caa a22 4500 477036910 CHVBK 20180405111307.0 cr unu---uuuuu 170330e19960101xx s 000 0 eng 10.1007/BF02433808 doi (NATIONALLICENCE)springer-10.1007/BF02433808 Antman S. Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, 20742, College Park, MD, USA aut Dynamical problems for geometrically exact theories of nonlinearly viscoelastic rods [Elektronische Daten] [S. Antman] Summary: This paper surveys recent results and open problems for the equations of motion for geometrically exact theories of nonlinearly viscoelastic and elastic rods. These rods can deform in space by undergoing not only flexure and torsion, but also extension and shear. The paper begins with a derivation of the governing equations, which for viscoelastic rods form a quasilinear system of hyperbolic-parabolic partial differential equations of high order. It then derives the energy equation and discusses difficulties that can arise in getting useful energy estimates. The paper next treats constitutive assumptions precluding total compression. The paper then discusses the curious asymptotic problems that arise when the inertia of the rod is small relative to that of a rigid body attached to its end. The paper concludes with discussions of traveling waves and shock structure, Hopf bifurcation problems, and problems of control. Springer-Verlag New York Inc., 1996 Journal of Nonlinear Science Springer-Verlag 6/1(1996-01-01), 1-18 0938-8974 6:1<1 1996 6 332 https://doi.org/10.1007/BF02433808 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02433808 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Antman S. Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, 20742, College Park, MD, USA aut NATIONALLICENCE 773 0- Journal of Nonlinear Science Springer-Verlag 6/1(1996-01-01), 1-18 0938-8974 6:1<1 1996 6 332 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer