Non-linear dynamics of a shallow arch under periodic excitation -II. 1:1 internal resonance

Win Min Tien, N. Sri Namachchivaya, Naresh Malhotra

Research output: Contribution to journalArticlepeer-review


In this paper the work presented in Tien et al. [Int. J. Non-Linear Mech. 29, 349-366 (1994)] is extended to study the dynamics of a shallow arch subjected to harmonic excitation in the presence of both external and 1:1 internal resonance. The method of averaging is used to yield a set of autonomous equations of the second-order approximations to the response of the system. The averaged equations are numerically examined to study the bifurcation behavior of the shallow arch system. In order to study the system with resonant fixed points, a new global perturbation technique developed by Kovacic and Wiggins [Physica D57, 185-225 (1992)] is used. This technique provides analytical results for the critical parameter values at which the dynamical system, through the Silnikov's type of homoclinic orbits, possesses a Smale horseshoe type of chaos.

Original languageEnglish (US)
Pages (from-to)367-386
Number of pages20
JournalInternational Journal of Non-Linear Mechanics
Issue number3
StatePublished - May 1994

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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