Coupled Torsional and Transverse Vibration Analysis of Panels Partially Supported by Elastic Beam

TL;DR

This paper develops a numerical method to analyze coupled torsional and transverse vibrations of a partially supported solar panel, demonstrating improved accuracy over existing methods through validation and case studies.

Contribution

It introduces the Modified Generalized Differential Quadrature method (MGDQ) for accurate vibration analysis of systems with local boundary conditions.

Findings

MGDQ outperforms GDQ in accuracy.

The method effectively handles local boundary and continuity conditions.

Results validate the method's applicability to complex vibration problems.

Abstract

This study presents torsional and transverse vibration analysis of a solar panel including a rectangular thin plate locally supported by an elastic beam. The plate is totally free in all boundaries, except for the local part attached to the beam. The response of the system, which is subjected to a combination of torsional and transverse vibration, identifies with a couple of PDEs developed by the Euler-Bernoulli assumption and classical plate theory. To calculate the system's natural frequencies, the domain of the solution is discretized by zeroes of the Chebyshev polynomials to apply the Modified Generalized Differential Quadrature method (MGDQ). Furthermore, governing equations along with continuity and boundary conditions are discretized. After obtaining solutions to the eigenvalue problem, several studies are investigated to validate the accuracy of the proposed method. As can be concluded from the tables, MGDQ improves the accuracy of results obtained by GDQ. Results for various case studies reveal that MGDQ is properly devised for the vibration analysis of systems with local boundary and continuity conditions.