摘要
提出了一种改进的Galerkin方法以计算非线性系统的非线性模态在不变流形定义下的解曲面。在已有的两种非线性模态Galerkin解法的基础上,该方法在假设函数中引入了有限元形式的展开式,并利用该问题中特定的Jacobian矩阵的稀疏性加速待求系数的非线性代数方程组的求解。以一种非线性双级隔振器为例,采用了这3种方法计算其主共振对应的非线性模态,并将解进行了比较。该方法在求解域较大时,仍能获得较为准确的解。该方法进一步与已有的Galerkin法进行了综合,在保证求解精度的基础上加速了计算。
An improved Galerkin method was 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,the 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 was taken as an example.Its nonlinear normal mode corresponding to the primary resonance was solved,and the solutions obtained by these three Galerkin methods were compared.The proposed method can yield more accurate solutions in large domains.Further,the method was integrated with the existing Galerkin method,and makes the calculation further accelerate to obtain an accurate solution.
作者
李诚
李鸿光
LI Cheng;LI Hongguang(Shanghai Institute of Satellite Engineering,Shanghai 201109,China;State Key Laboratory of Mechanical System and Vibration,Shanghai JiaoTong University,Shanghai 200240,China)
出处
《振动与冲击》
EI
CSCD
北大核心
2022年第18期157-165,183,共10页
Journal of Vibration and Shock
基金
国家自然科学基金(11972222)。
