In-plane vibration characteristics of isotropic plate with elastic edge restraints

It has been well-established that in-plane vibration modes in structures occur at high frequencies. Hence, it is important from the perspective of design consideration to analyse the dynamic behaviour of built up structures subjected to high frequency excitation. In light of the above, the present analysis has been undertaken for analysis of in-plane free vibration characteristics of isotropic rectangular plates using single Fourier series solution for the in-plane plate displacements. The Fourier series representation has been supplemented with auxiliary functions, so chosen, as to remove any potential discontinuities associated with Fourier series function defined over the entire x-y plane. Rayleigh-Ritz procedure has been applied to determine the in-plane natural frequencies of the plate and generation of natural modes. The demonstrated numerical examples provide an excellent accuracy and convergence of resulting solutions and bring out the effects of variation of boundary conditions on the in-plane vibration characteristics.