The thermo-electro-mechanical coupling vibrations of axially moving piezoelectric nanoplates are examined based on the nonlocal theory and Kirchhoff piezoelectric thin plate model.The governing differential equations of axially moving piezoelectric nanoplates subjected to biaxial forces,external electric voltage and temperature variation are derived by employing Hamilton's principle.Natural frequencies are determined numerically using Galerkin method.Subsequently,the effects of the smallscale parameters,biaxial forces,external electric voltage and temperature variation on the thermo-electro-mechanical vibration responses including their natural frequencies and sub-critical regions are discussed in detail.It is shown that the existence of biaxial compressive force,positive electric voltage,increasing temperature and small-scale parameters contributes to reduce the equivalent stiffness and further decrease the natural frequencies and sub-critical regions of axially moving piezoelectric nanoplates.However,the biaxial tensile forces,negative electric voltage,decreasing temperature result in stiffness strengthening effect on nanostructures.%基于非局部理论结合基尔霍夫压电薄板模型,研究了轴向运动压电纳米板的热-力-电耦合振动响应.考虑压电纳米板受到双向轴力、外部电压和温度变化等作用并做轴向运动,应用哈密顿原理推导了系统的控制方程组,利用伽辽金法数值求解轴向运动压电纳米板横向振动固有频率,进一步讨论小尺度参数、轴力、外部电压以及温度变化等因素对固有频率及亚临界区域的影响.结果表明:双轴压力、外部正电压、温度升高以及小尺度参数的存在使得压电纳米板的等效刚度降低,从而导致固有频率和亚临界区域的减小,而双轴拉力、外部负电压、温度降低则引起纳米结构等效刚度提高.
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