Analytic evaluation of periodic responses of a forced nonlinear oscillator

Alexander F. Vakakis, Cetin Cetinkaya

Research output: Contribution to journalArticlepeer-review


The periodic responses of a strongly nonlinear, single-degree-of-freedom forced oscillator with weak excitation and damping are examined. The presented methodology is based on a regular perturbation expansion, whose first term is the solution of the unforced, and undamped nonlinear problem. Higher order approximations are computed by explicitly solving linear differential equations possessing a periodically varying coefficient. The general theory is used for studying the periodic steady state motions of the periodically forced system. Moreover, it is shown that the presented analysis can be used to analytically study the orbital stability of the identified steady state motions. The proposed method can also be used for studying periodic responses due to nonperiodic transient forces, provided that these responses are close to the O(1) periodic generating solution.

Original languageEnglish (US)
Pages (from-to)37-51
Number of pages15
JournalNonlinear Dynamics
Issue number1
StatePublished - Jan 1995


  • Single-degree-of-freedom oscillations
  • nonlinear steady state motions

ASJC Scopus subject areas

  • Mechanical Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering
  • Control and Systems Engineering


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