Improved Galerkin method for computing nonlinear normal modes
LI Cheng1,LI Hongguang2
1.Shanghai Institute of Satellite Engineering, Shanghai 201109, China;
2.State Key Laboratory of Mechanical System and Vibration, Shanghai JiaoTong University, Shanghai 200240, China
Abstract:An improved Galerkin method is proposed to solve the nonlinear normal mode of the nonlinear system under the definition of invariant manifold. On the basis of two existing Galerkin methods for the nonlinear normal mode solution, this method introduces the finite element form of shape functions into the solution expansions, and applies a corresponding strategy for the approximation of the specific sparse Jacobian matrix to accelerate the calculation of the expansion coefficients. A nonlinear two-stage vibration isolator is considered. Its nonlinear normal mode corresponding to the primary resonance is solved, and the solutions obtained by these three methods are compared. The proposed method can yield more accurate solutions in large domains. Then this method is integrated with the existing Galerkin method, and the calculation is further accelerated to obtain an accurate solution.
Key words: nonlinear normal mode; invariant manifold; Galerkin method; sparse Jacobian matrix
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