A viscoelastic Timoshenko beam with dynamic frictionless impact

Jeongho Ahn; David E. Stewart

doi:10.3934/dcdsb.2009.12.1

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2009, Volume 12, Issue 1: 1-22. Doi: 10.3934/dcdsb.2009.12.1

This issue Previous Article Next Article Vibrations of a nonlinear dynamic beam between two stops

A viscoelastic Timoshenko beam with dynamic frictionless impact

Jeongho Ahn^1, and
David E. Stewart^2,

1.
Department of Mathematics and Statistics, Arkansas State University, State University, AR 72467
2.
Department of Mathematics, The University of Iowa, Iowa City, IA 52242

Received: September 30, 2008

Revised: January 31, 2009

Published: June 2009

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Abstract

Two coupled partial differential equations which describe the motion of a viscoelastic (Kelvin-Voigt type) Timoshenko beam are formulated with the complementarity conditions. This dynamic impact problem is considered a boundary thin obstacle problem. The existence of solutions is proved. A major concern is to pursue an investigation into conservation of energy (or energy balance), which is performed both theoretically and numerically.

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Mathematics Subject Classification: Primary: 74M20, 74K10; Secondary: 35L85.

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A viscoelastic Timoshenko beam with dynamic frictionless impact

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