In this paper, to improve the vibrational response of microstructures, the impact of the nonlinear modal analysis of axially functionally graded (AFG) truncated conical micro-scale tube including the thermal loading for the different type of cross sections such as uniform section, linear tapered section, convex section, the exponential section are studied that are applicable for various application, for example, the micro-thermal fins, macro-/micro-fluid-flow diffuser, fluid-flow nozzle, fluid-flow throat, micro-sensor, etc. The nonlinear equations are obtained applying Hamilton’s principles based on the modified couple stress to determine the size effect and Euler–Bernoulli beam theory considering the von-Kármán’s nonlinear strain. The material combination varies along the tube’s length, denouncing the AFG tube made by metal and ceramic phases. The nonlinear equations are solved by applying a couple of homotopy perturbation methods (HPM) to calculating the nonlinear results and the generalized differential quadrature method (GDQM) to providing the initial conditions. The linear and nonlinear results presented the effect of various cross sections and other parameters on the micro-tube frequency that are valuable to design and manufacture the micro-electro-mechanical systems (MEMS).

在本文中，为改善微结构的振动响应，轴向功能梯度（AFG）截头圆锥形微型管的非线性模态分析的影响包括均匀截面，线性锥形等不同类型截面的热负荷研究了截面，凸面，指数截面，这些截面适用于各种应用，例如微热翅片，大/微流体扩散器，流体喷嘴，流体喉管，微传感器，应用汉密尔顿原理，基于修正的耦合应力，确定尺寸效应，并考虑了冯-卡尔曼的非线性应变，通过欧拉-伯努利梁理论获得了非线性方程。材料组合沿管的长度变化，这表明由金属和陶瓷相制成的AFG管。通过应用几种同伦摄动方法（HPM）计算非线性结果以及应用广义微分正交方法（GDQM）提供初始条件来求解非线性方程。线性和非线性结果显示了各种横截面和其他参数对微管频率的影响，这对于设计和制造微机电系统（MEMS）很有用。