Computation of Normal Forms for High Dimensional Nonlinear Systems and Application to Nonplanar Motions of a Cantilever Beam

A new and efficient computation of normal forms is developed in this paper for high dimensional nonlinear systems, and the computational method is applied to nonplanar motion of a cantilever beam. The method is based on the adjoint operator method and has the advantage of directly calculating coefficients of normal forms. Moreover, the new method is easy to apply to engineering applications, and the final partial differential equations of various resonant cases appear in a canonical form whose solutions can be conveniently obtained using polynomial equations. With the aid of the Maple software, a symbolic program for computing the normal forms of high dimensional nonlinear systems is developed. Based on the symbolic program, the normal forms and their coefficients of the averaged equations for nonplanar motions of a cantilever beam are calculated for two resonant cases.