基于有限元法的周期压电智能梁滤波特性分析

周期结构具有通频和禁频特性,使其在动态载荷的滤波器、具有主动控制功能的结构研究中得到了重要应用。基于Timoshenko梁理论,考虑基梁和压电片的转动惯量和剪切效应,采用有限元法和传递矩阵法推导了波在周期性地粘贴压电片的Timoshenko梁中的传播模型,分析了几何尺寸和材料特性对其频带性质的影响,并与Bernoulli-Euler梁理论得到的结果进行了对比。研究表明,当基梁与压电层厚度比达到40时,禁带带宽减小了54%,因此对于周期结构中的深梁,应舍弃Bernoulli-Euler梁理论而采用Timoshenko梁理论建立的模型;对于不同尺寸和材料特性的压电周期结构,频带性质会有很大不同,可以通过调整结构的参数来改变其频带性质,从而改变波动在结构中的传播特性。

Study on filtering characteristics of a periodic piezoelectric beam by the finite element method

Periodic structures exhibit special dynamical characteristics of passbands and stopbands that enable one to design filters and control the propagation of waves and vibration with particular frequencies through the structures. The finite element and transfer matrix methods are combined to develop a model of wave propagation in a beam bonded with periodical piezoelectric patches using Timoshenko beams theory considering the effect of shear deformation and rotary inertia. The effects of geometric dimensions and material parameters on the wave propagation characteristics of the periodic structure are analyzed and compared with some results from Bernonlli-Euler beam theory. Research indicates that when the thickness ratio of base beam layer and piezoelectric layer reaches 40, the width of a stop band is reduced by 54%, so it is necessary to use the model based on Timoshenko theory rather than Bernonlli-Euler theory when the thickness of base layer is large and shear and rotational inertia become more important. For different configurations of the periodic piezoelectric beam, the frequency bands are very different. The characteristics of frequency bands and wave propagation in the structure can be altered by tuning different structural parameters. The investigation provides the basic guidelines to design periodic piezoelectric structures to achieve desired filtering characteristics.