Comparisons of experimental and theoretical frequencies for rectangular plates with various boundary conditions and added masses

This paper is concerned with a vibration analysis of rectangular plates with masses mounted on various locations. The edges of the plates may either be clamped or simply supported. The study is particularly useful in the understanding of the vibration of printed circuit boards used in the electronics industry. An energy method is developed to obtain analytical frequencies of the plates with various edge support conditions. The analytical procedure using the Rayleigh-Ritz approach is adopted in which each of single and multiple trigonometric series terms is used to represent the shape function. Two experimental methods, a spectrum analyser and a TV-holographic system, are used to study the behaviour of the plate vibrations. The holographic image produced at the corresponding mode frequencies by using the TV-holography technique has been applied to verify the frequency spectra obtained from the spectrum analyser. The experimental results have been used to illustrate the validity of the analytical model. The comparisons show that the analytical model predicts natural frequencies reasonably well, in which the EM 100-term model is suggested for vibration plates with higher modes or heavier loads.     

Buckling of rectangular plates with various boundary conditions loaded by non-uniform inplane loads

In the present paper, buckling loads of rectangular composite plates having nine sets of different boundary conditions and subjected to non-uniform inplane loading are presented considering higher order shear deformation theory (HSDT). As the applied inplane load is non-uniform, the buckling load is evaluated in two steps. In the first step the plane elasticity problem is solved to evaluate the stress distribution within the prebuckling range. Using the above stress distribution the plate buckling equations are derived from the principle of minimum total potential energy. Adopting Galerkin's approximation, the governing partial differential equations are converted into a set of homogeneous linear algebraic equations. The critical buckling load is obtained from the solution of the associated linear eigenvalue problem. The present buckling loads are compared with the published results wherever available. The buckling loads obtained from the present method for plate with various boundary conditions and subjected to non-uniform inplane loading are found to be in excellent agreement with those obtained from commercial software ANSYS. Buckling mode shapes of plate for different boundary conditions with non-uniform inplane loadings are also presented.     

基于MD.Nastran的某型机载雷达机箱力学仿真分析

基于MD.Nastran有限元分析软件,提出了某型机载雷达机箱的有限元建模方法,并对其分别进行了过载、模态和随机振动仿真分析.模态分析时采用Block lanczos方法求解了机箱的前十阶固有频率和振型.随机振动分析得出了各SRU(内场可更换单元)模块对基础激励的振动响应情况.仿真结果对该机箱的后续结构优化、减重设计有...     

Stability behaviour of arbitrarily laminated composite plates with free and elastically restrained unloaded edges

In this paper, the initial buckling loads and the corresponding buckling modes of symmetric rectangular laminated plates are investigated. The considered laminates are supposed to have a uniform thickness, are subjected to a linearly distributed inplane compressive normal load and are simply supported at the two loaded edges with one free unloaded plate edge and with one simply supported unloaded edge where elastic rotational restraints are considered. Unlike in many other investigations, the composite laminates presently under consideration may have arbitrary yet symmetric lamination schemes with bending–torsion coupling. The initial buckling loads of such plates are calculated using the RITZ-method for which some especially adjusted displacement shape functions are employed. Since a series expansion of the buckling shape is performed in the load direction only while in the perpendicular direction one single displacement function can be shown to be sufficient, the present approach is numerically very efficient when compared to approaches in which a series representation is chosen with respect to both inplane directions. Comparison with reference results and with finite element computations leads to an excellent agreement. Some new findings on the general stability behaviour of this class of laminated plates are presented as a closure.     

Buckling and vibration of stiffened plates subjected to partial edge loading

The buckling and vibration characteristics of stiffened plates subjected to in-plane partial and concentrated edge loadings are studied using finite element method. The initial stresses are obtained considering the pre-buckling conditions. Buckling loads and vibration frequencies are determined for different plate aspect ratios, edge conditions and different partial non-uniform edge loading cases. The non-uniform loading may also be caused due to the supports on the edges. The analysis presented determines the stresses all over the region for different kinds of loading and edge conditions. In the structural modelling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. The vibration characteristics are discussed and the results are compared with those available in the literature. Buckling results show that the stiffened plate is less susceptible to buckling for position of loading near the supported edges and near the position of stiffeners as well.     

组合结构金刚石圆锯片的有限元模态分析

提出新型组合结构圆锯片基体,为锯切大幅面制品提供了可能的有效途径。针对金刚石圆锯片在锯切加工过程中出现的振动问题,利用有限元软件ANSYS对普通圆锯片和组合结构圆锯片进行了模态分析,得到了各自低阶固有振动频率及主振型图并进行对比。结果表明:组合结构圆锯片和普通圆锯片的低阶振型都明显有节圆和节直径的特点,且都为少节圆或无节圆振型;前12阶扩展模态分布具有一定的规律性,在初始5阶模态状态时频率波动较小,从第6阶模态以后分布波动较大,且波动幅度最大约为30Hz。     

基于ANSYS的双齿辊破碎机破碎辊模态分析

为了获得各阶模态下双齿辊破碎机破碎辊的固有频率和振型,通过SolidWorks建立破碎辊的三维模型,利用ANSYS Workbench有限元分析软件对双齿辊破碎机破碎辊进行有限元模态分析。对数值模拟结果的分析可获知不同频率载荷对破碎辊的影响,找出外部激励应当避免的危险频率。     

Natural frequencies of shear deformable rhombic plates with clamped and simply supported edges

The natural vibrations of thick and thin rhombic plates with clamped and simply supported edges are analyzed, using assemblages of nine-node Lagrangian isoparametric quadrilateral C⁰ continuous finite elements based on a higher-order shear deformable thick plate theory. Here, additional nodal displacement degrees of freedom are derived by retaining higher-order powers of the thickness coordinate in the in-plane displacement fields, which in turn allows for the proper representation of the transverse shear strains of thick plates. Essential rotary inertia terms are derived and included in the present analysis. Nondimensional frequencies are calculated for thick and thin rhombic plates having various combinations of clamped and simply supported edge conditions, and skew angles. The efficacy of using higher-order shear deformable plate finite elements for predicting the in-plane vibration modes of rhombic plates is found to increase as the span-to-thickness ratio decreases and the skew angle increases. The present work shows that higher-order shear deformable finite elements essentially eliminate the transverse shear over-correction of thick rhombic plate frequencies that is produced when finite elements based on the widely used first-order Reissner-Mindlin plate theory are utilized.     

Nonlinear free and forced vibration of simply supported shear deformable laminated plates with piezoelectric actuators

This paper deals with the nonlinear vibration and dynamic response of simply supported shear deformable cross-ply laminated plates with piezoelectric actuators subjected to mechanical, electrical and thermal loads. The material properties are assumed to be independent of the temperature and electric field. Theoretical formulations are based on the higher order shear deformation plate theory and general von Kármán-type equation, which includes thermo-piezoelectric effects. Due to the bending and stretching coupling effects, a nonlinear static problem is first solved to determine the pre-vibration deformation caused by temperature field and control voltage. By adding an incremental dynamic state to the pre-vibration state, the equations of motion are solved by an improved perturbation technique to determine nonlinear frequencies and dynamic responses of hybrid laminated plates. The numerical illustrations concern nonlinear vibration characteristics of unsymmetric cross-ply laminated plates. The results presented show the effects of temperature rise, applied voltage and stacking sequence on the nonlinear vibration and dynamic response of the plates.     

并联天平动特性研究

固有频率对并联风洞天平的动态性能有重要的影响。本文主要研究基于Stewart平台的并联风洞天平的固有频率及固有振型,首先应用Kane方法研究了天平的动力学方程,通过线性化建立天平的固有频率方程,依据振动理论推导出并联天平的六阶固有频率,并研究六阶固有频率随上平台质量和连杆分支刚度的变化规律。结合数值算例,求解出天平的六阶固有频率及其对应的固有振型,并用有限元方法验证理论计算结论的正确性,结果证明并联风洞天平具有固有频率高的优点。     

Displacement fields in waves generated by flexural oscillations of plates

A technique has been suggested for calculating acoustic displacement fields in waves generated by flexural oscillations in plates of finite dimensions in gaseous media at different frequencies, plate dimensions, and elastic parameters in both pulsed and cw modes. Acoustic fields in flexural resonant transducers with emitters shaped as round plates have been studied both theoretically and experimentally.     

Vibration of stepped thickness plates

The vibration characteristics of stepped thickness plates of rectangular geometry with simply supported edges are investigated through an exact analysis. To illustrate the effect of sudden variation of thickness in the step form on the dynamic characteristics of plates, numerical calculations have been made for various combinations of thickness step, step-length ratio and side ratio. Natural frequencies for the first eight to nine modes are presented in the form of tables. Nodal lines are also plotted for a few selected cases. Several interesting features such as that of the thickness step splitting the degenerate frequencies of uniform rectangular plates into distinct ones, and the “frequency crossing” of some of the modes are observed.     

Buckling analysis of FGM plates under uniform,linear and non-linear in-plane loading

The paper investigates the buckling responses of functionally graded material (FGM) plate subjected to uniform, linear, and non-linear in-plane loads. New nonlinear in-plane load models are proposed based on trigonometric and exponential function. Non-dimensional critical buckling loads are evaluated using non-polynomial based higher order shear deformation theory. Navier’s method, which assures minimum numerical error, is employed to get an accurate explicit solution. The equilibrium conditions are determined utilizing the principle of virtual displacements and material property are graded in the thickness direction using simple Voigt model or exponential law. The present formulation is accurate and efficient in analyzing the behavior of thin, thick and moderately thick FGM plate for buckling analysis. It is found that with the help of displacement-buckling load curve, critical buckling load can be derived and maximum displacement due to the instability of inplane load can be obtained. Also, the randomness in the values of transverse displacement due to inplane load increases as the extent of uniformity of the load on the plate is disturbed. Furthermore, the parametric varying studies are performed to analyse the effect of span-to-thickness ratio, volume fraction exponent, aspect ratio, the shape parameter for non-uniform inplane load, and non-dimensional load parameter on the non-dimensional deflections, stresses, and critical buckling load for FGM plates.

     

Vibration analysis of rotating composite cantilever plates

A modeling method for the vibration analysis of rotating composite cantilever plates is presented in this paper. The coupling effects between inplane motions and the bending motion are considered and explicit mass and stiffness matrices are derived for the modal analysis. Numerical results are obtained and some of them are compared to those of a commercial program to confirm the accuracy of the present method. Numerical results show that the coupling effects become important only when laminates are stacked up unsymmetrically. Incidentally, natural frequencies loci veering, loci crossing, and associated mode shape variations are observed.     

Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method

We present an analysis of the free vibration of plates with internal discontinuities due to central cut-outs. A numerical formulation for a basic L-shaped element which is divided into appropriate sub-domains that are dependent upon the location of the cut-out is used as the basic building element. Trial functions formed to satisfy certain boundary conditions are employed to define the transverse deflection of each sub-domain. Mathematical treatments in terms of the continuities in displacement, slope, moment, and higher derivatives between the adjacent sub-domains are enforced at the interconnecting edges. The energy functional results, from the proper assembly of the coupled strain and kinetic energy contributions of each sub-domain, are minimized via the Ritz procedure to extract the vibration frequencies and mode shapes of the plates. The procedures are demonstrated by considering plates with central cut-outs that are subjected to two types of boundary conditions.     

Experimental analysis of vibration modes of plates using ESPI

In the world, there are several types of vibration, and these vibrations especially affect the mechanical industry. In this paper, experimental analysis of vibration modes of plates is discussed. Electronic speckle pattern interferometry (ESPI) is one of the optical nondestructive testing techniques. By using the ESPI, vibration modes of plates with various excitation points, ratio of longitudinal and lateral length, and materials are measured and qualitatively compared with the results of theoretical analysis proposed by Warburton. Finally, these vibration modes are quantitatively compared with the result of FEM analysis. The results of this study are as follows: (1) By comparing the theoretical and experimental frequencies, we confirmed qualitatively that deviations of frequencies are within 10% in accuracy. (2) By comparing the experimental vibration mode shapes with the numerical ones of the FEM analysis, we can conclude quantitatively that measuring vibration modes by using the ESPI has high accuracy.     

General sinusoidal stiffness matrices for buckling and vibration analyses of thin flat-walled structures

This paper is concerned with the derivation of stiffness matrices for the buckling or vibration analysis of any structure consisting of a series of long, thin, flat plates rigidly connected together at their longitudinal edges. Each plate is assumed to be subjected to a basic state of plane stress which is longitudinally invariant, and it is further assumed that the mode of buckling or vibration varies sinusoidally in the longitudinal direction. During buckling or vibration, the edges of any individual plate are subjected to additional systems of forces and moments which are sinusoidally distributed along the edges, and these give rise to sinusoidally varying edge displacements and rotations. Spatial phase differences between the forces and displacements are accounted for by defining them in terms of complex quantities. The sinusoidal edge forces and displacements are split into two uncoupled systems, corresponding to out-of-plane and in-plane displacements, and two stiffness matrices are defined. The out-of-plane stiffness matrix is shown to be in general complex, and Hermitian in form, but the inplane stiffness matrix is real and symmetrical. Explicit expressions are derived for the elements of the matrices, in which all the essential destabilizing effects of the basic stresses, as well as dynamic effects, are included. Finally, it is shown that buckling and vibration phenomena for any structure of this type are closely interrelated.     

Fluid bounding effect on natural frequencies of fluid-coupled circular plates

This study deals with the free vibration of two identical circular plates coupled with a bounded or unbounded fluid. An analytical method based on the finite Fourier-Bessel series expansion and Rayleigh-Ritz method is suggested. The proposed method is verified by the finite element analysis using commercial program with a good accuracy. The case of bounded or unbounded fluid is studied for the effect on the vibration characteristics of two circular plates. Also, the effect of gap between the plates on the fluid-coupled natural frequencies is investigated.     

高空作业车作业臂动力特性分析

对高空作业车的作业臂进行了有限元模态分析,得出了各阶模态下作业臂的固有频率和振型,找到了作业臂振动中的危险区域,为设计和改造提供理论依据。     

Transient dynamic large deflection analysis of elastic viscoplastic plates by the finite element method

The transient response of plates subjected to impulsive loads is analyzed by the finite element method taking into account the influences of geometry changes and material nonlinearities due to plasticity and strain rate sensitivity. The equations of motion are derived using the principle of virtual work in total lagrangian formulation. For plates the large deflection theory by von Kármán and the theory including the effect of transverse shear strain by Mindlin are employed. Time integration of the nonlinear system of finite element equations is effected using central difference and Newmark schemes. Numerical examples include beams and circular and rectangular plates. Comparisons are made to available experimental, analytical, and numerical results.