Effects of extreme temperature environments on nonlinear vibrations of the cable-stayed functionally graded beam

A cable-stayed functionally graded beam (CSFGB) model is proposed for the first time to study nonlinear behaviors of the system exposed to extreme temperatures. To this end, the in-plane one-to-one internal resonance between the global mode (FGB's mode) and the local mode (cable's mode) is explored under the condition of external primary resonance. First, governing differential equations of the system considering temperature effects are derived by using Hamilton's principle. To obtain the modal function of the FGB, the in-plane eigenvalue problem is solved through the separation-of-variables method. Subsequently, ordinary differential equations (ODEs) are yielded according to Galerkin discretization. The method of multiple time scales is then applied to deal with the ODEs and derive the modulation equations. Based on the above theoretical solutions, the frequency-/force-response curves at three different temperatures are delineated via Newton-Raphson method and the continuation of fixed points. Meanwhile, the time histories and phase portraits are also provided by directly integrating the ODEs. The results show that temperature changes have a significant influence on nonlinear characteristics of the system.