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Abstract
This research was based on showing how the relationship of the perturbation method to the wave function entering the dispersive medium area. Disperse medium is a medium where when the wave enters the area, it experiences changes in wave shape and wave energy. The purpose of this study is to show how the perturbation method can be reduced to a term that is still linear with the assumption that the next term is very small so that the wave term is still linear to the wave change. This research is qualitative research. The place of this research is at the TD Pardede Institute of Science and Technology. From the analysis in this study, it was found that the wave experienced a decreasing intensity towards the depth of the dispersive medium with the assumption that the attenuation coefficient ( ) was still continuous along the depth of the material passed by the wave. In the case of seismic waves when the wave moves through the medium, its intensity decreases with distance. The presence of disturbances in the layer passed by the wave causes the shift of the material to experience a disturbance characteristic where the wave amplitude is getting smaller. This is because the absorption of wave energy by the particles of the dispersive medium continues to experience attenuation.
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Copyright (c) 2025 Sumihar Simangunsong
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How to Cite
Linier Perturbation Method Analytic Shear Wave Propagation In A Dispersive Medium. (2025). PENDIPA Journal of Science Education, 9(1), 40–45. https://doi.org/10.33369/pendipa.9.1.40-45
References
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Aleksandra Risteska, & Vlado Gicev. (2018). The Response of a Shear Beam as 1D Medium to Seismic Excitations Dependent on the Boundary Conditions. Journal of Geological Resource and Engineering, 6(4), 135–142. https://doi.org/10.17265/2328-2193/2018.04.001
Aziman, M., Hazreek, Z. A. M., Azhar, A. T. S., & Haimi, D. S. (2016). Compressive and Shear Wave Velocity Profiles using Seismic Refraction Technique. Journal of Physics: Conference Series, 710(1). https://doi.org/10.1088/1742-6596/710/1/012011
Cáceres, M. O. (2021). Gravity waves on a random bottom: exact dispersion-relation. Waves in Random and Complex Media, June. https://doi.org/10.1080/17455030.2021.1918795
Cornille, P., Atomic, F., & Commission, E. (2011). Essays on The Formal Aspects of Electromagnetic Theory. Essays on The Formal Aspects of Electromagnetic Theory, November. https://doi.org/10.1142/9789814360005
Donà, M., Lombardo, M., & Barone, G. (2015). An experimental study of wave propagation in heterogeneous materials. Civil-Comp Proceedings, September 2020. https://doi.org/10.4203/ccp.108.208
Fang, L., & Leamy, M. J. (2024). A perturbation approach for predicting wave propagation at the spatial interface of linear and nonlinear one-dimensional lattice structures. Nonlinear Dynamics, 112(7), 5015–5036. https://doi.org/10.1007/s11071-024-09303-6
Guo, F., Dong, Y., Wang, Y., Zhang, X., & Su, Q. (2023). Estimation of wave velocity and analysis of dispersion characteristics based on wavelet decomposition. Vibroengineering Procedia, 53, 20–26. https://doi.org/10.21595/vp.2023.23749
Hou, Z., Okamoto, R. J., & Bayly, P. V. (2020). Shear Wave Propagation and Estimation of Material Parameters in a Nonlinear, Fibrous Material. Journal of Biomechanical Engineering, 142(5), 1–10. https://doi.org/10.1115/1.4044504
Leng, K., Chintanapakdee, C., & Hayashikawa, T. (2014). Seismic Shear Forces in Shear Walls of a Medium-Rise Building Designed by Response Spectrum Analysis. Engineering Journal, 18(4), 73–95. https://doi.org/10.4186/ej.2014.18.4.73
Luo, G., Cheng, P., Yu, Y., Geng, X., Zhao, Y., Xia, Y., Zhang, R., & Shen, Q. (2023). Influence on Elastic Wave Propagation Behavior in Polymers Composites: An Analysis of Inflection Phenomena. Polymers, 15(7). https://doi.org/10.3390/polym15071680
Lutedx, T. R. (2016). domain techniques Electromagnetic wave propagation in Department of Electroscience Lund Institute of Technology.
Magrini, F., & Boschi, L. (2021). Surface-Wave Attenuation From Seismic Ambient Noise: Numerical Validation and Application. Journal of Geophysical Research: Solid Earth, 126(1), 1–20. https://doi.org/10.1029/2020JB019865
Man, X., Luo, Z., Liu, J., & Xia, B. (2019). Hilbert fractal acoustic metamaterials with negative mass density and bulk modulus on subwavelength scale. Materials and Design, 180, 107911. https://doi.org/10.1016/j.matdes.2019.107911
Mari, J.-L. (2019). Chapter 1 Wave propagation. Seismic Imaging: A Practical Approach, 17–34. https://doi.org/10.1051/978-2-7598-2351-2.c003
Ridolfi, L., Torino, P., & Torino, P. (2015). Green ’ s Function of the Linearized de Saint- Venant Equations Green ’ s Function of the Linearized de Saint-Venant Equations. 9399(August). https://doi.org/10.1061/(ASCE)0733-9399(2006)132
Saydalimov, A. S. (2022). Experimental studying the propagation and absorption of electromagnetic waves on various rock-forming minerals in Uzbekistan. IOP Conference Series: Earth and Environmental Science, 1068(1). https://doi.org/10.1088/1755-1315/1068/1/012002
Shen, W., Ritzwoller, M. H., Kang, D., Kim, Y. H., Lin, F. C., Ning, J., Wang, W., Zheng, Y., & Zhou, L. (2016). A seismic reference model for the crust and uppermost mantle beneath China from surface wave dispersion. Geophysical Journal International, 206(2), 954–979. https://doi.org/10.1093/gji/ggw175
Zvietcovich, F., Helguera, M., Dalecki, D., Parker, K. J., Rolland, J. P., Grygotis, E., & Wayson, S. (2018). Viscoelastic characterization of dispersive media by inversion of a general wave propagation model in optical coherence elastography. 10496, 24. https://doi.org/10.1117/12.2287553
References
Aleksandra Risteska, & Vlado Gicev. (2018). The Response of a Shear Beam as 1D Medium to Seismic Excitations Dependent on the Boundary Conditions. Journal of Geological Resource and Engineering, 6(4), 135–142. https://doi.org/10.17265/2328-2193/2018.04.001
Aziman, M., Hazreek, Z. A. M., Azhar, A. T. S., & Haimi, D. S. (2016). Compressive and Shear Wave Velocity Profiles using Seismic Refraction Technique. Journal of Physics: Conference Series, 710(1). https://doi.org/10.1088/1742-6596/710/1/012011
Cáceres, M. O. (2021). Gravity waves on a random bottom: exact dispersion-relation. Waves in Random and Complex Media, June. https://doi.org/10.1080/17455030.2021.1918795
Cornille, P., Atomic, F., & Commission, E. (2011). Essays on The Formal Aspects of Electromagnetic Theory. Essays on The Formal Aspects of Electromagnetic Theory, November. https://doi.org/10.1142/9789814360005
Donà, M., Lombardo, M., & Barone, G. (2015). An experimental study of wave propagation in heterogeneous materials. Civil-Comp Proceedings, September 2020. https://doi.org/10.4203/ccp.108.208
Fang, L., & Leamy, M. J. (2024). A perturbation approach for predicting wave propagation at the spatial interface of linear and nonlinear one-dimensional lattice structures. Nonlinear Dynamics, 112(7), 5015–5036. https://doi.org/10.1007/s11071-024-09303-6
Guo, F., Dong, Y., Wang, Y., Zhang, X., & Su, Q. (2023). Estimation of wave velocity and analysis of dispersion characteristics based on wavelet decomposition. Vibroengineering Procedia, 53, 20–26. https://doi.org/10.21595/vp.2023.23749
Hou, Z., Okamoto, R. J., & Bayly, P. V. (2020). Shear Wave Propagation and Estimation of Material Parameters in a Nonlinear, Fibrous Material. Journal of Biomechanical Engineering, 142(5), 1–10. https://doi.org/10.1115/1.4044504
Leng, K., Chintanapakdee, C., & Hayashikawa, T. (2014). Seismic Shear Forces in Shear Walls of a Medium-Rise Building Designed by Response Spectrum Analysis. Engineering Journal, 18(4), 73–95. https://doi.org/10.4186/ej.2014.18.4.73
Luo, G., Cheng, P., Yu, Y., Geng, X., Zhao, Y., Xia, Y., Zhang, R., & Shen, Q. (2023). Influence on Elastic Wave Propagation Behavior in Polymers Composites: An Analysis of Inflection Phenomena. Polymers, 15(7). https://doi.org/10.3390/polym15071680
Lutedx, T. R. (2016). domain techniques Electromagnetic wave propagation in Department of Electroscience Lund Institute of Technology.
Magrini, F., & Boschi, L. (2021). Surface-Wave Attenuation From Seismic Ambient Noise: Numerical Validation and Application. Journal of Geophysical Research: Solid Earth, 126(1), 1–20. https://doi.org/10.1029/2020JB019865
Man, X., Luo, Z., Liu, J., & Xia, B. (2019). Hilbert fractal acoustic metamaterials with negative mass density and bulk modulus on subwavelength scale. Materials and Design, 180, 107911. https://doi.org/10.1016/j.matdes.2019.107911
Mari, J.-L. (2019). Chapter 1 Wave propagation. Seismic Imaging: A Practical Approach, 17–34. https://doi.org/10.1051/978-2-7598-2351-2.c003
Ridolfi, L., Torino, P., & Torino, P. (2015). Green ’ s Function of the Linearized de Saint- Venant Equations Green ’ s Function of the Linearized de Saint-Venant Equations. 9399(August). https://doi.org/10.1061/(ASCE)0733-9399(2006)132
Saydalimov, A. S. (2022). Experimental studying the propagation and absorption of electromagnetic waves on various rock-forming minerals in Uzbekistan. IOP Conference Series: Earth and Environmental Science, 1068(1). https://doi.org/10.1088/1755-1315/1068/1/012002
Shen, W., Ritzwoller, M. H., Kang, D., Kim, Y. H., Lin, F. C., Ning, J., Wang, W., Zheng, Y., & Zhou, L. (2016). A seismic reference model for the crust and uppermost mantle beneath China from surface wave dispersion. Geophysical Journal International, 206(2), 954–979. https://doi.org/10.1093/gji/ggw175
Zvietcovich, F., Helguera, M., Dalecki, D., Parker, K. J., Rolland, J. P., Grygotis, E., & Wayson, S. (2018). Viscoelastic characterization of dispersive media by inversion of a general wave propagation model in optical coherence elastography. 10496, 24. https://doi.org/10.1117/12.2287553
Aziman, M., Hazreek, Z. A. M., Azhar, A. T. S., & Haimi, D. S. (2016). Compressive and Shear Wave Velocity Profiles using Seismic Refraction Technique. Journal of Physics: Conference Series, 710(1). https://doi.org/10.1088/1742-6596/710/1/012011
Cáceres, M. O. (2021). Gravity waves on a random bottom: exact dispersion-relation. Waves in Random and Complex Media, June. https://doi.org/10.1080/17455030.2021.1918795
Cornille, P., Atomic, F., & Commission, E. (2011). Essays on The Formal Aspects of Electromagnetic Theory. Essays on The Formal Aspects of Electromagnetic Theory, November. https://doi.org/10.1142/9789814360005
Donà, M., Lombardo, M., & Barone, G. (2015). An experimental study of wave propagation in heterogeneous materials. Civil-Comp Proceedings, September 2020. https://doi.org/10.4203/ccp.108.208
Fang, L., & Leamy, M. J. (2024). A perturbation approach for predicting wave propagation at the spatial interface of linear and nonlinear one-dimensional lattice structures. Nonlinear Dynamics, 112(7), 5015–5036. https://doi.org/10.1007/s11071-024-09303-6
Guo, F., Dong, Y., Wang, Y., Zhang, X., & Su, Q. (2023). Estimation of wave velocity and analysis of dispersion characteristics based on wavelet decomposition. Vibroengineering Procedia, 53, 20–26. https://doi.org/10.21595/vp.2023.23749
Hou, Z., Okamoto, R. J., & Bayly, P. V. (2020). Shear Wave Propagation and Estimation of Material Parameters in a Nonlinear, Fibrous Material. Journal of Biomechanical Engineering, 142(5), 1–10. https://doi.org/10.1115/1.4044504
Leng, K., Chintanapakdee, C., & Hayashikawa, T. (2014). Seismic Shear Forces in Shear Walls of a Medium-Rise Building Designed by Response Spectrum Analysis. Engineering Journal, 18(4), 73–95. https://doi.org/10.4186/ej.2014.18.4.73
Luo, G., Cheng, P., Yu, Y., Geng, X., Zhao, Y., Xia, Y., Zhang, R., & Shen, Q. (2023). Influence on Elastic Wave Propagation Behavior in Polymers Composites: An Analysis of Inflection Phenomena. Polymers, 15(7). https://doi.org/10.3390/polym15071680
Lutedx, T. R. (2016). domain techniques Electromagnetic wave propagation in Department of Electroscience Lund Institute of Technology.
Magrini, F., & Boschi, L. (2021). Surface-Wave Attenuation From Seismic Ambient Noise: Numerical Validation and Application. Journal of Geophysical Research: Solid Earth, 126(1), 1–20. https://doi.org/10.1029/2020JB019865
Man, X., Luo, Z., Liu, J., & Xia, B. (2019). Hilbert fractal acoustic metamaterials with negative mass density and bulk modulus on subwavelength scale. Materials and Design, 180, 107911. https://doi.org/10.1016/j.matdes.2019.107911
Mari, J.-L. (2019). Chapter 1 Wave propagation. Seismic Imaging: A Practical Approach, 17–34. https://doi.org/10.1051/978-2-7598-2351-2.c003
Ridolfi, L., Torino, P., & Torino, P. (2015). Green ’ s Function of the Linearized de Saint- Venant Equations Green ’ s Function of the Linearized de Saint-Venant Equations. 9399(August). https://doi.org/10.1061/(ASCE)0733-9399(2006)132
Saydalimov, A. S. (2022). Experimental studying the propagation and absorption of electromagnetic waves on various rock-forming minerals in Uzbekistan. IOP Conference Series: Earth and Environmental Science, 1068(1). https://doi.org/10.1088/1755-1315/1068/1/012002
Shen, W., Ritzwoller, M. H., Kang, D., Kim, Y. H., Lin, F. C., Ning, J., Wang, W., Zheng, Y., & Zhou, L. (2016). A seismic reference model for the crust and uppermost mantle beneath China from surface wave dispersion. Geophysical Journal International, 206(2), 954–979. https://doi.org/10.1093/gji/ggw175
Zvietcovich, F., Helguera, M., Dalecki, D., Parker, K. J., Rolland, J. P., Grygotis, E., & Wayson, S. (2018). Viscoelastic characterization of dispersive media by inversion of a general wave propagation model in optical coherence elastography. 10496, 24. https://doi.org/10.1117/12.2287553