International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2578

Full Length Research Paper

An analytical approach on a mass grounded by linear and nonlinear springs in series

Mahdi Bayat1, Massoumeh Bayat2 and Mahmoud Bayat1*
1Department of Civil Engineering, Islamic Azad University, Shirvan Branch, Shirvan, Iran. 2Department of Computer Engineering, Islamic Azad University, Shirvan Branch, Shirvan, Iran.
Email: [email protected], [email protected]

  •  Accepted: 30 December 2010
  •  Published: 18 January 2011

Abstract

In this paper, He’s variational approach method is used to solve large amplitude freevibration of a mass grounded by linear and nonlinear springs in series. The conservative oscillation system is formulated as a nonlinear ordinary differential equation having linear and nonlinear stiffness components. By doing some simple mathematical operations on this method, we can obtain their natural frequencies. The main objective of present study is to obtain highly accurate analytical solution, which is valid for whole solution domain, for free vibration of a conservative oscillator with inertia and static type cubic nonlinearities. Other numerical results are finally presented and discussed to validate the present analysis.

 

Key words: Variational approach method, nonlinear oscillation, analytical method.

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