Validation of numerical results of impact of viscoelastic slug and elastic rod through viscoelastic discontinuity analysis

Standard linear solid model

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The study is about impact of a short elastic rod (or slug) on a stationary semi-infinite viscoelastic rod. The viscoelastic materials are modeled as standard linear solid which involve three material parameters and the motion is treated as one-dimensional. We first establish the governing equations pertaining to the impact of viscoelastic materials subject to certain boundary conditions for the case when an elastic slug moving at a speed V impacts a semi-infinite stationary viscoelastic rod. The objective is to validate the numerical results of stresses and velocities at the interface following wave transmissions and reflections in the slug after the impact using viscoelastic discontinuity. If the stress at the interface becomes tensile and the velocity changes its sign, then the slug and the rod part company. If the stress at the interface is compressive after the impact, the slug and the rod remain in contact. After modelling the impact and solve the governing system of partial differential equations in the Laplace transform domain, we invert the Laplace transformed solution numerically to obtain the stresses and velocities at the interface for several viscosity time constants and ratios of acoustic impedances. In inverting the Laplace transformed equations, we used the complex inversion formula because there is a branch cut and infinitely many poles within the Bromwich contour. In the viscoelastic discontinuity analysis, we look at the moving discontinuities in stress and velocity using the impulse-momentum relation and kinematical condition of compatibility. Finally, we discussed the relationship of the stresses and velocities using numeric and the validated stresses and velocities using viscoelastic discontinuity analysis.

Original languageEnglish
Title of host publicationInternational Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014
EditorsMohammad Fadzli Ramli, Nurshazneem Roslan, Ahmad Kadri Junoh, Maz Jamilah Masnan, Mohammad Huskhazrin Kharuddin
PublisherAmerican Institute of Physics Inc.
Volume1660
ISBN (Electronic)9780735413047
DOIs
Publication statusPublished - 15 May 2015
EventInternational Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014 - Penang, Malaysia
Duration: 28 May 201430 May 2014

Other

OtherInternational Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014
CountryMalaysia
CityPenang
Period28/05/1430/05/14

Fingerprint

discontinuity
rods
Laplace equation
acoustic impedance
partial differential equations
compatibility
time constant
impulses
poles
viscosity
inversions
boundary conditions
momentum

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

Haji Musa, A. B. (2015). Validation of numerical results of impact of viscoelastic slug and elastic rod through viscoelastic discontinuity analysis: Standard linear solid model. In M. F. Ramli, N. Roslan, A. K. Junoh, M. J. Masnan, & M. H. Kharuddin (Eds.), International Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014 (Vol. 1660). [070127] American Institute of Physics Inc.. https://doi.org/10.1063/1.4915844
Haji Musa, Abu Bakar. / Validation of numerical results of impact of viscoelastic slug and elastic rod through viscoelastic discontinuity analysis : Standard linear solid model. International Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014. editor / Mohammad Fadzli Ramli ; Nurshazneem Roslan ; Ahmad Kadri Junoh ; Maz Jamilah Masnan ; Mohammad Huskhazrin Kharuddin. Vol. 1660 American Institute of Physics Inc., 2015.
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title = "Validation of numerical results of impact of viscoelastic slug and elastic rod through viscoelastic discontinuity analysis: Standard linear solid model",
abstract = "The study is about impact of a short elastic rod (or slug) on a stationary semi-infinite viscoelastic rod. The viscoelastic materials are modeled as standard linear solid which involve three material parameters and the motion is treated as one-dimensional. We first establish the governing equations pertaining to the impact of viscoelastic materials subject to certain boundary conditions for the case when an elastic slug moving at a speed V impacts a semi-infinite stationary viscoelastic rod. The objective is to validate the numerical results of stresses and velocities at the interface following wave transmissions and reflections in the slug after the impact using viscoelastic discontinuity. If the stress at the interface becomes tensile and the velocity changes its sign, then the slug and the rod part company. If the stress at the interface is compressive after the impact, the slug and the rod remain in contact. After modelling the impact and solve the governing system of partial differential equations in the Laplace transform domain, we invert the Laplace transformed solution numerically to obtain the stresses and velocities at the interface for several viscosity time constants and ratios of acoustic impedances. In inverting the Laplace transformed equations, we used the complex inversion formula because there is a branch cut and infinitely many poles within the Bromwich contour. In the viscoelastic discontinuity analysis, we look at the moving discontinuities in stress and velocity using the impulse-momentum relation and kinematical condition of compatibility. Finally, we discussed the relationship of the stresses and velocities using numeric and the validated stresses and velocities using viscoelastic discontinuity analysis.",
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Haji Musa, AB 2015, Validation of numerical results of impact of viscoelastic slug and elastic rod through viscoelastic discontinuity analysis: Standard linear solid model. in MF Ramli, N Roslan, AK Junoh, MJ Masnan & MH Kharuddin (eds), International Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014. vol. 1660, 070127, American Institute of Physics Inc., International Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014, Penang, Malaysia, 28/05/14. https://doi.org/10.1063/1.4915844

Validation of numerical results of impact of viscoelastic slug and elastic rod through viscoelastic discontinuity analysis : Standard linear solid model. / Haji Musa, Abu Bakar.

International Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014. ed. / Mohammad Fadzli Ramli; Nurshazneem Roslan; Ahmad Kadri Junoh; Maz Jamilah Masnan; Mohammad Huskhazrin Kharuddin. Vol. 1660 American Institute of Physics Inc., 2015. 070127.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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T1 - Validation of numerical results of impact of viscoelastic slug and elastic rod through viscoelastic discontinuity analysis

T2 - Standard linear solid model

AU - Haji Musa, Abu Bakar

PY - 2015/5/15

Y1 - 2015/5/15

N2 - The study is about impact of a short elastic rod (or slug) on a stationary semi-infinite viscoelastic rod. The viscoelastic materials are modeled as standard linear solid which involve three material parameters and the motion is treated as one-dimensional. We first establish the governing equations pertaining to the impact of viscoelastic materials subject to certain boundary conditions for the case when an elastic slug moving at a speed V impacts a semi-infinite stationary viscoelastic rod. The objective is to validate the numerical results of stresses and velocities at the interface following wave transmissions and reflections in the slug after the impact using viscoelastic discontinuity. If the stress at the interface becomes tensile and the velocity changes its sign, then the slug and the rod part company. If the stress at the interface is compressive after the impact, the slug and the rod remain in contact. After modelling the impact and solve the governing system of partial differential equations in the Laplace transform domain, we invert the Laplace transformed solution numerically to obtain the stresses and velocities at the interface for several viscosity time constants and ratios of acoustic impedances. In inverting the Laplace transformed equations, we used the complex inversion formula because there is a branch cut and infinitely many poles within the Bromwich contour. In the viscoelastic discontinuity analysis, we look at the moving discontinuities in stress and velocity using the impulse-momentum relation and kinematical condition of compatibility. Finally, we discussed the relationship of the stresses and velocities using numeric and the validated stresses and velocities using viscoelastic discontinuity analysis.

AB - The study is about impact of a short elastic rod (or slug) on a stationary semi-infinite viscoelastic rod. The viscoelastic materials are modeled as standard linear solid which involve three material parameters and the motion is treated as one-dimensional. We first establish the governing equations pertaining to the impact of viscoelastic materials subject to certain boundary conditions for the case when an elastic slug moving at a speed V impacts a semi-infinite stationary viscoelastic rod. The objective is to validate the numerical results of stresses and velocities at the interface following wave transmissions and reflections in the slug after the impact using viscoelastic discontinuity. If the stress at the interface becomes tensile and the velocity changes its sign, then the slug and the rod part company. If the stress at the interface is compressive after the impact, the slug and the rod remain in contact. After modelling the impact and solve the governing system of partial differential equations in the Laplace transform domain, we invert the Laplace transformed solution numerically to obtain the stresses and velocities at the interface for several viscosity time constants and ratios of acoustic impedances. In inverting the Laplace transformed equations, we used the complex inversion formula because there is a branch cut and infinitely many poles within the Bromwich contour. In the viscoelastic discontinuity analysis, we look at the moving discontinuities in stress and velocity using the impulse-momentum relation and kinematical condition of compatibility. Finally, we discussed the relationship of the stresses and velocities using numeric and the validated stresses and velocities using viscoelastic discontinuity analysis.

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U2 - 10.1063/1.4915844

DO - 10.1063/1.4915844

M3 - Conference contribution

VL - 1660

BT - International Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014

A2 - Ramli, Mohammad Fadzli

A2 - Roslan, Nurshazneem

A2 - Junoh, Ahmad Kadri

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A2 - Kharuddin, Mohammad Huskhazrin

PB - American Institute of Physics Inc.

ER -

Haji Musa AB. Validation of numerical results of impact of viscoelastic slug and elastic rod through viscoelastic discontinuity analysis: Standard linear solid model. In Ramli MF, Roslan N, Junoh AK, Masnan MJ, Kharuddin MH, editors, International Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014. Vol. 1660. American Institute of Physics Inc. 2015. 070127 https://doi.org/10.1063/1.4915844