizes of the quadrature subdomain and influence domain on the dynamic properties are investigated. The numerical results show that the presented method can give quite accurate results for the elastic dynamic problem of the moderately thick plate.

6.

DUAL RECIPROCITY BOUNDARY ELEMENT METHOD FOR FLEXURAL WAVES IN THIN PLATE WITH CUTOUT





高锁文 汪越胜 章梓茂 马兴瑞《应用数学和力学(英文版)》,2005年第26卷第12期


The theoretical analysis and numerical calculation of scattering of elastic waves and dynamic stress concentrations in the thin plate with the cutout was studied using dual reciprocity boundary element method (DRM). Based on the work equivalent law, the dual reciprocity boundary integral equations for flexural waves in the thin plate were established using static fundamental solution. As illustration, numerical results for the dynamic stress concentration factors in the thin plate with a circular hole are given. The results obtained demonstrate good agreement with other reported results and show high accuracy.

7.

Time domain finite volume method for the transient response and natural characteristics of structuralacoustic coupling in an enclosed cavity





XUAN Lingkuan ;MING Pingjian ;ZHANG Wenping ;JIN Guoyong ;GONG Jingfeng《Chinese Journal of Acoustics》,2014年第3期


A time domain finite volume method（TDFVM）based on wave theory is developed to analyze the transient response and natural characteristics of structuralacoustic coupling problems in an enclosed cavity.In the present method,the elastic dynamic equations and acoustic equation in heterogeneous medium are solved in solid domains and fluid domains respectively.The structuralacoustic coupling is implemented according to the continuity condition of the particle velocity along the normal direction and the normal traction equilibrium condition on the interface.Several numerical examples are presented to validate the effectiveness and accuracy of the present TDFVM.Then the effects of water depth on the acoustic and vibration characteristics and the natural characteristics of a structuralacoustic coupling system are analyzed.The numerical results show that the increase of water depth leads to a stronger coupling between the water and structure and the decrease of natural frequencies of coupling system,The computational cost and memory of this method are small and it can be applicable to structuralacoustic coupling problems in the heterogeneous fluid.

8.

APPLICATION OF THE MODIFIED ITERATION METHOD TO NONLINEAR VIBRATION OF CORRUGATED CIRCULAR PLATES





李东 刘人怀《应用数学和力学(英文版)》,1990年第1期


In this paper,the modified iteration method is successfully extended to investigate thenonlinear free vibration of corrugated circular plates with full corrugations.The analyticalrelation for the amplitudefrequency response of corrugated circular plates is obtained anddiscussions on the influences of geometrical parameters on vibration behaviours ofcorrugated circular plates are made.The present results are practically important in thedesign of elastic elements in precision instruments.

9.

Free vibration and transverse stresses of viscoelastic laminated plates





胡明勇 王安稳《应用数学和力学(英文版)》,2009年第30卷第1期


Based on Reddy＇s layerwise theory, the governing equations for dynamic response of viscoelastic laminated plate are derived by using the quadratic interpolation function for displacement in the direction of plate thickness. Vibration frequencies and loss factors are calculated for free vibration of simply supported viscoelastic sandwich plate, showing good agreement with the results in the literature. Harmonious transverse stresses can be obtained. The results show that the transverse shear stresses are the main factor to the delamination of viscoelastic laminated plate in lowerfrequency free vibration, and the transverse normal stress is the main one in higherfrequency free vibration. Relationship between the modulus of viscoelastic materials and transverse stress is analyzed. Ratio between the transverse stress＇s maximum value and the inplane stress＇s maximumvalue is obtained. The results show that the proposed method, and the adopted equations and programs are reliable.

10.

Theoretical analysis of the sound absorption characteristics of periodically stiffened microperforated plates





HaiAn Zhou XiaoMing Wang YuLin Mei《Acta Mechanica Sinica》,2014年第30卷第5期


The vibroacoustic responses and sound absorption characteristics of two kinds of periodically stiffened microperforated plates are analyzed theoretically. The connected periodical structures of the stiffened plates can be ribs or blocklike structures. Based on fundamental acoustic formulas of the microperforated plate of Maa and Takahashi, semianalytical models of the vibrating stiffened plates are developed in this paper. Approaches like the space harmonic method, Fourier transforms and finite element method （FEM） are adopted to investigate both kinds of the stiffened plates. In the present work, the vibroacoustic responses of microperforated stiffened plates in the wavenumber space are expressed as functions of plate displacement amplitudes. After approximate numerical solutions of the amplitudes, the vibration equations and sound absorption coefficients of the two kinds of stiffened plates in the physical space are then derived by employing the Fourier inverse transform. In numerical examples, the effects of some physical parameters, such as the perforation ratio, incident angles and periodical distances etc., on the sound absorption performance are examined. The proposed approaches are also validated by comparing the present results with solutions of Takahashi and previous studies of stiffened plates. Numerical results indicate that the flexural vibration of the plate has a signif icant effect on the sound absorption coefficient in the water but has little influence in the air.

11.

BENDING RESPONSES OF AN EXPONENTIALLY GRADED SIMPLYSUPPORTED ELASTIC/VISCOELASTIC/ELASTIC SANDWICH PLATE





A.M.Zenkour《Acta Mechanica Solida Sinica》,2011年第3期


The bending response for exponentially graded composite (EGC) sandwich plates is investigated.The threelayer elastic/viscoelastic/elastic sandwich plate is studied by using the sinusoidal shear deformation plate theory as well as other familiar theories.Four types of sandwich plates are considered taking into account the symmetry of the plate and the thickness of each layer.The effective moduli and Illyushin’s approximation methods are used to solve the equations governing the bending of simplysupported EGC fiberreinforced viscoelastic sandwich plates.Then numerical results for deflections and stresses are presented and the effects due to time parameter,aspect ratio,sidetothickness ratio and constitutive parameter are investigated.

12.

Symmetric and AntiSymmetric Lamb Waves in a TwoDimensional Phononic Crystal Plate





李勇 侯志林 傅秀军 Badreddine M Assouar《中国物理快报》,2010年第27卷第7期


It is weft known that Lamb waves in a plate with a mirror plane can be separated into two uncoupled sets： symmetric and antisymmetric modes. Based on this property, we present a revised plane wave expansion method （PWE） to calculate the band structure of a phononie crystal （PC） plate with a mirror plane. The developed PWE method can be used to calculate the band structure of symmetric and antisymmetric modes separately, by which the depending relationship between the partial acoustic band gap （PABG）, which belongs to the symmetric and antisymmetric modes alternatively, and the position of the scatterers can be determined. As an example of its application, the band structure of the Lamb modes in a twodimensional PC plate with two layers of void circular inclusions is investigated. The results show that the band structure for the symmetric and antisymmetric modes can be changed by the position of the scatterers drastically, and larger PABGs will be opened when the scatterers are inserted into the area of the plate, where the elastic potential energy is concentrated.

13.

The vibroacoustic response and sound absorption performance of multilayer,microperforated ribstiffened plates





Haian Zhou Xiaoming Wang Huayong Wu Jianbing Meng《Acta Mechanica Sinica》,2017年第33卷第5期


The vibroacoustic response and sound absorption performance of a structure composed of multilayer plates and one rigid back wall are theoretically analyzed.In this structure, all plates are twodimensional, microperforated, and periodically ribstiffened.To investigate such a structural system,semianalytical models of onelayer and multilayer plate structures considering the vibration effects are first developed.Then approaches of the space harmonic method and Fourier transforms are applied to a onelayer plate,and finally the cascade connection method is utilized for a multilayer plate structure. Based on fundamental acoustic formulas, the vibroacoustic responses of microperforated stiffened plates are expressed as functions of a series of harmonic amplitudes of plate displacement, which are then solved by employing the numerical truncation method. Applying the inverse Fourier transform, wave propagation, and linear addition properties,the equations of the sound pressures and absorption coefficients for the onelayer and multilayer stiffened plates in physical space are finally derived.Using numerical examples,the effects of the most important physical parameters—for example, the perforation ratio of the plate, sound incident angles, and periodical rib spacing—on sound absorption performance are examined.Numerical results indicate that the sound absorption performance of the studied structure is effectively enhanced by the flexural vibration of the plate in water. Finally, the proposed approaches are validated by comparing the results of stiffened plates of the present work with solutions from previous studies.

14.

Research on 1:2 subharmonic resonance and bifurcation of nonlinear rotorseal system





李忠刚 陈予恕《应用数学和力学(英文版)》,2012年第33卷第4期


The 1:2 subharmonic resonance of the labyrinth sealsrotor system is investigated, where the lowfrequency vibration of steam turbines can be caused by the gas exciting force. The empirical parameters of gas exciting force of the Muszynska model are obtained by using the results of computational fluid dynamics (CFD). Based on the multiple scale method, the 1:2 subharmonic resonance response of the dynamic system is gained by truncating the system with three orders. The transition sets and the local bifurcations diagrams of the dynamics system are presented by employing the singular theory analysis. Meanwhile, the existence conditions of subharmonic resonance nonzero solutions of the dynamic system are obtained, which provides a new theoretical basis in recognizing and protecting the rotor from the subharmonic resonant failure in the turbine machinery.

15.

Effects of bottom shear stresses on the waveinduced dynamic response in a porous seabed：POROWSSI （shear） model





J.Ye D.S.Jeng《Acta Mechanica Sinica》,2011年第27卷第6期


When ocean waves propagate over the sea floor,dynamic wave pressures and bottom shear stresses exert on the surface of seabed.The bottom shear stresses provide a horizontal loading in the waveseabed interaction system,while dynamic wave pressures provide a vertical loading in the system.However,the bottom shear stresses have been ignored in most previous studies in the past.In this study,the effects of the bottom shear stresses on the dynamic response in a seabed of finite thickness under wave loading will be examined,based on Biot’s dynamic poroelastic theory.In the model,an "up" approximation will be adopted instead of quasistatic model that have been used in most previous studies.Numerical results indicate that the bottom shear stresses has certain influences on the waveinduced seabed dynamic response.Furthermore,wave and soil characteristics have considerable influences on the relative difference of seabed response between the previous model(without shear stresses) and the present model(with shear stresses).As shown in the parametric study,the relative differences between two models could up to 10% of p0,depending on the amplitude of bottom shear stresses.

16.

Vibromodulation and Guided wave techniques for contact defect detection in plate





B.W.Drinkwater S.A.Neild P.D.Wilcox《Chinese Journal of Acoustics》,2011年第30卷第1期


A nonlinear acoustic technique for detection of contact defects in plates was developed associating guided waves with vibromodulation techniques.The low frequency vibration varies the interface area within the contact defect;then the amplitude and phase of high frequency guided waves reflected from the contact defect will be modulated.Due to the exiting of contact defects,there was obvious low frequency component in the timefrequency distribution of modulated guided wave series.Furthermore the nonlinear responses at frequency of vibration were extracted out and used for defect imaging.It was shown that the nonlinear guided wave imaging method based on vibration modulation can effectively characterize and locate the nonlinear contact defects.

17.

AN ANALYSIS FOR DIFFRACTION OF FLEXURAL WAVES AND DYNAMIC STRESS CONCENTRATIONS IN THICK PLATES WITH A CAVITY





Hu Chao Ma Xingrui Huang Wenhu 《Acta Mechanica Solida Sinica》,1997年第10卷第2期


By using the complex variable method and conformal mapping,the diffraction of flexural waves and dynamic stress concentrations in thick plates with a cavity have been studied.A generalsolution of the stress problem of the thick plate satisfying the boundary conditions on the contour of anarbitrary cavity is obtained.By employing the orthogonal function expansion technique,the dynamicstress problem can be reduced to the solution of an infinite algebraic equation series.As an example,the numerical results for the dynamic stress concentration factor in thick plates with a circular,ellipticcavity are graphically presented.The numerical results are discussed.

18.

Axisymmetrical analytical solution for vertical vibration of endbearing pile in saturated viscoelastic soil layer





杨骁 潘元《应用数学和力学(英文版)》,2010年第31卷第2期


Based on elasticity and the theory of saturated porous media, and regarding the pile and the soil as a single phase elastic and a saturated viscoelastic media, respectively, the dynamical behavior of vertical vibration of an endbearing pile in a saturated viscoelastic soil layer is investigated in the frequency domain using the Helmholtz decomposition and variable separation method. The axisymmetrical analytical solutions for vertical vibrations of the pile in a saturated viscoelastic soil layer are obtained, and the analytical expression of the dynamical complex stiffness of the pile top is presented. Responses of dynamic stiffness factor and equivalent damping of pile top with respect to the frequency are shown in figures using a numerical method. Effects of the saturated soil parameters, modulus ratio of the pile to soil, slenderness ratio of pile and pile＇s Poisson ratio, etc. on the stiffness factor and damping are examined. It is shown that, due to the effect of the transversal deformation of the pile and the radial force of the saturated viscoelastic soil acting on the pile, the dynamic stiffness factor and the damping derived from the axisymmetrical solution are greatly different from those derived from the classical EulerBernoulli rod model, especially at some specific excitation frequencies. Therefore, there are limitations on applicability of the EulerBernoulli rod model in analyzing verticai vibration of the pile. More accurate analysis should be based on a threedimensional model.

19.

SEMIANALYTICAL SOLUTION FOR FREE VIBRATION OF THICK FUNCTIONALLY GRADED PLATES RESTED ON ELASTIC FOUNDATION WITH ELASTICALLY RESTRAINED EDGE





M.Shaban M.M.Alipour《Acta Mechanica Solida Sinica》,2011年第4期


This paper deals with free vibration analysis of functionally graded thick circular plates resting on the Pasternak elastic foundation with edges elastically restrained against translation and rotation.Governing equations are obtained based on the first order shear deformation theory(FSDT) with the assumption that the mechanical properties of plate materials vary continuously in the thickness direction.A semianalytical approach named differential transform method is adopted to transform the differential governing equations into algebraic recurrence equations.And eigenvalue equation for free vibration analysis is solved for arbitrary boundary conditions.Comparison between the obtained results and the results from analytical method confirms an excellent accuracy of the present approach.Afterwards,comprehensive studies on the FG plates rested on elastic foundation are presented.The effects of parameters,such as thicknesstoradius,material distribution,foundation stiffness parameters,different combinations of constraints at edges on the frequency,mode shape and modal stress are also investigated.

20.

Design of sandwich acoustic window for sonar domes





YUMengsa LIDongsheng GONGLi XUJian《Chinese Journal of Acoustics》,2005年第24卷第2期


Aimed at the low noise design of sonar dome in ships, a method has been presented for calculating the sonar self noise of a simplified sonar dome consisting of sandwich acoustic window and parallel acoustic cavity, which is excited by stationary random pressure fluctuation of turbulence boundary layer, using temporal and spatial double Fourier transform and wavenumberfrequency spectrum analysis. After numerically analyzing the influence of geometrical and physical parameters of acoustic window on the sonar self noise, the design method and reasonable parameters for sandwich acoustic window are proposed. The results show that the property of low noise induced by acoustic window of sandwich is dominated by the cutoff effect of longitudinal wave and transverse wave propagating in the viscoelastic layer of sandwich as well as the mismatch effect of impedance. If the thickness, density, Young‘s modulus and damping factor of plates and viscoelastic layer as well as the sound speed of longitudinal wave and transverse wave in the viscoelastic layer are selected reasonably, the maximum noise reduction of sandwich acoustic window is 6.5 dB greater than that of a single glass fiber reinforced plastic plate.
