New Analytical Free Vibration Solutions of Thin Plates Using the Fourier Series Method

This article aims at analytically solving the free vibration problem of rectangular thin plates with one corner and its opposite two adjacent edges rotationally-restrained, which is difficult to handle by conventional semi-inverse approaches such as Levy solution Naiver solution, etc. Based on classical Fourier series theory, this work presents a first endeavor treat two-dimensional half-sinusoidal series, quite similar Navier’s form plate deflection. By utilizing orthogonality present trial function Stoke’s transformation technique, procedure converts complicated into sets linear algebra equations, heavily decreases difficulties. Therefore, approach enables solve title in unified, simple straightforward way, very easily implemented researchers. Another advantage method over other analytical that it has general applicability various boundary conditions through different types can be extended for further dynamic/static analysis under shear deformation theories. Moreover, without any extra derivation processes, new, precise solutions three non-Levy-type are also obtained choosing rotating fixed coefficients. Consequently, we more than 400 comprehensive results classical/non-classical boundaries, all confirmed FEM/analytical used benchmark data research.