Natural frequencies of edge restrained tapered isotropic and orthotropic rectangular plates with a central free hole

Natural frequencies of tapered orthotropic rectangular plates with a central free hole and edges restrained against rotation and translation are studied by using orthogonal polynomials in the Rayleigh–Ritz method and applying a generalization of the Rayleigh–Schmidt method. The two methods are quite general and can be used to study plates with any combinations of boundary conditions, taper and geometric parameters. To demonstrate the accuracy of the present approach natural frequency coefficients are given for isotropic plates with a central free hole, from which comparison results are available. New results are also given for orthotropic plates with several complicating effects. The studied problems are of interest in several field of engineering, since holes are present in plates due to operational conditions.