Vibration analysis of a beam on a nonlinear elastic foundation

KARAHAN M. M. F., Pakdemirli M.

Structural Engineering and Mechanics, vol.62, no.2, pp.171-178, 2017 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 62 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.12989/sem.2017.62.2.171
  • Journal Name: Structural Engineering and Mechanics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.171-178
  • Keywords: Beam on elastic foundation, Direct perturbation method, Forced vibrations, Multiple scales Lindstedt Poincare (MSLP) method, Strongly nonlinear systems
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

Nonlinear vibrations of an Euler-Bernoulli beam resting on a nonlinear elastic foundation are discussed. In search of approximate analytical solutions, the classical multiple scales (MS) and the multiple scales Lindstedt Poincare (MSLP) methods are used. The case of primary resonance is investigated. Amplitude and phase modulation equations are obtained. Steady state solutions are considered. Frequency response curves obtained by both methods are contrasted with each other with respect to the effect of various physical parameters. For weakly nonlinear systems, MS and MSLP solutions are in good agreement. For strong hardening nonlinearities, MSLP solutions exhibit the usual jump phenomena whereas MS solutions are not reliable producing backward curves which are unphysical.