Deflection of Non-Uniform Beams Resting on a Non-Linear Elastic Foundation Using (GDQM)

2017 ◽  
pp. 52-56 ◽  
Author(s):  
Ramzy M. Abumandour ◽  
Islam M. Eldesoky ◽  
Mohamed A. Safan ◽  
R. M. Rizk-Allah ◽  
Fathi A. Abdelmgeed
Keyword(s):  
Elastic Foundation ◽  
Linear Elastic ◽  
Non Linear

NON-LINEAR VIBRATIONS OF A SLIGHTLY CURVED BEAM RESTING ON A NON-LINEAR ELASTIC FOUNDATION

1998 ◽  
Vol 212 (2) ◽  
pp. 295-309 ◽  
Author(s):  
H.R. Öz ◽  
M. Pakdemirli ◽  
E. Özkaya ◽  
M. Yilmaz
Keyword(s):  
Elastic Foundation ◽  
Curved Beam ◽  
Linear Elastic ◽  
Non Linear ◽  
Linear Vibrations

scholarly journals Dynamic Buckling of a Clamped Finite Column Resting on a Non – linear Elastic Foundation

2019 ◽  
pp. 1-47
Author(s):  
E. Julius, Bassey ◽  
M. Anthony, Ette ◽  
U. Joy, Chukwuchekwa ◽  
C. Atulegwu, Osuji
Keyword(s):  
Elastic Foundation ◽  
Governing Equation ◽  
Asymptotic Expansions ◽  
Perturbation Technique ◽  
Dynamic Buckling ◽  
Buckling Load ◽  
Linear Elastic ◽  
Non Linear ◽  
Relevant Variables ◽  
Independent Parameters

The analysis of the dynamic buckling of a clamped finite imperfect viscously damped column lying on a quadratic-cubic elastic foundation using the methods of asymptotic and perturbation technique is presented. The proposed governing equation contains two small independent parameters (δ and ϵ) which are used in asymptotic expansions of the relevant variables. The results of the analysis show that the dynamic buckling load of column decreases with its imperfections as well as with the increase in damping. The results obtained are strictly asymptotic and therefore valid as the parameters δ and ϵ become increasingly small relative to unity.

Non-linear Oscillations of Orthotropic Plates on a Non-linear Elastic Foundation

2008 ◽  
Vol 28 (7) ◽  
pp. 851-867 ◽  
Author(s):  
Chun-Sheng Chen ◽  
An-Hung Tan ◽  
Rean-Der Chien
Keyword(s):  
Elastic Foundation ◽  
Orthotropic Plates ◽  
Linear Elastic ◽  
Non Linear

TECHNICAL NOTE. CIRCULAR PLATE ON A NON-LINEAR ELASTIC FOUNDATION.

1985 ◽  
Vol 79 (4) ◽  
pp. 729-735
Author(s):  
A HASSAN ◽  
M NASSAR ◽  
C LANCZOS ◽  
Keyword(s):  
Circular Plate ◽  
Elastic Foundation ◽  
Technical Note ◽  
Linear Elastic ◽  
Non Linear

scholarly journals Oscillations of a Beam on a Non-Linear Elastic Foundation under Periodic Loads

2006 ◽  
Vol 13 (4-5) ◽  
pp. 273-284 ◽  
Author(s):  
Donald Mark Santee ◽  
Paulo Batista Gonçalves
Keyword(s):  
Mathematical Model ◽  
Elastic Foundation ◽  
Period Doubling ◽  
Algebraic Expression ◽  
Geometrical Parameters ◽  
Flexible Beam ◽  
Algebraic Relation ◽  
Structural Element ◽  
Linear Elastic ◽  
Non Linear

The complexity of the response of a beam resting on a nonlinear elastic foundation makes the design of this structural element rather challenging. Particularly because, apparently, there is no algebraic relation for its load bearing capacity as a function of the problem parameters. Such an algebraic relation would be desirable for design purposes. Our aim is to obtain this relation explicitly. Initially, a mathematical model of a flexible beam resting on a non-linear elastic foundation is presented, and its non-linear vibrations and instabilities are investigated using several numerical methods. At a second stage, a parametric study is carried out, using analytical and semi-analytical perturbation methods. So, the influence of the various physical and geometrical parameters of the mathematical model on the non-linear response of the beam is evaluated, in particular, the relation between the natural frequency and the vibration amplitude and the first period doubling and saddle-node bifurcations. These two instability phenomena are the two basic mechanisms associated with the loss of stability of the beam. Finally Melnikov's method is used to determine an algebraic expression for the boundary that separates a safe from an unsafe region in the force parameters space. It is shown that this can be used as a basis for a reliable engineering design criterion.

Mechanical Analysis of Three Kinds of Beams on Non-Linear Elastic Foundation Materials

2016 ◽  
Vol 867 ◽  
pp. 147-151
Author(s):  
Xiao Liang Chen ◽  
Zuan Tian ◽  
Jian Ping Ding
Keyword(s):  
Elastic Foundation ◽  
Reaction Force ◽  
Internal Force ◽  
Mechanical Analysis ◽  
Linear Elastic ◽  
Non Linear ◽  
Cubic Polynomial ◽  
Internal Forces ◽  
Newton Iteration Method ◽  
Relative Errors

The deformation and internal forces of beams on non-linear elastic foundation materials were studied. The reaction force between the beam and the foundation was fitted as a cubic polynomial about the deflection of beams by experimental data, and the corresponding control equations were derived by the finite difference method. MATLAB program with the Newton iteration method was used to obtain numerical results. Results of the numerical example show the deformation and internal force of short non-linear and linear elastic Winkler beams are same, but the relative errors can reach 10%-20% for moderate and long beams, so the non-linear foundation effect on the settlement of beams should be considered in engineering; the relative errors of the deformation and internal force between moderate non-linear and linear elastic Winkler beams vary with the length of beams, but keep invariant for long beams.

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