Parametric resonances of rotating composite laminated nonlinear cylindrical shells under periodic axial loads and hygrothermal environment

Abstract

This paper focuses on nonlinear parametric resonance behaviors of rotating composite laminated cylindrical shells subjected to periodic axial loads and hygrothermal environment. With effects of the time-varying axial loads, hygrothermal expansion deformation, Coriolis and centrifugal forces as well as the rotation-induced initial hoop tension taken into account, the nonlinear dynamic equations of the shell are obtained on the base of Love’s nonlinear shell theory and Hamilton’s principle. Then, an analytical formulation on the steady state response of the shell is derived by the method of multiple scales, and the stability conditions of trivial and nontrivial solutions are determined by the Routh–Hurwitz criterion. Some numerical results are utilized to conduct detailed parametric studies on vibration characteristics, amplitude–frequency response curves and instability regions of forward and backward travelling waves of the shell. Of particular interest in the process is the combined effect of dynamic axial loads and hygrothermal effects on the resonance behaviors of the rotating nonlinear cylindrical shell.