Analytical Solution for Study of Damped of Clamped and Simply Supported Right Triangular Plate under Elastic Foundation

This study investigates the analytical solution for damped vibrations analysis of clamped, simply supported right triangular plates using the separation of variable method. The governing equation is solved for various boundary conditions applicable to the right triangular plate. An approximate frequency equation is obtained using the Rayleigh Ritz technique with a two-term deflection function generated through Gram Schmidt orthogonalization. The calculations include determining the frequency parameter, time period, deflection, and logarithmic decrement at different points for two vibration modes based on variations in parameters such as taper constant, aspect ratio, damping parameters and elastic foundation.