基于压电分流阵列的板壳结构带隙特性及其隔振性能研究

Structural vibrations generally exist in aerospace engineering, vehicle engineering, civil engineering, etc. As the elementary components of engineering structures, plates and shells are the major media of vibration generation and transmission. Hence, it is of great significance to study the vibration control of plate and shell structures. Piezoelectric shunting arrays utilize band-gap property of phononic crystals and shunt damping to suppress the propagation of elastic waves of certain frequency regime in the host structure, resulting in the reduction of vibration transmission in structures. At this time, the research on two-dimensional piezoelectric shunting arrays is rather insufficient. The well-established band-gap calculation methods are inadequate to demonstrate the attenuation constant of elastic waves in all directions. Moreover, the investigation of physical mechanisms is not thorough and systematic. As a result, the similarity and difference in locally resonant band gaps formed by resonant shunts and mechanical vibrators, respectively, are not sufficiently disclosed. First and foremost, this project will improve the conventional band-gap calculation methods. Specifically, the nonlinear boundary conditions can be eliminated by parameter substitutions, realizing the evaluation of attenuation constant in any direction and sound description of band gaps. Then, parameter analyses and examination of wave modes will be performed to disclose the band-gap formation mechanisms and summarize the influencing factors. Also, coupling properties of different gaps will be examined. Finally, finite element simulations and experimental investigations are utilized to evaluate the effects of piezoelectric shunting arrays to the vibration transmission of host plates and shells. In addition, the application of piezoelectric shunting arrays in vibration isolation of satellite cabin plates will be explored. The work of this project will provide new idea and means to vibration control of engineering structures.

结构振动广泛存在于航空航天、车辆工程和土木工程等领域。板壳作为工程结构的基本构件，是产生和传递振动的主要载体，研究板壳结构的振动控制具有重要的意义。压电分流阵列可以利用声子晶体带隙特性和分流阻尼抑制基体结构中特定频率范围内弹性波的传播，从而减小结构中的振动传递。目前，二维压电分流阵列的研究还存在诸多不足，已有带隙算法难以描述任意方向弹性波衰减常数，带隙机理研究不够深入，未很好地揭示电路谐振与机械共振形成的局域共振带隙之间的异同点。本项目首先改进传统带隙算法，利用参数代换消除非线性边界条件，实现任意方向衰减常数的计算和带隙描述。然后，利用参数分析和波动模式研究揭示带隙机理，归纳带隙影响因素和规律，并分析带隙耦合特性。最后，利用有限元仿真和实验测试，研究分流阵列对板壳结构振动传递特性的影响，并探索压电分流阵列在卫星舱板隔振中的应用。项目研究将为工程中结构的振动控制提供新的思路和手段。

结构振动广泛存在于航空航天、车辆工程和土木工程等领域。板壳作为工程结构的基本构件，是产生和传递振动的主要载体，研究板壳结构的振动控制具有重要的意义。压电分流阵列可以利用声子晶体带隙特性和分流阻尼抑制基体结构中特定频率范围内弹性波的传播，从而减小结构中的振动传递。目前，二维压电分流阵列的研究还存在诸多不足，已有带隙算法难以描述任意方向弹性波衰减常数，带隙机理研究不够深入，未很好地揭示电路谐振与机械共振形成的局域共振带隙之间的异同点。本项目首先改进传统带隙算法，利用参数代换消除非线性边界条件，实现任意方向衰减常数的计算和带隙描述。然后，利用参数分析和波动模式研究揭示带隙机理，归纳带隙影响因素和规律，并分析带隙耦合特性。最后，利用有限元仿真和实验测试，研究分流阵列对板壳结构振动传递特性的影响，并探索压电分流阵列在卫星舱板隔振和飞行器壁板颤振控制中的应用。研究结果表明：压电分流阵列板壳同时具有布拉格带隙和局域共振带隙，布拉格带隙受到分流的影响较小，而局域共振带隙与分流电路的谐振特性强相关；布拉格带隙具有方向性，而局域共振带隙为完全带隙；电阻上的能量耗散效果可以使局域共振带隙的上下带边都形成较强的阻尼衰减，从而扩展带隙的宽度。但另一方面，谐振电路中的电阻会影响电路的谐振效果，使得带隙内最大衰减变小。分流电阻的大小对带隙位置的影响不明显，而且电阻的作用基本不受方向的影响。项目研究成果为工程结构的振动与噪声控制提供了新的途径与方法。