A finite element analysis on random vibration of nonlinear shell structures

The objective of this investigation is to study the random vibration of a nonlinear geometrically shell structure by using the finite element method in conjunction with the equivalent linearization approach. When the shell structure is subjected to excessive loadings, the large deformations of the shell structure must be considered. In that sense, the stiffness of the governing equation of the shell structure is related to deflection; therefore, it is nonlinear and difficult to solve. In this study, the applied loadings to the shell structure are assumed to be a nonstationary random excitation to characterize many physical loadings such as earthquake, wind, aerodynamic and acoustic loadings. The equivalent linearization and the finite element method are adopted to perform the nonlinear random vibration analysis of the shell structures, which can be quite nonuniform and complex in geometry or nonhomogeneous in material. These obtained statistical dynamics responses are very useful for estimating the structure safety and reliability. Meanwhile, some statistical responses obtained by the present approach are checked by the Monte Carlo simulation technique.