The Vibration of Piezoelectric Viscoelastic Nanobeam

压电材料因其具有独特的力电耦合特性而受到研究者的关注。当材料发生变形时可能表现出既有粘性又有弹性的特性，分数阶微积分理论可以很好地刻画材料所具备的这种特性。本文考虑了非局部弹性理论，利用Hamilton原理推导了粘弹性压电纳米材料的分数阶控制方程，采用Galerkin方法和预估校正法求解控制方程，讨论了外加电压、非局部参数、分数阶等参数对粘弹性压电纳米梁的影响。结果表明：分数阶对粘弹性材料产生影响；系统阻尼随着分数阶的增加而增加。此外，非局部因子和压电场对其非线性振动行为有显著影响。Piezoelectric materials have attracted the attention of researchers because of their unique electromechanical coupling characteristics. When the material is deformed, it may show both viscous and elastic characteristics, and the fractional calculus theory can well describe the characteristics of the material. In this paper, considering the theory of non-local elasticity, the fractional governing equations of viscoelastic piezoelectric nanomaterials are derived from Hamilton’s principle. The Galerkin method and the predictive correction method are used to solve the governing equations. The effects of applied voltage, non-local parameters, fractional order and other parameters on the viscoelastic piezoelectric nanobeams are discussed. The results show that the fractional order affects viscoelastic materials. The damping of the system increases as the fractional order increases. In addition, non-local factors and piezoelectric fields have a significant effect on the nonlinear vibration behavior.