Abstract

Nonlinear dynamic analysis of the assembled structures involves the complex nonlinearity of the joint interfaces. By combining the multi-harmonic balance method with the Newton–Raphson iteration process, a high-efficiency nonlinear dynamic analysis method is proposed to analyze the steady-state dynamic responses influenced by the hysteresis nonlinearity of the joint interfaces. The proposed method adopts a gradient vector based on the chain derivation of the continuous function to iterate the steady-state dynamic responses instead of the Jacobian matrix in each iteration process, and a 2-order interpolation function is chosen to compensate the continuity of the discrete harmonic coefficients. The proposed method is verified by a comparison with the Jacobian matrix-based Newton iteration method and the direct numerical integration by using a single degree-of-freedom (DOF) system, and the effects of the excitation amplitudes are also investigated. Based on the generalized mode superposition method, the complex lap-type bolted joint beam structure is reduced into a series of single DOF oscillators with coupling nonlinear dynamic behaviors of the joint interfaces. The proposed method is applied to calculate the frequency response function (FRF) and verified by a comparison with the prediction of the Jacobian matrix-based iteration method. The results show that the solutions of the proposed method agree well with the results predicted by the direct numerical integration and Jacobian matrix-based iteration in literature. Larger excitation amplitude will induce the loss of the joint stiffness and degrade the nonlinearity effects. The predicted FRFs of the bolted joint beam system agree well with the results iterated by the Jacobian matrix-based method, and indicate a better convergence performance and a higher efficiency with much less computational cost.

中文翻译：

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牛顿-拉夫森迭代过程的联合接口高效非线性动力学分析

摘要

组装结构的非线性动力学分析涉及关节界面的复杂非线性。通过将多重谐波平衡法与牛顿-拉夫逊迭代法相结合，提出了一种高效的非线性动力学分析方法，以分析受关节界面滞后非线性影响的稳态动态响应。所提出的方法采用基于连续函数链式推导的梯度向量迭代稳态动态响应，而不是在每个迭代过程中迭代雅可比矩阵，并选择了二阶插值函数来补偿离散量的连续性。谐波系数。通过与基于雅可比矩阵的牛顿迭代法进行比较，并通过使用单自由度（DOF）系统进行直接数值积分，验证了该方法的有效性，并研究了激励幅度的影响。基于广义模叠加法，将复杂的搭接式螺栓连接梁结构简化为一系列具有耦合界面非线性动力学行为的单自由度振子。将该方法应用于频率响应函数（FRF）的计算，并与基于雅可比矩阵的迭代方法的预测结果进行了比较。结果表明，该方法的求解结果与文献中直接数值积分和基于雅可比矩阵迭代的预测结果吻合良好。较大的激励幅度将引起接头刚度的损失并降低非线性效应。螺栓连接梁系统的预测FRF与基于Jacobian矩阵方法的迭代结果非常吻合，并显示出更好的收敛性能和更高的效率，而计算成本却更低。