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Analytical and numerical methods for vibration analysis of thick rectangular plates by modified Mindlin theory

Total deflection and angles of rotations in the Mindlin plate theory are decomposed into bending and transverse shear deflection, bending rotations and in-plane shear angles. Single differential equation of flexural vibrations is derived in terms of bending deflection as potential function for determination of all displacements and sectional forces. The equation is solved analytically for different combinations of boundary conditions. Shear locking-free rectangular finite element is formulated. Illustrative examples are solved analytically and numerically, and the obtained results are compared with the ones available in the relevant literature.

Mindlin plate theory; natural vibration; boundary conditions; analytical solution; shear locking; FEM

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