In this study, size-dependent nonlinear forced vibration of viscoelastic/flexoelectric nanobeams has been investigated. By calculating enthalpy and kinetic energy and using Hamilton’s principle, the coupled governing equations of viscoelastic/flexoelectric nanobeams are derived along with dependent electrical and mechanical boundary conditions. Furthermore, to take the effects of the small scale into account, the nonclassical theory of continuous medium has been used and the Euler–Bernoulli beam model has been adopted to model the nanobeams. Finally, the governing equations are solved using numerical methods for distributed loaded and clamped–clamped boundary conditions. By comparing the results, it is determined that the parameters of the size effect and the viscoelastic medium effect can increase the vibrational frequency of the nanobeams. Also, the results show that the frequency of nanobeams outside of the viscoelastic medium strongly depends on the size-dependent parameters, and the increase in the length and thickness of the nanobeam decreases the frequency. The results also show that with the increasing flexoelectric effect, the amplitude of the nonlinear oscillation increases.

在这项研究中，已经研究了粘弹性/柔性电纳米束的尺寸相关的非线性强迫振动。通过计算焓和动能并利用汉密尔顿原理，推导出粘弹性/柔电纳米束的耦合控制方程以及相关的电气和机械边界条件。此外，为了考虑到小规模的影响，使用了非经典的连续介质理论，并采用了Euler–Bernoulli光束模型对纳米束进行建模。最后，使用数值方法对分布的载荷和夹紧-夹紧边界条件求解控制方程。通过比较结果，确定尺寸效应和粘弹性介质效应的参数可以增加纳米束的振动频率。也，结果表明，粘弹性介质之外的纳米束的频率强烈依赖于尺寸相关的参数，纳米束的长度和厚度的增加会降低频率。结果还表明，随着柔电效应的增加，非线性振荡的幅度增大。