A FINITE ELEMENT BASED PERTURBATION METHOD FOR NONLINEAR FREE VIBRATION OF COMPOSITE CYLINDRICAL SHELLS

In this paper a finite element based perturbation approach for nonlinear vibrations is presented that is applicable to shell structures with an arbitrary geometry. The approach is based on a perturbation method to approximate the frequency-amplitude relation in the nonlinear vibration analysis of general structures with an arbitrary geometry. 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 frequency-amplitude relation with a modest additional computational cost. The perturbation approach has been implemented in a general purpose finite element code and applied in the finite element analysis of the nonlinear vibration behavior of composite cylindrical shells using a curved shell element. The finite element implementation of the approach for composite shells is described. Results for composite cylindrical shells are presented and compared with results obtained via semi-analytical methods published earlier by the second author.