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July  2009, 12(1): 1-22. doi: 10.3934/dcdsb.2009.12.1

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, United States
2. 

Department of Mathematics, The University of Iowa, Iowa City, IA 52242, United States

Received  October 2008 Revised  February 2009 Published  May 2009

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.
Keywords: Galerkin approximation., Time-discretization, Complementarity conditions, Signorini's contact conditions, Viscoelastic Timoshenko Beam.
Mathematics Subject Classification: Primary: 74M20, 74K10; Secondary: 35L8.
Citation: Jeongho Ahn, David E. Stewart. A viscoelastic Timoshenko beam with dynamic frictionless impact. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 1-22. doi: 10.3934/dcdsb.2009.12.1
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