Natural Frequencies of Clamped Orthotropic Rectangular Plates With Varying Thickness

The characteristic equation of a clamped orthotropic rectangular plate with thickness varying in one direction parallel to the side is derived analytically by the use of the double trigonometric series. By using the fundamental natural frequency determined from the characteristic equation, a formula is obtained numerically for estimating the fundamental natural frequency of a clamped orthotropic rectangular plate with thickness varying linearly in one direction. The accuracy of the formula and the influence of the flexural rigidity D₁ on the natural frequency are discussed.