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

Non-Linear Vibrations of Plates Under Thermal and Mechanical Loads

2005 ◽  
Author(s):  
P. Ribeiro
Keyword(s):  
Equations Of Motion ◽  
Time Integration ◽  
Implicit Time ◽  
Linear Elastic ◽  
Time Integration Method ◽  
Thermal Fields ◽  
Non Linear ◽  
Linear Vibrations ◽  
The Time Domain ◽  
Constitutive Material

The geometrically non-linear vibrations of plates under the combined effect of thermal fields and mechanical excitations are analyzed. With this purpose, an accurate model based on a p-version, hierarchical, first-order shear deformation finite element is employed. The constitutive material of the plates is linear elastic and isotropic. The equations of motion are solved in the time domain by an implicit time integration method. The temperature and the amplitude of the mechanical excitation are varied, and transitions from periodic to non-periodic motions are found.

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.

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