A Finite Element-based Perturbation Method for Nonlinear Free Vibration Analysis of Composite Cylindrical Shells

In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation and is subsequently converted to a finite element notation. After the determination of the linear natural frequency and corresponding vibration mode, the perturbation approach yields the initial curvature of the amplitude–frequency relation with a modest additional computational cost. The implementation of the perturbation approach in a general purpose finite element code using a laminated curved shell element is described. The effectiveness of the approach is illustrated by application to single-mode and coupled-mode nonlinear vibration analyses of cylindrical shells. Results for isotropic and composite cylindrical shells are presented and compared with results obtained via alternative approaches.