Blowup of solutions for the planar motions of rotating nonlinearly elastic rods |
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| Institution: | 1. Department of Mathematics, University of Maryland, College Park, Maryland 20742, U.S.A;2. Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, U.S.A;3. Institute for Systems Research, University of Maryland, College Park, Maryland 20742, U.S.A;4. Department of Mathematics, Zirve University, 27260 Gaziantep, Turkey;1. Department of Civil and Environmental Engineering, Virginia Tech, Blacksburg, VA 24061, USA;2. Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708, USA;1. Lehrstuhl für Informatik I, Universität Würzburg, Germany;2. Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic |
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| Abstract: | This paper treats the motion of flexible, extensible, shearable nonlinearly elastic rods, described by a geometrically exact theory, when they are confined to a plane rotating about a fixed axis at constant angular speed and when they are confined to a fixed plane with one end rotating at a constant angular speed about an axis perpendicular to the fixed plane. The paper gives restrictions on the constitutive equations and initial conditions that ensure that motions become unbounded at rapid rates as time becomes infinite. The analysis of these constitutive restrictions employs the theory of characteristics for single first-order semilinear partial differential equations. |
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| Keywords: | Nonlinear elasticity Rotational motions Blowup |
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