Abstract A numerical approach is used herein to study the primary resonant dynamics of functionally graded (FG) cylindrical nanoscale panels taking the strain gradient effects into consideration. The basic relations of the paper are written based upon Mindlin’s strain gradient theory (SGT) and three-dimensional (3D) elasticity. Since the formulation is developed using Mindlin’s SGT, it is possible to reduce it to simpler size-dependent theories including modified forms of couple stress and strain gradient theories (MCST & MSGT). The governing equations is derived and directly discretized via the variational differential quadrature technique. Then, a numerical solution technique is employed to study the nonlinear resonance response of nanopanels with various edge conditions under a harmonic load. The impacts of length scale parameter, material and geometrical parameters on the frequency–response curves of nanopanels are investigated. In addition, comparisons are provided between the predictions of MSGT, MCST and the classical elasticity theory.

中文翻译：

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基于 Mindlin 应变梯度理论和 3D 弹性的 FG 圆柱形纳米板非线性受迫振动分析

摘要 本文采用数值方法研究功能梯度 (FG) 圆柱形纳米面板的初级共振动力学，同时考虑了应变梯度效应。论文的基本关系是根据 Mindlin 的应变梯度理论 (SGT) 和三维 (3D) 弹性编写的。由于该公式是使用 Mindlin 的 SGT 开发的，因此可以将其简化为更简单的尺寸相关理论，包括修正形式的应力应变梯度理论 (MCST & MSGT)。控制方程是通过变分微分正交技术导出并直接离散化的。然后，采用数值求解技术研究谐波载荷下具有各种边缘条件的纳米板的非线性共振响应。长度尺度参数的影响，研究了纳米板频率响应曲线上的材料和几何参数。此外，还提供了 MSGT、MCST 和经典弹性理论的预测之间的比较。