Forced vibration analysis of multi-degree-of-freedom nonlinear systems with the extended Galerkin method

Shi, Baiyang; Yang, Jian; Wang, Ji

Abstract

In this study, the dynamic response behavior of a generalized nonlinear dynamic system is investigated using a newly proposed extended Galerkin method. The algebraic equations of vibration amplitudes are obtained through an integration of the weighted functions. The new method is equivalent to the harmonic balance method but with a much simpler calculation procedure and a higher efficiency. This is the first time to use the method for the analysis of nonlinear systems with high number of modes, manifesting that the method is applicable to forced vibrations of nonlinear behavior. The method is further validated by the numerical Runge-Kutta method.

• Journal Article Type: Article
• Acceptance Date: Dec 26, 2021
• Online Publication Date: Jan 20, 2022
• Publication Date: Jan 1, 2021
• Deposit Date: Feb 15, 2023
• Publicly Available Date: Feb 16, 2023
• Journal: Mechanics of Advanced Materials and Structures
• Print ISSN: 1537-6494
• Electronic ISSN: 1537-6532
• Publisher: Taylor & Francis
• Peer Reviewed: Peer Reviewed
• Volume: 30
• Issue: 4
• Pages: 794-802
• DOI: https://doi.org/10.1080/15376494.2021.2023922
• Keywords: Mechanical Engineering; Mechanics of Materials; Materials Science; Galerkin method; nonlinear vibration; multi-degree of freedom; Duffing oscillator; numerical continuation
• Public URL: https://uwe-repository.worktribe.com/output/10461538
• Publisher URL: https://www.tandfonline.com/doi/abs/10.1080/15376494.2021.2023922?journalCode=umcm20
• Additional Information: Peer Review Statement: The publishing and review policy for this title is described in its Aims & Scope.; Aim & Scope: http://www.tandfonline.com/action/journalInformation?show=aimsScope&journalCode=umcm20; Received: 2021-12-22; Accepted: 2021-12-26; Published: 2022-01-20