Reduced-Order Nonlinear Modal Equations of Circular Cylindrical Shells Based on the Finite-Element Method

This paper presents a procedure to derive reduced-order nonlinear modal equations of circular cylindrical shells. Modal analysis is applied to the nonlinear finite element equation by using base vectors obtained by the finite element analysis. Reduced-order modal equations are derived by transforming the equations of motion from the physical coordinates to the modal coordinates. Base vectors for the transformation consist of dominant linear eigenmodes and nonlinear displacement vectors derived approximately from the nonlinear finite element equation. Asymmetry of the deformation of the circular cylindrical shell with respect to its neutral surface is taken into consideration to determine the base vectors. Numerical results show good agreement with those presented in other papers.