Support motion of a finite bar with a viscously damped boundary. (17th November 2022)

• Record Type: Journal Article
• Authors: Chen, Jeng-Tzong; Kao, Hao-Chen; Lee, Jia-Wei; Lee, Ying-Te
• Is Part Of: Journal of mechanics. Volume 38:Number 1(2022)
• Page Start: 473
• Page End: 490
• Publication Date: 2022-11-17
• Subjects: support motion -- viscous damper -- mode superposition method -- quasi-static decomposition -- diamond rule; Mechanics, Analytic -- Periodicals; Mechanics -- Periodicals; 620.1005
• DOI: 10.1093/jom/ufac035
• Languages: English
• ISSNs: 1727-7191

Abstract

ABSTRACT: In this paper, we extended the previous experience to solve the vibration problem of a finite bar with a viscously damped boundary and the support motion on the other side. Two analytical methods, the mode superposition method in conjunction with the quasi-static decomposition method and the method of diamond rule based on the method of characteristics, were employed to derive two analytical solutions. One is a series solution by using the mode superposition method. The other is an exact solution by using the method of diamond rule. The non-conservative system with an external damper is solved straightforward by using the method of diamond rule to avoid the complex-valued eigen system. Agreement is made well. Both advantages and disadvantages of two methods were discussed.