基于波传播法的周期复合板振动带隙衰减特性研究

Band gap attenuation characteristics of periodic compound plate with wave propagation approach

运用波传播法对有限和无限周期对边简支复合板的振动带隙衰减特性进行了研究.在建立相邻板结构边界连续方程的基础上,分别运用传递矩阵和Bloch定理建立了有限和无限周期复合板的耦合运动方程,并详细对比分析了有限和无限周期复合板带隙衰减特性的关联关系.研究表明:周期板结构的振动带隙频率范围与激励方式和激励位置是相关的,若周期复合板在宽度方向按某阶模态进行线激励,则该激励下的振动带隙与无限周期复合板在该阶模态下的振动带隙是一致的;若周期板在点激励作用,则该点激励下的振动带隙是参与振动的各阶模态振动带隙的交集.此外,还进一步研究了结构阻尼对振动衰减带隙的影响.

The band gap attenuation characteristics of finite and infinite periodic compound plate simply supported along its longitudinal edges are investigated with the wave propagation approach. Base on the boundary continuum condition between two plates, the coupled equations of finite and infinite periodic compound plate are established by transfer matrix and Bloch theorem respectively, and the relations of band gap attenuation characteristics between finite and infinite periodic compound plate are analyzed in detail. It is shown that the frequency band gap of periodic compound plate is related to exciting form and position. The frequency band gap of finite compound plate is coincident with the frequency band gap of infinite compound plate with the same mode vibration if finite compound plate is excited with one mode along its longitudinal edges. If the plate is excited with a point force, the frequency band gap is the intersection of frequency band gap of all participated modes. Besides, the influence of the structural damping on band gap is also analyzed.