In this article, a first-order shear deformable model is expanded based on the nonlocal strain gradient theory to vibration analysis of smart nanostructures under different boundary conditions. The governing equations of motion of rotating magneto-viscoelastic functionally graded cylindrical nanoshell in the magnetic field and corresponding boundary conditions are obtained using Hamilton’s principle. To discretize the equations of motion, the generalized differential quadrature method is applied. The aim of this work is to investigate the effects of the temperature changes, nonlocal parameter, material length scale, viscoelastic coefficient, various boundary conditions, and the rotational speed of this smart structure on natural frequencies of rotating cylindrical nanoshell made of magneto-viscoelastic functionally graded material.

中文翻译：

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磁驱动粘弹性功能梯度纳米壳旋转热机械特性的非局部应变梯度理论

在本文中，基于非局部应变梯度理论将一阶剪切变形模型扩展到智能纳米结构在不同边界条件下的振动分析。利用Hamilton原理获得了旋转磁粘弹性功能梯度圆柱形纳米壳在磁场中的运动控制方程和相应的边界条件。为了离散化运动方程，应用了广义微分正交方法。这项工作的目的是研究温度变化、非局部参数、材料长度尺度、粘弹性系数、各种边界条件和这种智能结构的旋转速度对由磁粘弹性功能制成的旋转圆柱形纳米壳的固有频率的影响。分级材料。