A nonlocal strain gradient model is developed in this research to analyse the nonlinear frequencies of functionally graded porous curved nanotubes. It is assumed that the curved nanotube is in contact with a two-parameter nonlinear elastic foundation and is also subjected to the uniform temperature rise. The non-classical theory presented for curved nanotubes contains a nonlocal parameter and a material length scale parameter which can capture the size effect. A power law distribution function is used to describe the graded properties through the thickness direction of curved nanotubes. The even dispersion pattern is used to model the porosities distribution. The high-order shear deformation theory and the von Kármán type of geometric non-linearity are utilized to obtain the nonlinear governing equations of the structure. The size-dependent equations of motion for the large amplitude vibrations of curved nanotubes are obtained by employing Hamilton’s principle. The analytical solutions are extracted for the curved nanotube with immovable hinged-hinged boundary conditions. Size-dependent frequencies of the curved nanotube exposed to thermal field are obtained using the two-step perturbation technique and Galerkin procedure. The effects of important parameters such as nonlocal and length scale parameters, temperature field, elastic foundation, porosity, power law index and geometrical parameters are studied in detail.

在这项研究中开发了一个非局部应变梯度模型，以分析功能梯度多孔弯曲纳米管的非线性频率。假定弯曲的纳米管与两参数非线性弹性基础接触，并且也经受均匀的温度升高。针对弯曲纳米管提出的非经典理论包含非局部参数和可以捕获尺寸效应的材料长度尺度参数。幂律分布函数用于描述弯曲纳米管厚度方向上的渐变特性。均匀分散模式用于模拟孔隙率分布。利用高阶剪切变形理论和几何非线性的vonKármán类型来获得结构的非线性控制方程。利用汉密尔顿原理获得了弯曲纳米管大振幅振动的尺寸相关运动方程。提取了具有固定铰链铰接边界条件的弯曲纳米管的解析解。使用两步扰动技术和Galerkin程序可获得暴露于热场的弯曲纳米管的尺寸相关频率。详细研究了非局部和长度尺度参数，温度场，弹性基础，孔隙率，幂律指数和几何参数等重要参数的影响。使用两步扰动技术和Galerkin程序可获得暴露于热场的弯曲纳米管的尺寸相关频率。详细研究了非局部和长度尺度参数，温度场，弹性基础，孔隙率，幂律指数和几何参数等重要参数的影响。使用两步扰动技术和Galerkin程序可获得暴露于热场的弯曲纳米管的尺寸相关频率。详细研究了非局部和长度尺度参数，温度场，弹性基础，孔隙率，幂律指数和几何参数等重要参数的影响。