The objective of the present paper is to comprehensively study the nonlinear frequency response of viscoelastic piezoelectric nanoplates exposed to dual harmonic external excitation and thermo-electro-mechanical loads. To achieve this goal, firstly, a piezoelectric nanoplate resting on a viscoelastic foundation is modeled. Secondly, using the nonlocal piezoelectricity theory, Kelvin–Voigt model, von Karman nonlinear relations and Hamilton’s principle, the nonlinear governing differential equation of motion is derived. In the next step, employing the Galerkin technique and multiple time scales method, the partial differential equation is transformed to an ordinary one and solved. Finally, the modulation equation of viscoelastic piezoelectric nanoplates for combinational excitation is obtained. Emphasizing the effect of dual harmonic excitation and thermo-electro-mechanical loads on nonlinear frequency response of the system, jump and resonance phenomena are discussed. A detailed parametric study is conducted to examine the effect of nonlinearity, damping coefficient, nonlocal parameter, combinational excitation, electric voltage, initial stress and thermal environment.

中文翻译：

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粘弹性压电纳米板在热电机械作用下的双谐非线性激励振动

本文的目的是全面研究粘弹性压电纳米板在二次谐波外部激励和热电机械载荷作用下的非线性频率响应。为了实现该目标，首先，对粘弹性基础上的压电纳米板进行建模。其次，利用非局域压电理论，Kelvin-Voigt模型，von Karman非线性关系和汉密尔顿原理，推导了非线性控制运动微分方程。在下一步中，采用Galerkin技术和多时标方法，将偏微分方程转换为一个常微分方程并求解。最后，获得了用于组合激励的粘弹性压电纳米板的调制方程。着重讨论了双重谐波激励和热电机械负载对系统非线性频率响应的影响，讨论了跳跃和共振现象。进行了详细的参数研究，以检查非线性，阻尼系数，非局部参数，组合激励，电压，初始应力和热环境的影响。