Approximate Solutions for a Nonlinear Transverse Vibration of an Elastically Restrained Tapered Beam

Durmaz S., Altay Demirbağ S., Kaya M. O.

1st International Congress on Advances in Applied Physics and Materials Science (APMAS), Antalya, Turkey, 12 - 15 May 2011, vol.1400, pp.71-76 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1400
  • Doi Number: 10.1063/1.3663088
  • City: Antalya
  • Country: Turkey
  • Page Numbers: pp.71-76
  • Keywords: Tapered beam, nonlinear frequency, Hamiltonian approach method, high order Hamiltonian approach method
  • Istanbul Technical University Affiliated: Yes


This paper introduces the approximate solutions of the mathematical model of elastically restrained tapered beam. At the beginning of the study, the equation of motion is derived. The frequency-amplitude relation is deduced and numerically solved. Hamiltonian approach method is implemented to solve the established model. The numerical results for the first, the second and the third order approximations are further compared with the approximate analytical solutions for both small and large amplitude of oscillations, and a very good agreement is observed.