Nonlinear vibration of a two-mass system with nonlinear stiffnesses

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

22 Scopus Citations
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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)233-249
Journal / PublicationNonlinear Dynamics
Volume49
Issue number1-2
Publication statusPublished - Jul 2007

Abstract

An analytical approach is developed for nonlinear free vibration of a conservative, two-degree-of-freedom mass-spring system having linear and nonlinear stiffnesses. The main contribution of the proposed approach is twofold. First, it introduces the transformation of two nonlinear differential equations of a two-mass system using suitable intermediate variables into a single nonlinear differential equation and, more significantly, the treatment a nonlinear differential system by linearization coupled with Newton's method and harmonic balance method. New and accurate higher-order analytical approximate solutions for the nonlinear system are established. After solving the nonlinear differential equation, the displacement of two-mass system can be obtained directly from the governing linear second-order differential equation. Unlike the common perturbation method, this higher-order Newton-harmonic balance (NHB) method is valid for weak as well as strong nonlinear oscillation systems. On the other hand, the new approach yields simple approximate analytical expressions valid for small as well as large amplitudes of oscillation unlike the classical harmonic balance method which results in complicated algebraic equations requiring further numerical analysis. In short, this new approach yields extended scope of applicability, simplicity, flexibility in application, and avoidance of complicated numerical integration as compared to the previous approaches such as the perturbation and the classical harmonic balance methods. Two examples of nonlinear two-degree-of-freedom mass-spring system are analyzed and verified with published result, exact solutions and numerical integration data. © Springer Science+Business Media B.V. 2007.

Research Area(s)

  • Duffing equation, Newton-harmonic balance (NHB) method, Nonlinear stiffness, Two-degree-of-freedom oscillation systems, Two-mass system

Citation Format(s)

Nonlinear vibration of a two-mass system with nonlinear stiffnesses. / Lai, S. K.; Lim, C. W.
In: Nonlinear Dynamics, Vol. 49, No. 1-2, 07.2007, p. 233-249.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review