PIEZO–BEAM SYSTEMS SUBJECTED TO WEAK ELECTRIC FIELD: EXPERIMENTS AND MODELLING OF NON-LINEARITIES
PIEZO–BEAM SYSTEMS SUBJECTED TO WEAK ELECTRIC FIELD: EXPERIMENTS AND MODELLING OF NON-LINEARITIES
复制标题
弱电场下的压电梁系统：非线性实验和建模
DOI：
10.1006/jsvi.2002.5024
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发表时间：
2002
影响因子：
4.7
通讯作者：
P. Hagedorn
中科院分区：
文献类型：
--
作者：
U. Wagner;P. Hagedorn
在用压电陶瓷和在弱电场作用下共振的压电光束系统的实验中，观察到典型的非线性效应，如共振频率与振幅的依赖关系、光谱中的超谐波以及激励电压与振动振幅的非线性关系。这些非线性效应可以在压电31和33效应中观察到。与众所周知的压电陶瓷在强电场作用下的非线性效应相反，我们的发现尚未在文献中详细描述。在本文中，这些现象的第一个描述是通过制定非线性本构关系，特别是通过引入一个非恒定的杨氏模量E c和压电系数d31在压电梁系统的情况下给出。利用哈密顿原理，用里兹方法导出了所考虑系统的运动方程。确定了非线性参数，并将数值结果与实验结果进行了比较。用有限元模型对里兹法的结果进行了验证。当结构通过压电元件在谐振频率附近被激发时，本文所述的效应可能会产生重大影响。
Abstract Typical non-linear effects, e.g., dependence of the resonance frequency on the amplitude, superharmonics in spectra and a non-linear relationship between excitation voltage and vibration amplitude are observed in experiments with piezoceramics and in piezo–beam systems excited at resonance by weak electric fields. These non-linear effects can be observed for both the piezoelectric 31 and the 33-effect. In contrast to the well-known non-linear effects for piezo-ceramics in the presence of strong electric fields, our findings have not been described yet in detail in the literature. In this paper, a first description of these phenomena is given by formulating non-linear constitutive relations, in particular by introducing a non-constant Young's modulus E c and piezo electric factor d 31 in the case of a piezo–beam system. The equations of motion for the system under consideration are derived via the Ritz method using Hamilton’s principle. The “non-linear” parameters are determined and the numerical results are compared to those obtained experimentally. A finite element model is used for verification of the results obtained by the Ritz method. The effects described herein may have a significant influence whenever structures are excited close to resonance frequencies via piezoelectric elements.