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:
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.
   
     
 
       

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