Vibration of Plates Having Orthogonal Straight Edges with Clamped Boundaries

A domain decomposition procedure is employed to investigate the vibratory characteristics of plates having orthogonal straight edges with fully clamped boundary conditions. Three rectangular segments are used to construct an L-shaped plate element by enforcing continuities along the adjacent segments in displacement, slope, and higher derivatives. The strain and kinetic energies of each plate segment are coupled through the continuity matrices, resulting in a global energy functional for the entire plate domain. A governing eigenvalue equation is derived by minimizing the energy functional by following the Ritz procedure. A set of beam characteristic orthogonal polynomials is employed as the admissible displacement function for each plate segment. By virtue of symmetry in geometry, the basic L-shaped plate element is employed to construct plates of I and cross shapes, and vibration solutions of these plates are obtained via the domain decomposition procedure.