基于传递函数方法的约束层阻尼梁动力学分析

DYNAMIC ANALYSIS OF A CONSTRAINED LAYER DAMPING BEAM BY TRANSFER FUNCTION METHOD

主要采用传递函数方法对约束层阻尼梁进行动力学分析。首先应用Ham ilton原理推导出梁的六阶微分方程和边界条件,然后引入状态向量,使用分布参数传递函数方法建立系统的状态空间方程,得到了系统的固有频率、损耗因子和频响曲线。算例的计算结果和相关文献比较,吻合良好,表明该方法的正确性。且传递函数方法计算简捷,无需求解复杂变系数的微分方程组,更适宜分析粘弹性材料力学性能随频率变化的结构动力学问题。

Dynamic problem of a constrained layer damping(CLD) beam is investigated using transfer function method.The six-order differential equation of motion and boundary conditions are derived by using the Hamilton principle.Introducing the state vector,the governing equation in state space is established by using the transfer function method With distributed parameters.The closed-form solutions of natural frequencies,loss factors and frequency response curves of the CLD beam are obtained.The good agreement between the results of numerical examples and those of the related references shows that the transfer function method is effective for structural dynamics problem considering the frequency dependence of viscoelastic material.