局部覆盖约束层阻尼梁动力学问题的解析解

采用传递函数方法对局部覆盖约束层阻尼梁进行了动力学分析。由Hamilton原理导出了约束层阻尼梁的运动方程和边界条件,经Laplace变换后引入状态向量建立了系统的状态空间方程,由边界条件和连接条件共同构成的定解条件,利用传递函数方法求解方程得到了系统的固有频率、损耗因子和频响曲线。算例计算结果与相关文献或NAS-TRAN计算结果吻合良好,验证了传递函数方法的有效性和精确性,且本文方法更适合于阻尼层粘弹性材料采用随频率变化的复模量模型的情况。同时还讨论了约束层阻尼的位置和覆盖率对系统固有频率和损耗因子的影响,为今后的优化研究奠定了基础。

Analytical Solution for A Beam with Partially Covered Constrained Layer Damping

The dynamic problem of a beam with partially covered constrained layer damping is investigated using the transfer function method.Its equations of motion and boundary conditions are derived by using Hamilton principle.After Laplace transformation,the state vector is introduced and the governing equation is established in state space.The boundary conditions and connect conditions form the conditions to determine a solution.By the distributed parameter transfer function method,the closed-form solutions of the natural frequencies,loss factors and curves of frequency response of the system are obtained.Numerical predictionresults agree very well with the results of the related literatures or those with NASTRAN,they show the effectiveness and accuracy of the transfer function method.Furthermore,the effect of the CLD location and the percent age of the CLD coverage is discussed.All the results will lay a foundation for the future optimization study.