Generalized viscoelastic 1-DOF deterministic nonlinear oscillators

Harry H. Hilton, Sung Yi

Research output: Contribution to journalArticlepeer-review


The theory of deterministic generalized viscoelastic linear and nonlinear 1-D oscillators is formulated and evaluated. Examples of viscoelastic Duffing, Mathieu, Rayleigh, Roberts and van der Pol oscillators and pendulum responses are investigated. Material behavior as well as additional effects of structural damping on oscillator performance are also considered. Computational protocols are developed and their results are discussed to determine the influence of viscoelastic and structural (Coulomb friction) damping on oscillator motion. Illustrative examples show that the inclusion of linear or nonlinear viscoelastic material properties significantly affects oscillator responses as related to amplitudes, phase shifts and energy loses when compared to equivalent elastic ones.

Original languageEnglish (US)
Pages (from-to)281-298
Number of pages18
JournalNonlinear Dynamics
Issue number2-4
StatePublished - Jun 2004


  • Damping
  • Integral-differential equations
  • Linear and nonlinear viscoelasticity
  • Mathieu
  • Nonlinear deterministic oscillators
  • Numerical analysis
  • Pendulum
  • Rayleigh, Roberts and van der Pol oscillators
  • Structural damping
  • Viscoelastic duffing

ASJC Scopus subject areas

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


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