A cracked infinite Kirchhoff plate supported by a two-parameter elastic foundation

2014 ◽  
Vol 34 (11) ◽  
pp. 2737-2744 ◽  
Author(s):  
A. Nobili ◽  
E. Radi ◽  
L. Lanzoni
Keyword(s):  
Elastic Foundation ◽  
Kirchhoff Plate ◽  
Two Parameter

scholarly journals The edge waves on a Kirchhoff plate bilaterally supported by a two-parameter elastic foundation

2015 ◽  
Vol 23 (12) ◽  
pp. 2014-2022 ◽  
Author(s):  
J Kaplunov ◽  
A Nobili
Keyword(s):  
Phase Velocity ◽  
Elastic Foundation ◽  
Moving Load ◽  
Kirchhoff Plate ◽  
Winkler Foundation ◽  
Edge Waves ◽  
Bending Waves ◽  
Pasternak Elastic Foundation ◽  
Two Parameter ◽  
Limiting Value

In this paper, the bending waves propagating along the edge of a semi-infinite Kirchhoff plate resting on a two-parameter Pasternak elastic foundation are studied. Two geometries of the foundation are considered: either it is infinite or it is semi-infinite with the edges of the plate and of the foundation coinciding. Dispersion relations along with phase and group velocity expressions are obtained. It is shown that the semi-infinite foundation setup exhibits a cut-off frequency which is the same as for a Winkler foundation. The phase velocity possesses a minimum which corresponds to the critical velocity of a moving load. The infinite foundation exhibits a cut-off frequency which depends on its relative stiffness and occurs at a nonzero wavenumber, which is in fact hardly observed in elastodynamics. As a result, the associated phase velocity minimum is admissible only up to a limiting value of the stiffness. In the case of a foundation with small stiffness, asymptotic expansions are derived and beam-like one-dimensional equivalent models are deduced accordingly. It is demonstrated that for the infinite foundation the related nonclassical beam-like model comprises a pseudo-differential operator.

scholarly journals Snap-through buckling of a shallow arch resting on a two-parameter elastic foundation

2013 ◽  
Vol 37 (16-17) ◽  
pp. 7953-7963 ◽  
Author(s):  
Adel Abdelgawad ◽  
Ahmed Anwar ◽  
Mohamed Nassar
Keyword(s):  
Elastic Foundation ◽  
Shallow Arch ◽  
Two Parameter

On Post-Critical Behavior of a Beam on an Elastic Foundation

2018 ◽  
Vol 18 (06) ◽  
pp. 1850082 ◽  
Author(s):  
Lidija Z. Rehlicki ◽  
Marko B. Janev ◽  
Branislava N. Novaković ◽  
Teodor M. Atanacković
Keyword(s):  
Total Energy ◽  
Elastic Foundation ◽  
Nonlinear Problem ◽  
Bifurcation Analysis ◽  
Nontrivial Solutions ◽  
Buckling Mode ◽  
Nonlinear Equilibrium ◽  
The Stability ◽  
The One ◽  
Two Parameter

In this paper, we analyze the nonlinear equilibrium equation corresponding to the two-parameter bifurcation problem arising in the stability analysis of an elastic simply supported beam on the Winkler type elastic foundation for the case when bimodal buckling occurs. We perform the bifurcation analysis of the nonlinear problem, by using Lyapunov–Schmidt reduction, thus obtaining the number of the nontrivial solutions to the nonlinear problem and qualitatively characterizing the solution patterns. We also give the formulation of the problem and bifurcation analysis from the total energy viewpoint and determine the energy of each bifurcating solution. We assert that the solution with the smallest energy is the one that will be observed in the post-critical state. For specific choice of parameters, the bifurcating solution in the form of the second buckling mode has the smallest total energy. The numerical results illustrating the theory are also provided.

scholarly journals Free Vibration and Static Bending Analysis of Piezoelectric Functionally Graded Material Plates Resting on One Area of Two-Parameter Elastic Foundation

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Hong Nguyen Thi
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Engineering Practice ◽  
Parameter Study ◽  
Bending Analysis ◽  
Wide Range ◽  
Graded Material ◽  
Two Parameter

Free vibration and static bending analysis of piezoelectric functionally graded material plates resting on one area of the two-parameter elastic foundation is firstly investigated in this paper. The third-order shear deformation theory of Reddy and 8-node plate elements are employed to derive the finite element formulations of the structures; this theory does not need any shear correction factors; however, the mechanical response of the structure is described exactly. Verification problems are performed to evaluate the accuracy of the proposed theory and mathematical model. A wide range of parameter study is investigated to figure out the effect of geometrical, physical, and material properties such as the plate dimension, volume fraction index, piezoelectric effect, elastic foundation coefficients, and the square size of the area of the foundation on the free vibration and static bending of piezoelectric functionally graded material plates. These numerical results of this work aim to contribute to scientific knowledge of these smart structures in engineering practice.

Beams on Variable Two‐Parameter Elastic Foundation

1987 ◽  
Vol 113 (10) ◽  
pp. 1454-1466 ◽  
Author(s):  
Moshe Eisenberger ◽  
Jose Clastornik
Keyword(s):  
Elastic Foundation ◽  
Two Parameter
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