Dynamic stability of spinning viscoelastic cylinders at finite deformation

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:51

Article

Govindjee, Sanjay¹  Potter, Trevor²  Wilkening, Jon² 

[1] Univ Calif Berkeley, Dept Civil Engn, Berkeley, CA 94720 USA

[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

关键词: Rolling;    Tires;    Stability;    Bifurcation;    Standing wave;    Viscoelasticity;   

DOI  :  10.1016/j.ijsolstr.2014.06.022

来源: Elsevier

【 摘 要 】

The study of spinning axisymmetric cylinders undergoing finite deformation is a classic problem in several industrial settings the tire industry in particular. We present a stability analysis of spinning elastic and viscoelastic cylinders using ARPACK to compute eigenvalues and eigenfunctions of finite element discretizations of the linearized evolution operator. We show that the eigenmodes correspond to N-peak standing or traveling waves for the linearized problem with an additional index describing the number of oscillations in the radial direction. We find a second hierarchy of bifurcations to standing waves where these eigenvalues cross zero, and confirm numerically the existence of finite-amplitude standing waves for the nonlinear problem on one of the new branches. In the viscoelastic case, this analysis permits us to study the validity of two popular models of finite viscoelasticity. We show that a commonly used finite deformation linear convolution model results in non-physical energy growth and finite-time blow-up when the system is perturbed in a linearly unstable direction and followed nonlinearly in time. On the other hand, Sidoroff-style viscoelastic models are seen to be linearly and nonlinearly stable, as is physically required. (C) 2014 Elsevier Ltd. All rights reserved.

【 授权许可】

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