DOI: 10.1177/10775463231221315 ISSN: 1077-5463
An improved Fourier series solution for vibration analysis of elastically restrained beams in Rayleigh–Ritz method
Jianzheng Wang, Ruiping Zhou, Yukuo Guo, Xiaoyuan Luo- Mechanical Engineering
- Mechanics of Materials
- Aerospace Engineering
- Automotive Engineering
- General Materials Science
A combination of Fourier cosines series and polynomials (4 terms, 4th order) in Rayleigh–Ritz method is proposed to solve the vibration problem of a generally restrained beam. The characteristics of auxiliary polynomials, which actually are determined by homogeneous boundary conditions of the beam under consideration, can directly change the convergence properties and numerical instabilities of vibration results significantly. Fast convergence and reliability of the proposed polynomials are illustrated with numerical examples in comparisons with available results.