Please use this identifier to cite or link to this item: http://hdl.handle.net/11452/21713
Title: Free vibrations of a mass grounded by linear and nonlinear springs in series
Authors: Uludağ Üniversitesi/Mühendislik Fakültesi/Makine Mühendisliği Bölümü.
Telli, Sevda
Kopmaz, Osman
AAG-4708-2019
7801643721
6603311475
Keywords: Mechanics
Engineering
Acoustics
Algebra
Differential equations
Electric grounding
Equations of motion
Nonlinear control systems
Springs (components)
Equivalent spring rate
Harmonic balance techniques
Vibrations (mechanical)
Issue Date: 7-Feb-2006
Publisher: Academic Press
Citation: Telli, S. ve Kopmaz, O. (2006). ''Free vibrations of a mass grounded by linear and nonlinear springs in series''. Journal of Sound and Vibration, 289(4-5), 689-710.
Abstract: In many technical applications spring-like flexible elements or real springs connected in series are used. The operation range of these components determines whether the system behaviour has a linear or nonlinear characteristic. In the relevant literature, there exists the knowledge how the equivalent spring is obtained for linear springs connected serially. However, some cases occur in which one linear and one nonlinear spring arranged in series are used. In such cases, it is not possible to define an equivalent spring rate. This study is concerned with such a system that consists of a mass grounded two springs, one of them linear and the other nonlinear. Two methods are developed to analyze the dynamic behaviour of system. One method makes use of a set of differential-algebraic equations (DAE in short). The other is based on getting a single equation of motion using relative displacement variables. For the second method, analytical solutions are also obtained by means of the Lindstedt and the harmonic balance techniques. It is observed, that numerical and analytical solutions found for both methods are in very good agreement when v(0) <= 1 and 0.1 <= xi <= 10 where v(0) is the initial deflection of nonlinear spring and xi is the ratio of linear portion coefficient of the nonlinear spring to that of the linear spring.
URI: https://doi.org/10.1016/j.jsv.2005.02.018
https://www.sciencedirect.com/science/article/pii/S0022460X05001549
http://hdl.handle.net/11452/21713
ISSN: 0022-460X
1095-8568
Appears in Collections:Scopus
Web of Science

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