基于加速动态拉格朗日法的摩擦片阻尼分析

提出了一种可用于增强薄壁结构阻尼的波纹形片状干摩擦阻尼器，并利用一种改进的非线性动力学计算方法对其稳态响应特性进行了分析。首先通过两重减缩使非线性系统自由度变成接触节点间相对位移的形式从而降低矩阵规模，在高阶谐波平衡法的基础上引入了速度型动态拉格朗日法，并通过提供解析形式的雅克比矩阵来提高计算效率与数值稳定性，从而构成了用于预测非线性系统强迫响应的算法。在一个集中参数模型上用切向/法向刚度法与时域推进法这两种主流非线性计算方法对本文算法的合理性进行了验证。利用该算法对带有波纹形阻尼器的薄壁板结构进行分析，结果表明，摩擦片对薄壁板有很好的振动抑制作用，在质量仅占主体结构0.6%的情况下，能够使共振峰值下降75.4%。该算法表现出较高的计算效率，减缩模型使用和解析雅克比矩阵的引入使CPU时间减小到原来的0.5%以下。

Damping performance analysis of friction patches using an accelerated dynamic Lagrange method

Dry friction patches with a corrugated shape is designed and analyzed using an accelerated numerical method for steady-state response of nonlinear structural systems. In order to reduce the scale of the DOFs, a double-reduction scheme is introduced and the nonlinear equations of motion is rewritten as a relative displacement form, The steady-state response is predicted by the multi-harmonic balance method combined with a velocity-based dynamic Lagrange method. The efficiency and stability of the algorithm are improved by the closed-form Jacobian matrix. The accuracy of this method is verified against the elastic frequency-time technique and the time-marching procedure based on a lumped parameter model. A good vibration attenuation of the dry friction damper on the thin-walled structures is observed by the simulation. The results show that with added mass equals to only 0.6% of the host structure, the resonant amplitude can be reduced by 75.4%. The computational efficiency can be improved significantly using the proposed method, where the CPU time can be reduced to less than 0.5% of the original approach.