压电材料迟滞非线性特性的幂函数多项式模型

Power function polynomial model for hysteretic nonlinear characteristics of piezoelectric materials

针对现有迟滞模型多应用于迟滞电学响应分析和控制方面的研究,且较少运用于动力学分析的问题,本文综合考虑压电材料的特性和迟滞曲线特点提出了建立动力学分析的迟滞模型。分别建立幂函数多项式介电迟滞模型和压电迟滞模型,并且通过与实验结果或已有模型对比,表明幂函数多项式介电迟滞模型和压电迟滞模型能准确描述压电材料的迟滞特性。同时分析了迟滞参数η和ζ对饱和极化强度和剩余应变的影响,结果表明:η的变化会影响压电迟滞曲线的形状和剩余应变的大小,当ζ不变、η增大时,饱和极化强度未改变,但剩余应变变小;ζ的变化主要影响最大变形量,当η不变、ζ增大时,产生的最大变形增大,而剩余应变变化很小。该迟滞模型比较简单,为动力学分析提供了便利。

Hysteresis is the essence characteristic of the piezoelectric materials,and it will have effect on piezoelectric response.The existing hysteretic models are frequently applied to analyze hysteretic response of electric and control,but rarely be suitable for dynamics analysis model.On account of piezoelectric properties and hysteresis curve characteristics of piezoelectric materials,a new method for hysteretic model used in dynamics analysis is proposed.Using this method,a power function polynomial dielectric hysteretic model and a piezoelectric hysteretic model are established.Compared with experimental results,the simple models can describe hysteresis characteristics accurately,and the effect of hysteresis parameters on saturated polarization and residual strain are analyzed.The models proposed are useful for establishing dynamic equations of piezoelectric structures.