Computer simulation via a couple of homotopy perturbation methods and the generalized differential quadrature method for nonlinear vibration of functionally graded non-uniform micro-tube

• DOI: 10.1007/s00366-021-01395-7
• Publication Date: 2021-04-13T20:05:40Z
• Authors: Xiaoping Huang; Yemao Zhang; Zohre Moradi; Navvab Shafiei
• Keywords: Homotopy Analysis Method; Quadrature (astronomy); Axial symmetry

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-Karman’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).