Large shearing oscillations of incompressible nonlinearly elastic bodies

1984 ◽  
Vol 14 (3) ◽  
pp. 249-262 ◽  
Author(s):  
Stuart S. Antman ◽  
Guo Zhong-Heng
Keyword(s):  
Elastic Bodies ◽  
Nonlinearly Elastic

The Quasilinear Wave Equation for Antiplane Shearing of Nonlinearly Elastic Bodies

2001 ◽  
Vol 171 (1) ◽  
pp. 201-226 ◽  
Author(s):  
Dawn A. Lott ◽  
Stuart S. Antman ◽  
William G. Szymczak
Keyword(s):  
Wave Equation ◽  
Quasilinear Wave Equation ◽  
Elastic Bodies ◽  
Nonlinearly Elastic

Contact between nonlinearly elastic bodies

2006 ◽  
Vol 136 (6) ◽  
pp. 1239-1266 ◽  
Author(s):  
Daniel Habeck ◽  
Friedemann Schuricht
Keyword(s):  
Variational Methods ◽  
Lagrange Equation ◽  
Existence Results ◽  
Necessary Condition ◽  
Generalized Gradients ◽  
Mechanical Problem ◽  
Elastic Bodies ◽  
Essential Tool ◽  
Nonlinearly Elastic

We study the contact between nonlinearly elastic bodies by variational methods. After the formulation of the mechanical problem, we provide existence results based on polyconvexity and on quasiconvexity. We then derive the Euler—Lagrange equation as a necessary condition for minimizers. Here Clarke's generalized gradients are an essential tool for treating the nonsmooth obstacle condi

scholarly journals Influence of Impulse Moments On Single-Frequency Torsional Oscillations of Nonlinearly Elastic Bodies

2021 ◽  
Author(s):  
Mariia Sokil ◽  
Andriy Andrukhiv ◽  
Solomiia Fedushko ◽  
Natalia Kryvinska ◽  
Yuriy Syerov ◽  
...  
Keyword(s):  
Cross Section ◽  
The Body ◽  
Single Frequency ◽  
Oscillatory Process ◽  
Periodic Action ◽  
Torsional Oscillations ◽  
Elastic Bodies ◽  
Classical Boundary ◽  
Nonlinear Elastic ◽  
Nonlinearly Elastic

Abstract Analytical study of the impulse moment influences on the nonlinear torsional oscillations in the homogeneous constant cross-section of a body under classical boundary conditions of the first, second, and third types has been developed. For the case when the elastic material properties meet the body close to the power law of elasticity, mathematical models of the process are obtained. They are the boundary value problems for an equation of hyperbolic type with a small parameter at the discrete right-hand side. The latter expresses the effect of pulse momentum on the oscillatory process. The peculiarities of resonant oscillations are established. Relative torsional oscillations of a nonlinear elastic body that rotates around the axis with a constant portable angular velocity are considered, taking into account the periodic action of pulse momentum acting in a fixed cross-section. The reliability of the obtained calculation formulas is confirmed.

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