On the existence of Sobolev quasi-periodic solutions of multidimensional nonlinear beam equation

2016 ◽  
Vol 57 (10) ◽  
pp. 102701 ◽  
Author(s):  
Yunfeng Shi
Keyword(s):  
Periodic Solutions ◽  
Beam Equation ◽  
Nonlinear Beam

Quasi-periodic solutions of nonlinear beam equation with prescribed frequencies

2015 ◽  
Vol 56 (5) ◽  
pp. 052701 ◽  
Author(s):  
Jing Chang ◽  
Yixian Gao ◽  
Yong Li
Keyword(s):  
Periodic Solutions ◽  
Beam Equation ◽  
Nonlinear Beam

Periodic solutions of a nonlinear beam equation

1983 ◽  
Vol 7 (10) ◽  
pp. 1141-1147
Author(s):  
Ding Weiyue ◽  
Hong Chongwei
Keyword(s):  
Periodic Solutions ◽  
Beam Equation ◽  
Nonlinear Beam

An Asymptotic Solution for the Response of Face-Sheet Delaminations/Debonds Under Compression

2000 ◽  
Author(s):  
George A. Kardomateas ◽  
Haiying Huang
Keyword(s):  
Transverse Shear ◽  
Critical Strain ◽  
Linear Equations ◽  
Face Sheet ◽  
Beam Equation ◽  
System Of Linear Equations ◽  
Postbuckling Behavior ◽  
Nonlinear Beam ◽  
First Order ◽  
Higher Order Terms

Abstract The buckling and initial postbuckling behavior of face-sheet delaminations or face-sheet/core debonds is studied by a perturbation procedure. The procedure is based on the nonlinear beam equation with transverse shear included, and an asymptotic expansion of the load and deformation quantities. First the characteristic equation for the critical load is formulated and this is a nonlinear algebraic equation. Subsequently, the first order load is found from a system of linear equations and the initial postbuckling behavior can thus be studied. The procedure can be easily expanded to the higher order terms. The effect of transverse shear is illustrated with results on the critical strain and the initial postbuckling displacement.

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