考虑连接非线性的复合材料组合梁动力学分析与振动控制
Dynamic Analysis and Vibration Control of Composite Assembled Beams Considering Connection Nonlinearity
摘要: 针对传统组合梁模型在处理连接处时忽略非线性的问题，本文提出采用一组立方非线性弹簧对连接处的非线性力学现象进行模拟，以有效表征连接界面复杂的非线性刚度效应，使模型更接近组合梁的真实装配状态。基于欧拉–伯努利(Euler-Bernoulli)梁理论构建了固定边界条件下的组合梁非线性动力学模型，应用瑞利–里茨(Rayleigh-Ritz)法求解系统固有频率，分析了线性连接弹簧对系统固有频率的影响。随后采用谐波平衡法(HBM)与龙格库塔(Runge-Kutta)法分别求解系统的非线性稳态幅频响应并进行对比验证。进一步，引入一种镍钛合金钢丝绳(NiTi-ST)减振技术，探究其非线性刚度与迟滞阻尼对含有非线性连接的复合材料组合梁系统的减振效果。研究表明：连接处立方非线性刚度会导致组合梁系统幅频响应曲线峰值向高频偏移，呈现出典型的非线性硬特性。镍钛合金钢丝绳可以大幅削减共振峰值，实现良好的减振效果。
Abstract: To address the neglect of joint nonlinearity in traditional assembled beam models, this thesis proposes using cubic nonlinear springs to simulate the complex nonlinear stiffness effects at connection interfaces, closely representing the true assembly state. Based on Euler-Bernoulli beam theory, a nonlinear dynamic model under fixed boundaries is constructed. The Rayleigh-Ritz method is applied to solve natural frequencies and analyze the impact of linear connection springs. Subsequently, the harmonic balance method (HBM) and Runge-Kutta method are employed to solve and cross-verify the nonlinear steady-state amplitude-frequency responses. Furthermore, a Nickel-Titanium alloy wire rope (NiTi-ST) is introduced to investigate the vibration suppression effects of its nonlinear stiffness and hysteretic damping on the composite assembled beam. Results indicate that the cubic nonlinear stiffness at the connections causes the amplitude-frequency response peaks to shift to higher frequencies, exhibiting typical nonlinear hardening characteristics. NiTi-ST can significantly reduce resonance peaks, achieving excellent vibration suppression.
文章引用：顾秀伦, 张振. 考虑连接非线性的复合材料组合梁动力学分析与振动控制[J]. 声学与振动, 2026, 14(2): 102-116. https://doi.org/10.12677/ojav.2026.142009

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