Vibrations of Perforated Plates with Rounded Corners

Abstract

This paper presents a free-vibration study of a new class of perforated plates with rounded corners. In contrast to the commonly used discretization methods, the vibration analysis is performed on a continuum-plate domain. The global Ritz minimization procedure with a set of orthogonally generated polynomials as admissible function is employed in this analysis. This method consists of constructing an appropriate-boundary basic function that implicitly satisfies the kinematic boundary conditions. By minimizing the energy functional, a governing eigenvalue equation is derived. This solution method offers simplicity and easy automation. To illustrate the applicability of the proposed method, the vibration responses for perforated plates with rounded corners are determined. These results are verified, when possible, through existing literature. Comparisons show that the present results are in good agreement with the available experimental values and other approximated solutions. In this paper, a comprehensive set of first-known vibration frequencies and mode shapes is presented to serve the aim of increasing the existing data base. These might be useful for design applications or also for future reference.