Analysis of free in-plane vibrations of a rectangular plate with various boundary conditions canonical form using the modified Riley-Ritz method

Abstract

This paper investigates the free in-plane vibrations of rectangular sheets under various boundary conditions using an improved Riley-Ritz method. A novel approach involving graph theory and canonical forms is introduced, marking a first in the study of symmetric structures. The research presents an advanced version of Riley’s theory for accurately computing the natural frequencies of structures, showing significant improvements in efficiency and precision over traditional methods like Monte Carlo simulations. Key findings include the ability of the upgraded Riley theory and graphs to conduct comprehensive structural reliability and sensitivity analyses, particularly in evaluating changes in failure risk and aiding in precise design. Numerical analysis demonstrates the method’s rapid convergence and accuracy, proving its effectiveness in structural analysis. The study also explores the impact of geometric parameter variations on the free vibrations of rectangular sheets, offering crucial insights for various engineering applications. These findings have broad implications in mechanical, marine, aerospace, and civil engineering, particularly in the design and analysis of structural components such as fuselages, airplanes, missiles, and tank bottoms.