双激励压电悬臂梁的力电响应分析

Electro-Mechanical Response Analysis of a Piezoelectric Cantilever Beam with Double Excitations

压电能量收集器因其结构简单、能量密度高、不受电磁干扰、能够在较低的频率收集振动能等优点,在机械、电子和航空航天等领域具有良好的应用前景。针对提高压电振动能量收集器发电效率的动力学设计,旨在研究双激励环境下压电悬臂梁的力电响应特性。根据Euler-Bernoulli梁理论、压电材料本构关系以及克希霍夫定律,建立双激励压电悬臂梁的机电耦合动力学模型。在此基础上,应用Galerkin法与模态叠加原理推导压电悬臂梁的力电响应表达式,建立根部应变与输出电压的关系模型。测试不同参数下单/双激励压电悬臂梁的力电响应特性,验证理论推导的合理性。最后,分析相位对双激励下压电悬臂梁输出电压的影响。结果表明:压电悬臂梁在双激励下的应变幅频响应变化规律与电压响应规律基本吻合;双激励下压电悬臂梁的力电响应曲线均呈现先增大,在接近共振频率达到极值时减小的变化趋势;激励幅值的增大导致压电悬臂梁的刚度和共振频率降低,试验测得的压电悬臂梁最大频率降为1.5 Hz;调节2种激励信号的相位,会影响输出电压响应,而且在一个周期内呈先减小后增大的趋势。

Piezoelectric energy harvester has a good application prospect in the fields of mechanical,electronic and aerospace,and so on,because of its advantages of simple structure,high energy density,no electromagnetic interference,and the ability to collect vibration energy at a lower frequency.According to the dynamic design of improving generating efficiency for piezoelectric vibration energy harvester,the purpose is to study the electro-mechanical response characteristics of a piezoelectric cantilever beam under double excitation environments.According to the Euler-Bernoulli beam theory,the piezoelectric constitutive relation and the Kirchhoff’s voltage laws,the electro-mechanical coupling dynamic model of double excited piezoelectric cantilever beam was established.Based on the Galerkin method and the modal superposition principle,the expression of electro-mechanical response of the piezoelectric cantilever beam was derived,and the model of root strain and output voltage was established.The electro-mechanical response characteristics of single or double excited piezoelectric cantilever beams were tested to verify the rationality of the theoretical derivation.Finally,the influence of phase on the output voltage of piezoelectric cantilever beam under double excitation was analyzed.The results show that the trends of strain amplitude frequency response of the piezoelectric cantilever beam under double excitations are consistent with the voltage response;under double excitations,the electro-mechanical amplitude frequency response of piezoelectric cantilever increases first,and decreases after reaching the extreme value at resonance frequency;the increased excitation amplitude decreases the stiffness and resonance frequency of the piezoelectric cantilever beam,and the maximum frequency drops to 1.5 Hz;the phase of the two excitation signals in the double excitations can affect the output voltage,which first decreases and then increases in a cycle.