Bifurcations and postbuckling behavior of vibrating of the nonhomogeneous, nonlinear elastic system with multiple independent bifurcation parameters

1990 ◽  
Vol 26 (8) ◽  
pp. 821-831
Author(s):  
Victor Z. Gristchak
Keyword(s):  
Elastic System ◽  
Postbuckling Behavior ◽  
Nonlinear Elastic

Two-Mode Buckling of an Elastically Supported Plate and Its Relation to Catastrophe Theory

1980 ◽  
Vol 47 (3) ◽  
pp. 607-612 ◽  
Author(s):  
D. Hui ◽  
J. S. Hansen
Keyword(s):  
Infinite Plate ◽  
Single Mode ◽  
Postbuckling Behavior ◽  
Imperfection Sensitivity ◽  
Mode Behavior ◽  
Quartic Term ◽  
Compressive Loads ◽  
Nonlinear Elastic ◽  
Elastically Supported ◽  
Spring Constants

Classical buckling and initial postbuckling of a geometrically imperfect infinite plate on a nonlinear elastic foundation under two independent applied compressive loads are analyzed. The plate is assumed to have imperfections of the same form as the buckling modes. It is found that single mode behavior occurs when the two independent loads Nx and Ny are unequal. A two-mode case occurs when the two applied loads are equal and the form of the instability falls into the category of the parabolic umbilic type one or type two, depending on the quadratic and cubic spring constants. The importance of the contribution of the quartic term and imperfection-sensitivity is examined. The analysis is studied within the context of Koiter’s general theory of multimode postbuckling behavior.

scholarly journals Exponentially Complex “Classically Entangled” States in Arrays of One-Dimensional Nonlinear Elastic Waveguides

Materials ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 3553 ◽  
Author(s):  
Deymier ◽  
Runge ◽  
Hasan ◽  
Calderin
Keyword(s):  
Hilbert Space ◽  
Elastic System ◽  
Multiple Time ◽  
One Dimensional ◽  
Wave Guides ◽  
External Driver ◽  
Scale Perturbation ◽  
Nonlinear Elastic ◽  
Exponential Complexity ◽  
Nonseparable States

We demonstrate theoretically, using multiple-time-scale perturbation theory, the existence of nonseparable superpositions of elastic waves in an externally driven elastic system composed of three one-dimensional elastic wave guides coupled via nonlinear forces. The nonseparable states span a Hilbert space with exponential complexity. The amplitudes appearing in the nonseparable superposition of elastic states are complex quantities dependent on the frequency of the external driver. By tuning these complex amplitudes, we can navigate the state’s Hilbert space. This nonlinear elastic system is analogous to a two-partite two-level quantum system.

1448: Elastic System Fibers in the Corpora Cavernosa of Potent and Patients with Erectile Dysfunction

2004 ◽  
Vol 171 (4S) ◽  
pp. 381-381
Author(s):  
Waldemar S. Costa ◽  
Fabrício B. Carrerete ◽  
Ronaldo Damião ◽  
Marcia A. Babinski ◽  
Francisco J.B. Sampaio ◽  
...  
Keyword(s):  
Erectile Dysfunction ◽  
Elastic System ◽  
Corpora Cavernosa

Remarks on nonlinear elastic waves with null conditions

2020 ◽  
Vol 26 ◽  
pp. 121
Author(s):  
Dongbing Zha ◽  
Weimin Peng
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elastic Waves ◽  
Wave Equations ◽  
Alternative Proof ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Hyperelastic Materials ◽  
Variational Structure ◽  
Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

Driven elastic system in a random environment

1999 ◽  
Vol 09 (PR10) ◽  
pp. Pr10-69-Pr10-71 ◽  
Author(s):  
P. Chauve ◽  
T. Giamarchi ◽  
P. Le Doussal
Keyword(s):  
Random Environment ◽  
Elastic System
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