Dynamic stability of spinning viscoelastic cylinders at finite deformation
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. In contrast, Sidoroff-style viscoelastic models are seen to be linearly and nonlinearly stable, as is physically required.
- Research Organization:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- Grant/Contract Number:
- AC02-05CH11231
- OSTI ID:
- 1329493
- Alternate ID(s):
- OSTI ID: 1523954
- Journal Information:
- International Journal of Solids and Structures, Journal Name: International Journal of Solids and Structures Vol. 51 Journal Issue: 21-22; ISSN 0020-7683
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
Newton-Krylov method for computing the cyclic steady states of evolution problems in nonlinear mechanics: Newton-Krylov method for computing the cyclic steady states of evolution problems in nonlinear mechanics
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journal | August 2018 |
Design of dissipative multimaterial viscoelastic‐hyperelastic systems at finite strains via topology optimization
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journal | May 2019 |
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