The extended Rayleigh-Ritz method for an analysis of nonlinear vibrations

Abstract

An extension has been made with the popular Rayleigh-Ritz method by integrating the energy functional over the time of one period of vibration to eliminate the harmonics from the deformation function. An eigenvalue problem is obtained for the frequency-amplitude dependence of nonlinear vibrations of small deformation. This is the extension of Rayleigh-Ritz method of the energy formulation and Galerkin method with the inclusion of time, which is equivalent to the harmonics matching in nonlinear vibrations. The extended Rayleigh-Ritz method can be utilized for the analysis of free and forced nonlinear vibrations of structures as a new technique with significant advantages.

Keywords:

• Approximation
• energy
• frequency
• nonlinear
• vibration

Data availability

The data used and generated in this research will be publicly available from the publication’s website and author’s website.

Additional information

Funding

This research is supported in part by the National Natural Science Foundation of China (Grant 11672142). Additional support is through the Technology Innovation 2025 Program (Grant 2019B10122) of the Municipality of Ningbo, Zhejiang Province, China.