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Periodic and nonperiodic modes of postbuckling and nonlinear vibration of beams attached to nonlinear foundations
Faculty
Engineering
Year:
2019
Type of Publication:
ZU Hosted
Pages:
14
Authors:
Salwa Amien Mohamed ebrhiem
Staff Zu Site
Abstract In Staff Site
Journal:
Structural Engineering and Mechanics Elsevier
Volume:
Keywords :
Periodic , nonperiodic modes , postbuckling and nonlinear vibration
Abstract:
This manuscript presents the influence of periodic (sine and cosine) and nonperiodic imperfections modes on buckling, postbuckling and dynamics of beam rested on nonlinear elastic foundations. The geometric von Kármán nonlinear strains induced by mid-plane stretching is considered. So, the generated equation of motion of imperfect beam is obtained as nonlinear integro-partial-differential equation. Elastic cubic nonlinear and linear springs and shearing layer are proposed to model elastic medium around the imperfected beam. Numerical differential-integral quadrature method (DIQM) in combination with Newton’s method are used to find buckling loads and modes of imperfect beam that described by nonlinear integro-differential equation. In linear vibration analysis, the problem is discretized by DIQM and solved as a linear eigenvalue problem. The closed form solutions for static response and linear vibration problem of imperfect beam are obtained. Excellent agreement is observed between proposed numerical and analytical solutions. The numerical results indicate that imperfection modes and its amplitude have a weighty influence on the buckling load, postbuckling configurations and natural frequencies. Finally, numerical results for clamped-clamped (C-C) and simply supported (SS-SS) beams with local (nonperiodic) imperfection modes are presented.
Author Related Publications
Salwa Amien Mohamed ebrhiem, "A novel differential-integral quadrature method for the solution of nonlinear integro-differential equations", John Wiley & Sons Ltd, 2021
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Salwa Amien Mohamed ebrhiem, "Thermal vibration characteristics of pre/post‑buckled bi‑directional functionally graded tapered microbeams based on modifed couple stress Reddy beam theory", Springer, 2020
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Salwa Amien Mohamed ebrhiem, "Nonlinear thermal buckling and postbuckling analysis of bidirectional functionally graded tapered microbeams based on Reddy beam theory", Springer, 2020
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Salwa Amien Mohamed ebrhiem, "New Smoother to Enhance Multigrid-Based Methods for Bratu Problem", Elsevier, 2008
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Salwa Amien Mohamed ebrhiem, "Optimally efficient multigrid algorithms for incompressible Euler equations", Emerald Group Publishing Limited, 2008
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Ola Ragab Abdou Mohamed, "Analysis of Composite Plates Using Moving Least Squares Differential Quadrature Method", Science Direct, 2014
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Ola Ragab Abdou Mohamed, "Efficient Quadrature Solution for Composite Plate Problems", medwelljournals, 2014
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Mohamed Mohamed Ali Mohamed Saied, "Three Resultant Applications In Surface Modeling For Computer Graphics", Second National Conference of Mathematics, Cairo 6-11 April 1996, 1996
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Ahmed Saad Rashed Rashed Elsahar, "Similarity Analysis of Mass and Heat Transfer of FHD Steady Flow of Nanofluid Incorporating Magnetite Nanoparticles (Fe3O4)", East African Scholars Publisher, Kenya, 2020
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