### Abstract

The study is about impact of a short viscoelastic 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 a viscoelastic slug moving at a speed V impacts a semi-infinite stationary viscoelastic rod. The objective is to investigate how the viscosity time constants in the slug and in the rod give rise to different interface stresses and interface velocities following wave transmission in the slug. After modeling the impact and solving 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. In inverting the Laplace transformed equations we used the complex inversion formula (Bromwich contour). In validating the numerical results, the method of multiple scales in perturbation is engaged to determine the first discontinuity jump at the interface. Finally, we discussed the relationship between the viscosity time constants, ratios of acoustic impedances and the results of the viscoelastic impacts obtained numerically and the predictions acquired using the multiple scales in perturbation.

Original language | English |
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Title of host publication | Proceedings of the 20th National Symposium on Mathematical Sciences, SKSM 2012 - Research in Mathematical Sciences |

Subtitle of host publication | A Catalyst for Creativity and Innovation |

Pages | 148-157 |

Number of pages | 10 |

Volume | 1522 |

DOIs | |

Publication status | Published - 06 May 2013 |

Event | 20th National Symposium on Mathematical Sciences - Research in Mathematical Sciences: A Catalyst for Creativity and Innovation, SKSM 2012 - Putrajaya, Malaysia Duration: 18 Dec 2012 → 20 Dec 2012 |

### Other

Other | 20th National Symposium on Mathematical Sciences - Research in Mathematical Sciences: A Catalyst for Creativity and Innovation, SKSM 2012 |
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Country | Malaysia |

City | Putrajaya |

Period | 18/12/12 → 20/12/12 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*Proceedings of the 20th National Symposium on Mathematical Sciences, SKSM 2012 - Research in Mathematical Sciences: A Catalyst for Creativity and Innovation*(Vol. 1522, pp. 148-157) https://doi.org/10.1063/1.4801118

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*Proceedings of the 20th National Symposium on Mathematical Sciences, SKSM 2012 - Research in Mathematical Sciences: A Catalyst for Creativity and Innovation.*vol. 1522, pp. 148-157, 20th National Symposium on Mathematical Sciences - Research in Mathematical Sciences: A Catalyst for Creativity and Innovation, SKSM 2012, Putrajaya, Malaysia, 18/12/12. https://doi.org/10.1063/1.4801118

**Validation of numerical solution of wave propagation in vicoeslastic material (standard linear solid model) through perturbation.** / Haji Musa, Abu Bakar.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Validation of numerical solution of wave propagation in vicoeslastic material (standard linear solid model) through perturbation

AU - Haji Musa, Abu Bakar

PY - 2013/5/6

Y1 - 2013/5/6

N2 - The study is about impact of a short viscoelastic 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 a viscoelastic slug moving at a speed V impacts a semi-infinite stationary viscoelastic rod. The objective is to investigate how the viscosity time constants in the slug and in the rod give rise to different interface stresses and interface velocities following wave transmission in the slug. After modeling the impact and solving 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. In inverting the Laplace transformed equations we used the complex inversion formula (Bromwich contour). In validating the numerical results, the method of multiple scales in perturbation is engaged to determine the first discontinuity jump at the interface. Finally, we discussed the relationship between the viscosity time constants, ratios of acoustic impedances and the results of the viscoelastic impacts obtained numerically and the predictions acquired using the multiple scales in perturbation.

AB - The study is about impact of a short viscoelastic 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 a viscoelastic slug moving at a speed V impacts a semi-infinite stationary viscoelastic rod. The objective is to investigate how the viscosity time constants in the slug and in the rod give rise to different interface stresses and interface velocities following wave transmission in the slug. After modeling the impact and solving 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. In inverting the Laplace transformed equations we used the complex inversion formula (Bromwich contour). In validating the numerical results, the method of multiple scales in perturbation is engaged to determine the first discontinuity jump at the interface. Finally, we discussed the relationship between the viscosity time constants, ratios of acoustic impedances and the results of the viscoelastic impacts obtained numerically and the predictions acquired using the multiple scales in perturbation.

UR - http://www.scopus.com/inward/record.url?scp=84876928932&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84876928932&partnerID=8YFLogxK

U2 - 10.1063/1.4801118

DO - 10.1063/1.4801118

M3 - Conference contribution

AN - SCOPUS:84876928932

SN - 9780735411500

VL - 1522

SP - 148

EP - 157

BT - Proceedings of the 20th National Symposium on Mathematical Sciences, SKSM 2012 - Research in Mathematical Sciences

ER -