## Graded Nanobeams(分级纳米束)研究综述

Graded Nanobeams 分级纳米束 - In this study a formulation based on the meshless method is developed to study the dynamic behavior of 2D-functionally graded nanobeams.^{[1]}It is found that these variables significantly affect the dynamic behavior of the functionally graded nanobeams, and they could be adjusted to control this behavior.

^{[2]}The size-dependent bending of perfectly/imperfectly bonded multilayered/stepwise functionally graded nanobeams, e.

^{[3]}The dynamics of rotating functionally graded nanobeams are affected by both external kinematic and voltage factors and inherent scale factor and their coupling effects.

^{[4]}The free vibration of rotating functionally graded nanobeams under different boundary conditions is studied based on nonlocal elasticity theory within the framework of Euler-Bernoulli and Timoshenko beam theories.

^{[5]}An integrated nonlinear couple stress-surface energy continuum model is developed to study the nonlinear vibration characteristics of size-dependent functionally graded nanobeams for the first time.

^{[6]}From our knowledge, it is the first time that size-dependent dynamics of graded nanobeams made of anisotropic materials is investigated.

^{[7]}The governing equations of the functionally graded nanobeams with porosities are derived by employing Hamilton\'s principle.

^{[8]}In the current study, the vibration behavior of axially functionally graded nanobeams is investigated in the framework of Eringen's two-phase local-nonlocal model which considers both local and nonlocal phases in modelling nano-scale structures.

^{[9]}

在这项研究中，开发了一种基于无网格方法的公式来研究二维功能梯度纳米束的动态行为。

^{[1]}发现这些变量显着影响功能梯度纳米束的动态行为，并且可以对其进行调整以控制这种行为。

^{[2]}完美/不完美结合的多层/逐步功能梯度纳米束的尺寸依赖性弯曲，例如。

^{[3]}旋转功能梯度纳米束的动力学受外部运动学和电压因子以及固有比例因子及其耦合效应的影响。

^{[4]}在Euler-Bernoulli和Timoshenko梁理论的框架内，基于非局部弹性理论研究了旋转功能梯度纳米梁在不同边界条件下的自由振动。

^{[5]}首次开发了集成的非线性耦合应力-表面能连续体模型来研究尺寸相关的功能梯度纳米梁的非线性振动特性。

^{[6]}据我们所知，这是第一次研究由各向异性材料制成的分级纳米束的尺寸相关动力学。

^{[7]}利用Hamilton原理推导出具有孔隙度的功能梯度纳米束的控制方程。

^{[8]}在目前的研究中，轴向功能梯度纳米梁的振动行为在 Eringen 的两相局部-非局部模型的框架内进行了研究，该模型在建模纳米级结构时考虑了局部和非局部相。

^{[9]}

## Functionally Graded Nanobeams 功能梯度纳米束

In this study a formulation based on the meshless method is developed to study the dynamic behavior of 2D-functionally graded nanobeams.^{[1]}It is found that these variables significantly affect the dynamic behavior of the functionally graded nanobeams, and they could be adjusted to control this behavior.

^{[2]}The size-dependent bending of perfectly/imperfectly bonded multilayered/stepwise functionally graded nanobeams, e.

^{[3]}The dynamics of rotating functionally graded nanobeams are affected by both external kinematic and voltage factors and inherent scale factor and their coupling effects.

^{[4]}The free vibration of rotating functionally graded nanobeams under different boundary conditions is studied based on nonlocal elasticity theory within the framework of Euler-Bernoulli and Timoshenko beam theories.

^{[5]}An integrated nonlinear couple stress-surface energy continuum model is developed to study the nonlinear vibration characteristics of size-dependent functionally graded nanobeams for the first time.

^{[6]}The governing equations of the functionally graded nanobeams with porosities are derived by employing Hamilton\'s principle.

^{[7]}In the current study, the vibration behavior of axially functionally graded nanobeams is investigated in the framework of Eringen's two-phase local-nonlocal model which considers both local and nonlocal phases in modelling nano-scale structures.

^{[8]}

在这项研究中，开发了一种基于无网格方法的公式来研究二维功能梯度纳米束的动态行为。

^{[1]}发现这些变量显着影响功能梯度纳米束的动态行为，并且可以对其进行调整以控制这种行为。

^{[2]}完美/不完美结合的多层/逐步功能梯度纳米束的尺寸依赖性弯曲，例如。

^{[3]}旋转功能梯度纳米束的动力学受外部运动学和电压因子以及固有比例因子及其耦合效应的影响。

^{[4]}在Euler-Bernoulli和Timoshenko梁理论的框架内，基于非局部弹性理论研究了旋转功能梯度纳米梁在不同边界条件下的自由振动。

^{[5]}首次开发了集成的非线性耦合应力-表面能连续体模型来研究尺寸相关的功能梯度纳米梁的非线性振动特性。

^{[6]}利用Hamilton原理推导出具有孔隙度的功能梯度纳米束的控制方程。

^{[7]}在目前的研究中，轴向功能梯度纳米梁的振动行为在 Eringen 的两相局部-非局部模型的框架内进行了研究，该模型在建模纳米级结构时考虑了局部和非局部相。

^{[8]}