利用谐波平衡法计算局部非线性动力系统的稳态响应

Calculation of the steady state response of locally nonlinear dynamic systems by harmonic balance method

利用谐波平衡法研究了局部非线性系统在周期激励下的稳态响应问题。通过对系统的响应和非线性内力进行谐波分解将问题归结为一组非线性代数方程组。针对系统具有局部非线性的特点，对相应线性子结构的自由度进行减缩处理。采用Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ迭代方法求解仅含非线性自由度的代数方程组。最后对算例进行计算，所得结果合理可靠。

? In this paper, the harmonic balance method has been developed for calculating the steady state response of locally nonlinear dynamic systems under periodic excitation. By resolving the response and nonlinear force into Fourier series, a set of nonlinear equations is obtained. Since the nonlinear behavior of the systems is localized, the unknowns related to linear substructure can be significantly reduced. The Newton Raphson algorithm is employed to solve resulting nonlinear equations in which only unknowns of linear substructure are related. Finally, a numerical example in reference is used to illustrate the effectiveness of the method. 