In this study, the nonlinear forced vibration of simply supported multilayered nanoplates in the framework of the first-order shear deformation of Mindlin plate theory based on the nonlocal strain gradient elasticity theory is investigated. The nonlinear von Karman strain–displacement relation is employed. The interaction of van der Waals forces between adjacent layers of a multilayered nanoplate is considered. The harmonic balance method is used to analyze the nonlinear resonance behavior of a thick nanoplate. The primary resonance and the secondary resonance which consist of superhamonic and subharmonic resonance are investigated. As a main result, by increasing the thickness of a thick nanoplate, the subharmonic resonance disappears and the frequency response curves imply non-resonant behavior, responses with finite amplitudes and different shapes for different thicknesses of thick nanoplates. At the end, the natural frequencies of thick multilayered nanoplates are obtained, and the effect of variation of nonlocal parameter, strain gradient parameter, number of layers and thickness of the nanoplate on the frequency response curves and stable and unstable regions is investigated.

中文翻译：

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基于非局部应变梯度弹性理论的厚多层纳米板的非线性共振行为

本研究在基于非局部应变梯度弹性理论的Mindlin板理论的一阶剪切变形框架内研究了简支多层纳米板的非线性受迫振动。采用非线性 von Karman 应变-位移关系。考虑了多层纳米板相邻层之间范德华力的相互作用。谐波平衡法用于分析厚纳米板的非线性共振行为。研究了由超谐波和次谐波组成的初级共振和次级共振。主要结果是，通过增加厚纳米板的厚度，次谐波共振消失，频率响应曲线暗示非共振行为，对于不同厚度的厚纳米板，具有有限振幅和不同形状的响应。最后，得到了厚多层纳米片的固有频率，研究了非局部参数、应变梯度参数、纳米片层数和厚度的变化对频率响应曲线和稳定区和不稳定区的影响。