NONLINEAR DYNAMICS OF A SHALLOW ARCH UNDER PERIODIC EXCITATION .2. 1 1 INTERNAL RESONANCE/

In this paper the work presented in Tien et al. [Int. J. Non-Linear Me ch. 29, 349-366 (1994)] is extended to study the dynamics of a shallow arch subjected to harmonic excitation in the presence of both externa l and 1:1 internal resonance. The method of averaging is used to yield a set of autonomous equations of the second-order approximations to t he response of the system. The averaged equations are numerically exam ined to study the bifurcation behavior of the shallow arch system. In order to study the system with resonant fixed points, a new global per turbation technique developed by Kovacic and Wiggins [Physica D 57,185 -225 (1992)] is used. This technique provides analytical results for t he critical parameter values at which the dynamical system, through th e Silnikov's type of homoclinic orbits, possesses a Smale horseshoe ty pe of chaos.