Transverse Vibration of Thin Rectangular Orthotropic Plates on Translational and Rotational Elastic Edge Supports: A Semi-analytical Approach

The free vibration analysis of thin orthotropic plates with elastically constrained edges is presented using the energy-based Rayleigh-Ritz (RR) method. Various edge conditions are modeled with rotational and translational linear springs. The complete set of admissible functions, which is a combination of (1) trigonometric functions, (2) the unit function, (3) the linear function, and (4) the lowest order polynomial, has been used in the RR method. It has been demonstrated that the use of a combination of the lowest order polynomial and the cosine series results in a rapid convergence of the solution, without any ill-conditioning of the admissible functions upon expansion. In particular, this work proposes a simple guideline for determining a set of trial functions that can be universally utilized for the vibration analysis of plates with non-classical boundary conditions. The convergence and exactness of this approach have been demonstrated through several examples. The results indicate that the elastically restrained stiffness and the plate aspect ratio impact the frequency parameters considerably.