Vibration analysis of composite annular plates by an integral equation technique

In layered plates, coupling between bending and stretching makes the analysis complicated. A numerical method, namely an integral equation technique which has been used for solving static and dynamic problems, is extended to vibration analysis of layered annular plates which are fixed at the inner and outer radii. The results obtained are compared with those of other investigators and a parametric study is made of the effect of layer thickness, the layers being made up of two different materials.     

Vibration and damping analysis of annular plates with constrained damping layer treatments

The natural frequencies and modal loss factors of annular plates with fully and partially constrained damping treatments are considered. The equations of free vibration of the plate including the transverse shear effects are derived by a discrete layer annular finite element method. The extensional and shear moduli of the viscoelastic material layer are described by the complex quantities. Complex eigenvalues are then found numerically, and from these, both frequencies and loss factors are extracted. The effects of viscoelastic layer stiffness and thickness, constraining layer stiffness and thickness, and treatment size on natural frequencies and modal loss factors are presented. Numerical results also show that the longer constrained damping treatment in radial length does not always provide better damping than the shorter ones.     

An exact frequency analysis of annular plates with small core having elastically restrained outer edge and sliding inner edge

The present study deals with an exact analysis of free transverse vibrations of annular plates having small core and sliding inner edge and the outer edge being elastically restrained based on classical plate theory. This study focuses mainly on the influence of variations in the elastic restraint parameters on the fundamental frequencies of plate vibration. The natural frequencies for the first six modes of annular plate vibrations are computed for different materials and varying values of the radius parameter and these natural frequencies may correspond to either axisymmetric and/or non-axisymmetric modes of plate vibration. The extensive data of values of fundamental frequency parameter presented in this paper is believed to be of use in the design of acoustic underwater transducers, ocean and naval structures, compressor and pump elements, offshore platforms. These results may serve as bench mark values for researchers to validate their results obtained using approximate numerical methods.     

Vibration analysis of functionally graded annular plates with mixed boundary conditions in thermal environment

The free vibration analysis of functionally graded annular plates with mixed boundary conditions in thermal environment is carried out by the 3D elasticity theory and the Chebyshev–Ritz method. The material properties are assumed to be temperature dependent and graded in the thickness direction. The mixed boundary conditions which include upper and lower surfaces partially fixed, inner side partially fixed and outer side partially fixed are considered, respectively. The accuracy of the present approach for solving the free vibration of the plates with different boundary conditions is validated by comparing the present numerical results with the results available. The effects of the different mixed boundary conditions, the temperature rise, the material graded index and the geometrical parameters on the eigen-frequencies are studied.     

Vibration coupling effects between two concentric cylindrical shells through periodic annular plates and entrained fluid

The coupling effects on two concentric cylindrical shells with periodic annular plates as well as entrained fluid were investigated theoretically. Expressions for the reactive forces by the annular plates were derived on the assumption that only quasi-longitudinal waves exist in the annular plates and an analytical expression for the outer shell was developed. Comparisons of numerical results for infinite two-walled cylindrical shell to measured data for a cabin model are in good agreement. Numerical results were presented for analyzing the characteristics of the loadings due to the acoustic fluid and the periodic annular plates, and their influences on the outer shell＇s far field acoustic radiation.     

通过周期环板和附连流体的两同心圆柱壳体间的振动耦合效应

理论研究了两个同心圆柱壳体间通过周期环饭和附连流体的耦合效应。在环板内只有准纵波存在的假定下,给出环板的反作用力的表达式,并建立外壳体的声辐射解析表达式。无限长双层壳体的数值分析结果和舱段模型的实验结果一致。通过数值结果同时分析了声学流体和周期环板的载荷特征,以及它们对外壳体远场声辐射的影响。     

Vibration of electro-elastic versus magneto-elastic circular/annular plates using the Chebyshev–Ritz method

The aim of this paper is to analyze three-dimensional free vibration of magneto-elastic/electro-elastic circular/annular plates with different boundary conditions using the Chebyshev–Ritz method, in which a set of duplicate Chebyshev polynomial series multiplied by the boundary function satisfying the boundary conditions are chosen as the trial functions of the displacement components, the electric potential and the magnetic potential. Convergence of the method is checked using various Chebyshev polynomial terms. The effect of geometrical parameters and material properties of magneto-elastic/electro-elastic circular/annular plates on the eigenfrequencies of free vibration is considered.     

Vibrations of nearly annular and circular plates

A general procedure is presented to determine the natural frequencies and mode shapes of nearly annular and circular plates. A straightforward perturbation procedure is used with a transfer of the boundary conditions to obtain solutions given by simple expressions. As well as yielding good accuracy quantitatively, the method accurately predicts qualitative behavior. Numerical results are presented for clamped elliptical and square plates.     

Vibration analysis of annular-like plates

The existence of eccentricity of the central hole for an annular plate results in a significant change in the natural frequencies and mode shapes of the structure. In this paper, the vibration analysis of annular-like plates is presented based on numerical and experimental approaches. Using the finite element analysis code Nastran, the effects of the eccentricity, hole size and boundary condition on vibration modes are investigated systematically through both global and local analyses. The results show that analyses for perfect symmetric conditions can still roughly predict the mode shapes of “recessive” modes of the plate with a slightly eccentric hole. They will, however, lead to erroneous results for “dominant” modes. In addition, the residual displacement mode shape is verified as an effective parameter for identifying damage occurring in plate-like structures. Experimental modal analysis on a clamped-free annular-like plate is performed, and the results obtained reveal good agreement with those obtained by numerical analysis. This study provides guidance on modal analysis, vibration measurement and damage detection of plate-like structures.