Addressed in this article, as the first attempt, is the forced coupled nonlinear mechanics of functionally graded (FG) nanobeams subject to dynamic loads via developing a high-dimensional model. A geometric nonlinear Euler-Bernoulli theory is used to define the displacement distribution. To incorporate small-size influences a nonlocal strain gradient theory (NSGT) scheme, possessing two independent length scale characteristics, is employed. The FG material distribution is on the basis of the Mori-Tanaka homogenisation technique. The two-parameter constitutive relation is used and the corresponding potential energy is formulated considering the variation nature of the material properties. The energy due to the motion of the nanobeam is also formulated and nanobeam's energies are dynamic-wise balanced by the work of the external dynamic loading; this is performed in the framework of Hamilton's principle. The coupled transvers/axial motion equations in the nonlinear regime are obtained. In the framework of a weighted residual method, the truncated/discretised model is obtained and numerically solved for force/frequency diagrams for nonlinear mechanics analysis. For a simple linear version of the problem, a linear analysis is also performed via the finite element method for verification purposes.

在本文中，作为第一个尝试，研究了功能梯度（FG）纳米束的强制耦合非线性力学，该力学通过开发高维模型来承受动态载荷。几何非线性Euler-Bernoulli理论用于定义位移分布。为了纳入小规模的影响，采用了具有两个独立的长度尺度特征的非局部应变梯度理论（NSGT）方案。FG的材料分布是基于Mori-Tanaka均质技术的。考虑到材料特性的变化特性，使用了两参数本构关系，并制定了相应的势能。还对由于纳米束运动而产生的能量进行了公式化，并通过外部动态载荷的作用来动态平衡纳米束的能量。这是在汉密尔顿原理的框架内进行的。得到了非线性状态下的横向/轴向耦合运动方程。在加权残差法的框架下，获得了截断/离散模型，并通过数值求解了力/频率图，以进行非线性力学分析。对于问题的简单线性版本，还可以通过有限元方法进行线性分析以进行验证。