TY - JOUR
T1 - Periodic and nonperiodic modes of postbuckling and nonlinear vibration of beams attached to nonlinear foundations
AU - Eltaher, M. A.
AU - Mohamed, N.
AU - Mohamed, S. A.
AU - Seddek, L. F.
N1 - Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2019/11/1
Y1 - 2019/11/1
N2 - 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.
AB - 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.
KW - Closed form solution
KW - Differential-integral quadrature method (DIQM)
KW - Nonlinear foundation
KW - Periodic and nonperiodic imperfections
KW - Postbuckling and nonlinear vibration
UR - http://www.scopus.com/inward/record.url?scp=85066954114&partnerID=8YFLogxK
U2 - 10.1016/j.apm.2019.05.026
DO - 10.1016/j.apm.2019.05.026
M3 - Article
AN - SCOPUS:85066954114
SN - 0307-904X
VL - 75
SP - 414
EP - 445
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
ER -