SINGULARITIES AND NONLINEAR VIBRATION OF ELASTIC STRAIGHT BARS IN THERMAL FIELD UNDER HARMONIC EXCITATION

The nonlinear vibration equation of the elastic straight bar under thermal expansion and harmonic excitation is obtained by Galerkin principle. The bifurcation equation of the primary resonant of the system is acquired by the method of multiple scales. The primary resonant response curves are analyzed. With the temperature decreasing, amplitudes of response curves increase and the resonant regions shrink. The temperature response curves of the system have two kinds of topological structures. By means of singularity theory the transition variety and bifurcation diagram of the bifurcation equation of the system is acquired.