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为了对主动约束层阻尼结构建立精确完善的数学模型 ,以便进一步进行控制研究 ,采用了两种不同的离散方法 ,用有限元建模 ,并考虑到压电片的机电耦合效应和粘弹性材料的本构关系随温度、频率的变化而变化的特点 ,将有限元法与粘弹性材料的 GHM模型相结合 ,使由于粘弹性材料导致的非线性微分方程转化为一般的二阶定常数性系统 ,从而避免繁琐的迭代求解 ,以便直接求解模态频率、模态阻尼及结构响应。为进一步设计控制器 ,形成闭环控制作准备。算例中两种离散法计算所得的模态频率和模态阻尼吻合较好 ,单位阶跃电压下悬臂梁自由端的横向位移响应曲线相当一致。这表明两种离散法的计算结果是可信的 ,所采用的算法简单、有效、尤其适用于质量轻、柔度大、低频刻集的主动约束层阻尼结构。
In order to establish an accurate and perfect mathematical model for the active constrained layer damping structure for further control research, two different discrete methods are used, which are modeled by the finite element method and taking into account the electromechanical coupling effect of the piezoelectric sheet and the viscoelastic material The constitutive relationship changes with the change of temperature and frequency, and the finite element method is combined with the GHM model of viscoelastic material to transform the nonlinear differential equation caused by viscoelastic material into a general second-order constant system. Thus avoiding tedious iterative solution, in order to directly solve the modal frequency, modal damping and structural response. In order to further design the controller to form a closed-loop control in preparation. In the example, the modal frequencies obtained by the two discrete methods coincide well with the modal damping, and the lateral displacement response curves at the free end of the cantilever beam are quite consistent under the unit step voltage. This shows that the results of the two discrete methods are credible and the proposed algorithm is simple and effective. It is especially suitable for the active constrained layer damping structure with light weight, high flexibility and low frequency.