Damped vibration of tapered and bidirectional graded plate subjected to arbitrary radial load rested on elastic medium

In present work, the effects of elastic and viscous medium, arbitrary variation of material properties in transverse and radial directions, linear and nonlinear tapering, Poisson’s ratio, arbitrary radial load and various boundary conditions on angular frequency of circular plate are investigated. The total potential energy is minimized by using the spectral Ritz method due to fast convergence and adaptation to different boundary conditions. The novelty of this work is that the difficulties of the employing adhesive or auxiliary functions are resolved by introducing generalized basis of orthogonal Laguerre polynomials. Moreover, the optimization is performed by calculating the determinant root of total potential energy Hessian and eliminating the inverses of high-order matrices in iterative steps. The accuracy of the results has been confirmed by observing convergence and a good agreement between results of current work and previously published works in literature. By increasing the power index and decreasing the taper constant, decreasing indeterminacy degree and Poisson ratio, increasing attenuation and decreasing stiffness, decreasing the elastic modulus at the edge of the plate and applying more compressive load near to the center of the plate, the angular frequency of free vibration will be reduced.