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Steel and Composite Structures
  Volume 44, Number 3, August10 2022 , pages 371-388

A semi-analytical procedure for cross section effect on the buckling and dynamic stability of composite imperfect truncated conical microbeam
Peng Zhang, Yanan Gao, Zohre Moradi, Yasar Ameer Ali and Mohamed Amine Khadimallah

    The present study tackles the problem of forced vibration of imperfect axially functionally graded shell structure with truncated conical geometry. The linear and nonlinear large-deflection of the structure are considered in the mathematical formulation using von-Kármán models. Modified coupled stress method and principle of minimum virtual work are employed in the modeling to obtain the final governing equations. In addition, formulations of classical elasticity theory are also presented. Different functions, including the linear, convex, and exponential cross-section shapes, are considered in the grading material modeling along the thickness direction. The grading properties of the material are a direct result of the porosity change in the thickness direction. Vibration responses of the structure are calculated using the semi-analytical method of a couple of homotopy perturbation methods (HPM) and the generalized differential quadrature method (GDQM). Contradicting effects of small-scale, porosity, and volume fraction parameters on the nonlinear amplitude, frequency ratio, dynamic deflection, resonance frequency, and natural frequency are observed for shell structure under various boundary conditions.
Key Words
    functionally graded material; forced nonlinear vibration; homotopy perturbation; micro-structures; semianalytical solution
Peng Zhang:Faculty of Architecture and Civil Engineering, Huaiyin Institute of Technology, Huaian, 223001, China

Yanan Gao:Faculty of Architecture and Civil Engineering, Huaiyin Institute of Technology, Huaian, 223001, China

Zohre Moradi:Faculty of Engineering and Technology, Department of Electrical Engineering, Imam Khomeini International University, 34149-16818 Qazvin, Iran

Yasar Ameer Ali:Building and Construction Techniques Engineering Department, Al-Mustaqbal University College, Babylon, Iraq

Mohamed Amine Khadimallah:1)Prince Sattam Bin Abdulaziz University, College of Engineering, Civil Engineering Department, Al-Kharj, 16273, Saudi Arabia
2)Laboratory of Systems and Applied Mechanics, Polytechnic School of Tunisia, University of Carthage, Tunis, Tunisia

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