Vibrational analysis of Levy-type plates by using SEM

The use of the frequency-dependent spectral method in structural dynamic related problems is known to provide very accurate solutions while reducing the number of degree-of-freedom to resolve the computational and cost drawbacks. This paper investigated the vibrational characteristics of a rigid pavement road which is modeled by an isotropic Levy-type rectangular thin plates. The Spectral Element Method (SEM) in the frequency domain is developed to formulate the free vibration problems of the plate. Transcendental stiffness matrices are well established in vibration, derived from the exact analytical solutions of the differential equations of a plate element. The present spectral element model has four line-type degree-of-freedoms (DOF) on each edge of the Levy-type rectangular plate. Natural frequencies are found using the Wittrick-Williams algorithm. Numerical examples are given to show the effectiveness, efficiency, and accuracy of the SEM by using one element, unlike the FEM, the SEM gives exact solutions of the natural frequencies of plates without element discretization procedures.