• Journal of applied mathematics & informatics
• /
• v.29 no.1_2
• /
• pp.311-326
• /
• 2011

In this paper, we adopt discontinuous Galerkin methods with penalty terms namely symmetric interior penalty Galerkin methods, to solve nonlinear viscoelasticity type equations. We construct finite element spaces and define an appropriate projection of u and prove its optimal convergence. We construct extrapolated fully discrete discontinuous Galerkin approximations for the viscoelasticity type equation and prove ${\ell}^{\infty}(L^2)$ optimal error estimates in both spatial direction and temporal direction.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.4
• /
• pp.829-850
• /
• 2012

In this paper, we adopt symmetric interior penalty discontinuous Galerkin (SIPG) methods to approximate the solution of nonlinear viscoelasticity-type equations. We construct finite element space which consists of piecewise continuous polynomials. We introduce an appropriate elliptic-type projection and prove its approximation properties. We construct semidiscrete discontinuous Galerkin approximations and prove the optimal convergence in $L^2$ normed space.

• Structural Engineering and Mechanics
• /
• v.61 no.1
• /
• pp.143-160
• /
• 2017

The paper studies the attenuation of the axisymmetric longitudinal waves propagating in the bi-layered hollow cylinder made of linear viscoelastic materials. Investigations are made by utilizing the exact equations of motion of the theory of viscoelasticity. The dispersion equation is obtained for an arbitrary type of hereditary operator of the materials of the constituents and a solution algorithm is developed for obtaining numerical results on the attenuation of the waves under consideration. Specific numerical results are presented and discussed for the case where the viscoelasticity of the materials is described through fractional-exponential operators by Rabotnov. In particular, how the rheological parameters influence the attenuation of the axisymmetric longitudinal waves propagating in the cylinder under consideration, is established.

• Proceedings of the KSME Conference
• /
• 2003.11a
• /
• pp.1672-1677
• /
• 2003

In this paper, the spectral element model is derived for the vibration and stability analyses of an axially moving viscoelastic beam subjected to axial tension. The viscoelastic material is represented by using a one-dimensional constitutive equation of hereditary integral type. The accuracy of the present spectral element model is first verified by comparing the eigenvalues obtained by the present spectral element model-based SEM with those obtained by the exact theory and the conventional FEM. The effects of viscoelasticity on the vibration and stability of an example moving viscoelastic beam are numerically investigated.

• Journal of Mechanical Science and Technology
• /
• v.18 no.7
• /
• pp.1159-1168
• /
• 2004

In this paper, a spectral element model is derived for the axially moving viscoelastic beams subject to axial tension. The viscoelastic material is represented in a general form by using the one-dimensional constitutive equation of hereditary integral type. The high accuracy of the present spectral element model is verified first by comparing the eigenvalues obtained by the present spectral element model with those obtained by using the conventional finite element model as well as with the exact analytical solutions. The effects of viscoelasticity and moving speed on the dynamics of moving beams are then numerically investigated.

• Korea-Australia Rheology Journal
• /
• v.12 no.2
• /
• pp.135-141
• /
• 2000

The linear viscoelastic behavior of acrylonitrile-butadiene-styrene (ABS) polymers with different rubber content has been investigated in the frame of a linear viscoelastic model, which takes into account the inter-connectivity of the dispersed rubber particles. The model developed in our previous work has been shown to properly predict the low frequency plateau for the storage modulus, which is generally observed in polymer blends containing core-shell-type impact modifiers. In the present study, further experiments have been carried out on ABS polymers with different rubber content to verify the validity of our linear viscoelastic model. It has been found that our model describes quite properly the rheological behavior of ABS polymers with different rubber content, especially at low frequencies. The experimental data confirm that our model describes the rheological properties of rubber-modified thermoplastic polymers with strong adhesion at the particle/matrix interface more accurately than the Palierne model.