中文摘要：

通过在加筋板结构上附加周期性排列的＂弹簧-质量＂共振子单元,构造了一种局域共振型加筋板结构.针对这种新型结构,基于有限元法和周期结构Bloch定理,建立了其弹性波传播与振动特性理论计算方法;采用该方法深入研究了局域共振型加筋板的弯曲波带隙特性和减振特性.研究表明,局域共振子能够对加筋板的弯曲波传播特性产生显著影响,一方面使其产生更加低频的带隙,另一方面还能拓宽其中高频带隙.进一步深入分析了共振子的弹簧刚度、共振子的质量对带隙特性和减振特性的影响,发现了有价值的带隙调控现象、规律和减振特性,可为局域共振型加筋板的带隙特性设计与工程减振应用提供理论指导和有益参考.

英文摘要：

A locally resonant stiffened plate is constructed by attaching a two-dimensional periodic array of spring-mass resonators to a traditional periodic stiffened plate. A method based on the finite element method and Bloch theorem is presented for calculating the flexural wave dispersion relation and forced vibration response of the proposed locally resonant stiffened plate. The method is validated by comparing the predictions with simulations by FEM software COMSOL. The effects of the spring-stiffness and mass ratio of local resonators on the flexural wave band gap and vibration reduction performance are analysed, which can facilitate the design of the locally resonant stiffened plate for vibration-reduction applications in engineering. The main findings of this work are as follows.1） The local resonator can have a significant effect on the propagation of flexural wave in stiffened plate. On the one hand, the local resonator is able to create a low-frequency local resonance band gap; on the other hand, it can enhance the high-frequency Bragg band gap. Within the band gap frequency range, the vibration of the locally resonant stiffened plate can be reduced remarkably.2） The spring-stiffness of local resonators shows a notable influence on the band gap and vibration reduction performance of the locally resonant stiffened plate. As the spring-stiffness gradually increases, the nature frequency of local resonator is gradually tuned to higher frequency, and the phenomenon of band-gap transition and band-gap near-coupling may arise. Under the near-coupling condition, the pass band between two band gaps turns narrow, and it seems that these two band gaps form a super-wide pseudo-gap（within which only a very narrow pass band exists）.This behaviour is of great interest for the broad band vibration reduction applications. Moreover, the complete band gap will disappear if the nature frequency of local resonator is tuned to a higher value than a threshold frequency, which is dependent on the geometrical and material par