Dynamic response of circular plates to transient and harmonic transverse loads including the effect of transverse shear and rotary inertia

Using an improved theory of plate vibration suggested by R. D. Mindlin which takes into account the effects of transverse shear and rotary inertia, free and forced transverse vibrations of uniform circular plates are studied and the results compared with those obtained using the classical theory of plate vibration. The governing equations are developed in polar coordinates using the equations of elasticity. Frequency equations for axisymmetric and antisymmetric vibrations are derived for solid circular plates under different boundary conditions and for an annular plate rigidly mounted on a shaft. The response of plates to different types of rapidly applied axisymmetric steady loads and pulse loads is investigated in detail using an improved normal-mode solution suggested by D. Williams. Frequency equations for plates loaded with arbitrary impedance at the center are derived by three different methods. Two methods make use of conventional mode summation techniques and result in series forms of the frequency equation. The third method results in a closed-form frequency equation which makes it very convenient for use in many applications. A number of typical applications of the closed-form frequency equation are also considered. The driving-point impedance and transmissibility of free and constrained circular plates driven by harmonically oscillating forces at the center are studied by extending the principles used in the derivation of the closed-form frequency equation. The effect of attaching dynamic vibration absorbers at the center of the plate and their tuning are also investigated. Internal material damping is treated in general, but no numerical results are presented for damped systems. Several examples are given detailed consideration. Numerical results are given in nondimensional quantities and are presented in a series of graphs and tables --Abstract, pages ii-iii