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由薄板的基本方程出发,考虑粘弹性层与基板、约束层间的法向和切向相互作用力的影响,导出部分带状覆盖被动约束层阻尼(Passive Constrained Layer Damping,PCLD)板在两端简支另两端任意边界情况下的一阶常微分矩阵方程,方程的状态向量由4个独立的位移变量和内力变量组成,可方便地应用于位移和应力边界条件。同时,利用精细积分法和传递矩阵原理求解特征方程,计算了多种情况下PCLD板的固有频率和损耗因子。通过与参考文献结果相比,验证了本文方法的正确性。最后,分析了覆盖位置和覆盖率对结构减振特性的影响。
Considering the influence of the interaction between the viscoelastic layer and the substrate and the normal and tangential directions of the constraining layers, the strip-shaped passive passive layer damping (Passive Constrained Layer Damping, PCLD) The first-order ordinary differential matrix equation under the arbitrary boundary of two ends of simple support is composed of four independent displacement and internal force variables, which can be easily applied to the displacement and stress boundary conditions. At the same time, the eigenvalue equation is solved by the principle of precise integration and transfer matrix, and the natural frequency and dissipation factor of PCLD board are calculated under various conditions. Compared with the reference results, the correctness of the method in this paper is verified. Finally, the influence of the covering position and coverage on the vibration characteristics of the structure is analyzed.