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Steel and Composite Structures Volume 41, Number 6, December25 2021 , pages 787-803 DOI: https://doi.org/10.12989/scs.2021.41.6.787 |
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Nonlinear thermal vibration of pre/post-buckled two-dimensional FGM tapered microbeams based on a higher order shear deformation theory |
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Asmaa A. Hendi, Mohamed A. Eltaher, Salwa A. Mohamed, Mohamed A. Attia and A.W. Abdalla
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| Abstract | ||
| The size-dependent nonlinear thermomechanical vibration analysis of pre- and post-buckled tapered two-directional functionally graded (2D-FG) microbeams is presented in this study. In the context of the modified couple stress theory, the formulations are derived based on the parabolic shear deformation beam theory and von Karman nonlinear strains. Different thermomechanical material properties are assumed to be temperature-dependent and smoothly vary in both length and thickness directions using the power law and the physical neutral axis concept is employed. The nonlinear governing equations are derived using the Hamilton principle and the resulting variable coefficient equations of motion are solved using the differential quadrature method (DQM) and iterative Newton's method for clamped-clamped and simply supported boundary conditions. Comparison studies are presented to validate the derived model and solution procedure. The impacts of induced thermal moments, temperature power index, two gradient indices, nonuniform cross-section, and microstructure length scale parameter on the frequency-temperature configurations are explored for both clamped and simply supported microbeams. | ||
| Key Words | ||
| 2D-FG tapered microbeams; nonlinear temperature profile; nonlinear thermal vibration; stability analysis | ||
| Address | ||
| Asmaa A. Hendi:Department of Physics, Faculty of Science, University of Jeddah, Jeddah 21589, Saudi Arabia/ Department of Physics, Faculty of Science, AL Faisaliah Campus, King Abdulaziz University, Jeddah 21589, Saudi Arabia Mohamed A. Eltaher:Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University (KAU), P.O. Box 80204, Jeddah, Saudi Arabia/ Department of Mechanical Design and Production Engineering, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt Salwa A. Mohamed:Engineering Mathematics Department, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt Mohamed A. Attia:4Department of Mechanical Design and Production Engineering, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt A.W. Abdalla:Engineering Mathematics Department, Faculty of Engineering, Zagazig University, Zagazig 44519, Egypt | ||