Natural frequencies of an inhomogeneous square thin plate

Plates, which geometric and physical parameters slightly differ from constant depend only on the radial coordinate, are analyzed. For free vibration frequencies of a plate, thickness and/or Young’s modulus coordinate asymptotic formulas obtained by means perturbation method. As examples, vibrations square plate with linearly or parabolically examined. The double plates similar edge support all edges special interest, since any variation stiffness causes some loss symmetry one may expect split frequencies. permit to determine, two equal unperturbed corresponding wave numbers n m increases faster small parameter. wide range parameter values, results for lower well agree finite element analysis COMSOL Multiphysics 5.4.