Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-05T14:26:07.913Z Has data issue: false hasContentIssue false
  • English
  • Français

Reflection of Longitudinal Micro-Rotational Wave at Viscoelastically Supported Boundary of Micropolar Half-Space

Published online by Cambridge University Press:  27 October 2016

P. Zhang ,
P.-J. Wei  and
Y.-Q. Li
P. Zhang
Affiliation:
Department of Applied MechanicsUniversity of Science and Technology BeijingBeijing, China
P.-J. Wei*
Affiliation:
Department of Applied MechanicsUniversity of Science and Technology BeijingBeijing, China
Y.-Q. Li
Affiliation:
Department of MathematicsQiqihar UniversityQiqihar, China
*
*Corresponding author ([email protected])
Get access

Abstract

The reflection of longitudinal micro-rotational wave at the viscoelastically supported boundary of micropolar half-space is studied in this paper. The viscoelastic boundary is described by spring-dashpot model with parallel or serial connection. Both the spring and the dashpot contribute to the displacements and micro-rotation and the boundary conditions include the force stress and couple stress components. From the boundary conditions, the amplitude ratios and phase shifts of reflection waves with respect to the incident wave are obtained. Further, the energy flux ratios of the reflection waves to the incident wave are estimated. In order to validate the numerical results, the energy flux conservation with consideration of the energy dissipation of dashpot is used. Based on the numerical results, the influences of elastic parameters and viscous parameters are studied, respectively. It is found that the elastic parameters and the viscous parameters have evident influences on the amplitude ratio, the phase shift and the energy partition. The causes resulting in these deviations are related with the instantaneous elasticity of spring and the time-delay effects of dashpot.

Keywords

Micropolar solidViscoelastic boundaryPhase shiftReflection Ratio
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 3 , June 2018 , pp. 243 - 255
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Eringen, A. C., “Linear theory of micropolar elasticity,” Indiana University Mathematics Journal, 15, pp. 909–923 (1966).CrossRefGoogle Scholar
2. Parfitt, V. R. and Eringen, A. C., “Reflection of plane waves from the flat boundary of a micropolar elastic half-space,” The Journal of the Acoustical Society of America, 45, pp. 1258–1272 (1969).Google Scholar
3. Ariman, T., “Wave propagation in a micropolar elastic half-space,” Acta Mechanica, 13, pp. 11–20 (1972).CrossRefGoogle Scholar
4. Tomar, S. K., Kumar, R. and Kaushik, V. P., “Wave propagation of micropolar elastic medium with stretch,” International Journal of Engineering Science, 36, pp. 683–698 (1998).Google Scholar
5. Kumar, R. and Singh, B., “Reflection of plane waves from the flat boundary of a micropolar generalized thermoelastic half-space with stretch,” Indian Journal of Pure and Applied Mathematics, 29, pp. 657–669 (1998).Google Scholar
6. Singh, B. and Kumar, R., “Reflection of plane waves from the flat boundary of a micropolar generalized thermoelastic half-space,” International Journal of Engineering Science, 36, pp. 865–890 (1998).Google Scholar
7. Kumar, R., “Wave propagation in micropolar viscoelastic generalized thermoelastic solid,” International Journal of Engineering Science, 38, pp. 1377–1395 (2000).Google Scholar
8. Tomar, S. K. and Gogna, M. L., “Reflection and refraction of a longitudinal microrotational wave at an interface between two micropolar elastic solids in welded contact,” International Journal of Engineering Science, 30, pp. 1637–1646 (1992).Google Scholar
9. Tomar, S. K. and Gogna, M. L., “Reflection and refraction of coupled transverse and micro-rotational waves at an interface between two different micropolar elastic media in welded contact,” International Journal of Engineering Science, 33, pp. 485–496 (1995).CrossRefGoogle Scholar
10. Tomar, S. K. and Kumar, R., “Wave propagation at liquid/micropolar elastic solid interface,” Journal of Sound and Vibration, 222, pp. 858–869 (1999).Google Scholar
11. Singh, B., “Reflection of plane sound wave from a micropolar generalized thermoelastic solid half-space,” Journal of Sound and Vibration, 235, pp. 685–696 (2000).Google Scholar
12. Singh, B., “Wave propagation in an orthotropic micropolar elastic solid,” International Journal of Solids and Structures, 44, pp. 3638–3645 (2007).Google Scholar
13. Chiriţă, S. and Ghiba, I. D., “Rayleigh waves in Cosserat elastic materials,” International Journal of Engineering Science, 51, pp. 117–127 (2012).CrossRefGoogle Scholar
14. Murty, G. S., “Reflection, transmission and attenuation of elastic waves at a loosely-bonded interface of two half spaces,” Geophysical Journal International, 44, pp. 389–404 (1976).CrossRefGoogle Scholar
15. Schoenberg, M., “Elastic wave behavior across linear slip interfaces,” The Journal of the Acoustical Society of America, 68, pp. 1516–1521 (1980).CrossRefGoogle Scholar
16. Kumar, R. and Singh, B., “Reflection and transmission of elastic waves at a loosely bonded interface between an elastic and micropolar elastic solid,” Indian Journal of Pure and Applied Mathematics, 28, pp. 1133–115 (1997).Google Scholar
17. Singh, B. and Kumar, R., “Reflection and refraction of micropolar elastic waves at a loosely bonded interface between viscoelastic solid and micropolar elastic solid,” International Journal of Engineering Science, 36, pp. 101–117 (1998).CrossRefGoogle Scholar
18. Kumar, R., Sharma, N. and Ram, P., “Reflection and transmission of micropolar elastic waves at an imperfect boundary,” Multidiscipline Modeling in Materials and Structures, 4, pp. 15–36 (2008).Google Scholar
19. Kumar, R., Kaur, M. and Rajvanshi, S. C., “Propagation of waves at an imperfect boundary between heat conducting micropolar thermoelastic solid and fluid media,” Multidiscipline Modeling in Materials and Structures, 8, pp. 63–95 (2012).CrossRefGoogle Scholar
20. Sharma, K. and Marin, M., “Reflection and transmission of waves from imperfect boundary between two heat conducting micropolar thermoelastic solids,” Analele Stiintifice ale Universitatii Ovidius Constanta, 22, pp. 151–175 (2014).Google Scholar
21. Zhang, P., Wei, P. and Tang, Q., “Reflection of micropolar elastic waves at the non-free surface of a micropolar elastic half-space,” Acta Mechanica, 226, pp. 2925–2937 (2015).Google Scholar
22. Higdon, R. L., “Absorbing boundary conditions for elastic waves,” Geophysics, 56, pp. 231–241 (1991).CrossRefGoogle Scholar
23. Kim, H. S., “A Study on the Performance of Absorbing Boundaries Using Dashpot,” Engineering, 6, pp. 593–600 (2014).Google Scholar
24. Kim, H. S., “Finite Element Analysis with paraxial & viscous boundary conditions for elastic wave propagation,” Engineering, 4, pp. 843–849 (2012).Google Scholar
25. Liu, J., et al., “3D viscous-spring artificial boundary in time domain,” Earthquake Engineering and Engineering Vibration, 5, pp. 93–102 (2006).Google Scholar
26. Liu, J. and Li, B., “A unified viscous-spring artificial boundary for 3-D static and dynamic applications,” Science in China Series E Engineering & Materials Science, 48, pp. 570–584 (2005).Google Scholar
27. Kari, L., et al., “Constrained polymer layers to reduce noise: reality or fiction?—An experimental inquiry into their effectiveness,” PolymerTesting, 21, pp. 949–958 (2002).Google Scholar
28. Jones, D. I. G., Handbook of Viscoelastic Vibration Damping, Baffins Lane, Chichester (2001).Google Scholar
29. Martinez-Agirre, M. and Elejabarrieta, M. J., “Characterisation and modelling of viscoelastically damped sandwich structures,” International Journal of Mechanical Sciences, 52, pp. 1225–1233 (2010).Google Scholar
30. Gauthier, R. D., Mechanics of Micropolar Media, World Scientific, Singapore, pp. 395–463 (1982).Google Scholar