1 Formulation of the equations of motion 2 Element energy functions 3 Introduction to the finite element displacement method 4 In-plane vibration of plates 5 Vibration of solids 6 Flexural vibration of plates 7 Vibration of stiffened plates and folded plate structures 8 Vibration of shells 9 Vibration of laminated plates and shells 10 Hierarchical finite element method 11 Analysis of free vibration 12 Forced response 13 Forced response II 14 Computer analysis technique

Introduction to finite element vibration analysis

A review and catalogue of plate bending finite elements

Introduction to Finite Element Vibration Analysis: Frontmatter

The buckling and frequency of flexural vibration of rectangular isotropic and orthotropic plates using rayleigh's method

Finite elements applied to panel flutter.

A method of computing the natural frequencies of vibration of flat plates of arbitrary shape is outlined in which the plate is considered as an assemblage of elements.Both stiffness and inertia matrices are derived for a rectangular isotropic plate element of uniform thickness, and these matrices are used to find the natural frequencies of square plates subject to various boundary conditions. Comparison of finite element frequencies with known exact, experimental and energy solutions shows the method to give good results even for relatively few elements.

A Finite Element Approach to Plate Vibration Problems

In a previous paper the application of the finite element method to plate vibration problems was discussed. It was shown that the method gave good results when applied to the vibration of plates of uniform thickness.The present paper extends the method to include plates of variable thickness. In particular stiffness and inertia matrices are derived for an isotropic rectangular plate element of linearly variable thickness in one co-ordinate direction. These matrices are used to find the natural frequencies and mode shapes of a number of rectangular planform cantilever plates of non-uniform thickness. Experimental results provide a basis for comparison with the finite element results.

D. J. Dawe

Papers

A Finite Element Approach to Plate Vibration Problems

Vibration of Rectangular Plates of Variable Thickness