The main purpose of this paper is to render a novel higher-order shear deformation theory (HSDT), which can model the dynamic analysis of the 2D-FG nanoplates subjected to hygro-thermo loading using a new shear strain shape function. The transverse component of displacement is composed of bending and shear parts. Thickness stretching influence is considered according to higher-order shear and normal deformation theory. The present model is suitable to deal with thin and thick nanoplates since it includes the HSDT and the thickness stretching influence. Assume the plate's materials properties, including density, Young’s modulus, and thermal and moisture parameters vary continuously with an arbitrary function in two directions. Size-dependent nonlocal elasticity theory is dedicated to consider the nonlocality. The temperature variation and moisture expansion vary through the thickness of the nanoplate nonlinearly. To achieve the equations of motion of the 2D-FG nanoplate with simply-supported boundary conditions, Hamilton’s principle is utilized. Navier method is utilized for a closed-form solution of the 2D-FG nanoplates. The impacts of several parameters, including thermal effects, are investigated on the vibration characteristics of the 2D-FG nanoplates. The results demonstrate that with increasing the FG indexes, their impacts on the natural frequency of the system will enhance/reduce when the temperature variation increases/reduces.

本文的主要目的是提出一种新的高阶剪切变形理论 (HSDT)，该理论可以使用新的剪切应变形状函数对承受湿热载荷的 2D-FG 纳米板的动态分析进行建模。位移的横向分量由弯曲部分和剪切部分组成。根据高阶剪切和法向变形理论考虑厚度拉伸影响。本模型适用于处理薄和厚的纳米板，因为它包括 HSDT 和厚度拉伸影响。假设板的材料属性，包括密度、杨氏模量以及热和湿度参数在两个方向上随任意函数连续变化。尺寸相关的非局部弹性理论致力于考虑非局部性。温度变化和水分膨胀随纳米板的厚度呈非线性变化。为了获得具有简支边界条件的 2D-FG 纳米板的运动方程，利用了汉密尔顿原理。Navier 方法用于 2D-FG 纳米板的封闭形式解决方案。研究了包括热效应在内的几个参数对 2D-FG 纳米板振动特性的影响。结果表明，随着FG指标的增加，它们对系统固有频率的影响会随着温度变化的增加/减少而增加/减少。Navier 方法用于 2D-FG 纳米板的封闭形式解决方案。研究了包括热效应在内的几个参数对 2D-FG 纳米板振动特性的影响。结果表明，随着FG指标的增加，它们对系统固有频率的影响会随着温度变化的增加/减少而增加/减少。Navier 方法用于 2D-FG 纳米板的封闭形式解决方案。研究了包括热效应在内的几个参数对 2D-FG 纳米板振动特性的影响。结果表明，随着FG指标的增加，它们对系统固有频率的影响会随着温度变化的增加/减少而增加/减少。