Free Vibration Analysis of Square Structure Plate with Different Boundary Conditions

- A mathematical model is presented to analyse the free vibration of viscoelastic square structure plate by employing a Rayleigh-Ritz method. Visco-elastic plates find a large range of applications, mainly in weight responsive structures like aircraft and spaceship due to their high strength-to-weight ratio and high stiffness-to-weight ratio. This paper deals with free vibration of visco-elastic square plate using different boundary conditions and thickness of the plate is assumed to be varying circularly in x-direction and temperature variation in visco-elastic plate is also taken linearly in x-direction. Boundary conditions for square structure plate is supposed to be clamped (C-C-C-C) and simply supported (SS-SS-SS-SS). A High-level Mathematical computational software MAPLE does all the calculations. The first two modes of vibration are calculated to see the effects of two factors taper constants and thermal gradient, and the findings of the present analysis are presented in tables and graphs.