Abstract
Though the free in-plane vibration problem of rectangular plates with classical boundary conditions have been studied using various numerical methods like direct separation of variables, the elastic boundary restraint is more general in the practical structural applications compared with the perfect classical boundary condition. Thus, in this paper, an innovative exact solution on the basis of the method of reverberation ray matrix (MRRM) and golden section search (GSS) algorithm is presented to study the exact free in-plane vibration characteristics of rectangular plates with arbitrary boundary conditions. In the present method, the exact natural frequencies and mode shapes can be very easily obtained when two opposite plate edges have either type of the simply supported boundary conditions and the resting plate edges have the arbitrary boundary conditions including the classical case and general elastic restraints. By the comparison with other published exact solutions, it is shown that the present exact solutions have some obvious advantages which are performed in the excellent accuracy, reliability and efficiency. Performing the study, some of the first-known exact results for the free in-plane vibrations of rectangular plates with elastic boundary restraints are also obtained, which can be worked as the benchmark data for the future approximate methods.
Published Version
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