The Behavior of Shear Waves in the Composite Multi-Material Structure with the Periodic Asymmetric Surfaces
The behavior of surface horizontally polarized shear waves (SH waves) in the composite multi-material structure with a periodic irregular surface and interface is investigated analytically in the present study. To unravel the enshrouded features of the SH-wave propagation in a multi-layer structure,...
Ausführliche Beschreibung
Autor*in: |
Uma Bharti [verfasserIn] Pramod Kumar Vaishnav [verfasserIn] Shao-Wen Yao [verfasserIn] Hijaz Ahmad [verfasserIn] |
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Format: |
E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2023 |
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Übergeordnetes Werk: |
In: Symmetry - MDPI AG, 2009, 15(2023), 2, p 491 |
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Übergeordnetes Werk: |
volume:15 ; year:2023 ; number:2, p 491 |
Links: |
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DOI / URN: |
10.3390/sym15020491 |
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Katalog-ID: |
DOAJ079962327 |
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520 | |a The behavior of surface horizontally polarized shear waves (SH waves) in the composite multi-material structure with a periodic irregular surface and interface is investigated analytically in the present study. To unravel the enshrouded features of the SH-wave propagation in a multi-layer structure, we consider a model of three distinct composite materials. In the schematic of the problem, the guiding layer (M-I) contains fluid-saturated porous materials of finite thickness, the intermediate layer (M-II) contains fiber-reinforced composites, and the substrate contains the functionally graded orthotropic materials (M-III). The free surface of M-I and the upper interface of the medium are considered to be irregular on a periodic basis, but the interface of M-II and M-III is supposed to be regular. The dispersion relation is obtained analytically and demonstrated graphically for the phase velocity versus the wave number to analyze the propagation behavior of the SH-wave propagation in the proposed structure. The acquired results resemble the typical Love wave results, confirming the validity of the present work. The current work provides a comprehensive evaluation of the impact of regular and irregular boundaries of the composite materials on the phase velocity of the SH waves. It is notable that the behavior of the reinforced parameters, initial stress, and porosity on the phase velocity is consistent in both scenarios. More than the irregularity of the free surface, the periodic irregularity of the interface had an impact on the phase velocity. The obtained results are useful to understand the compositions of the materials on the mountain surface. | ||
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10.3390/sym15020491 doi (DE-627)DOAJ079962327 (DE-599)DOAJ6573085eda494f0a9927acd95327d60b DE-627 ger DE-627 rakwb eng QA1-939 Uma Bharti verfasserin aut The Behavior of Shear Waves in the Composite Multi-Material Structure with the Periodic Asymmetric Surfaces 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The behavior of surface horizontally polarized shear waves (SH waves) in the composite multi-material structure with a periodic irregular surface and interface is investigated analytically in the present study. To unravel the enshrouded features of the SH-wave propagation in a multi-layer structure, we consider a model of three distinct composite materials. In the schematic of the problem, the guiding layer (M-I) contains fluid-saturated porous materials of finite thickness, the intermediate layer (M-II) contains fiber-reinforced composites, and the substrate contains the functionally graded orthotropic materials (M-III). The free surface of M-I and the upper interface of the medium are considered to be irregular on a periodic basis, but the interface of M-II and M-III is supposed to be regular. The dispersion relation is obtained analytically and demonstrated graphically for the phase velocity versus the wave number to analyze the propagation behavior of the SH-wave propagation in the proposed structure. The acquired results resemble the typical Love wave results, confirming the validity of the present work. The current work provides a comprehensive evaluation of the impact of regular and irregular boundaries of the composite materials on the phase velocity of the SH waves. It is notable that the behavior of the reinforced parameters, initial stress, and porosity on the phase velocity is consistent in both scenarios. More than the irregularity of the free surface, the periodic irregularity of the interface had an impact on the phase velocity. The obtained results are useful to understand the compositions of the materials on the mountain surface. shear waves porous material orthotropic material reinforced material periodic irregularity initial stress Mathematics Pramod Kumar Vaishnav verfasserin aut Shao-Wen Yao verfasserin aut Hijaz Ahmad verfasserin aut In Symmetry MDPI AG, 2009 15(2023), 2, p 491 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:15 year:2023 number:2, p 491 https://doi.org/10.3390/sym15020491 kostenfrei https://doaj.org/article/6573085eda494f0a9927acd95327d60b kostenfrei https://www.mdpi.com/2073-8994/15/2/491 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 15 2023 2, p 491 |
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10.3390/sym15020491 doi (DE-627)DOAJ079962327 (DE-599)DOAJ6573085eda494f0a9927acd95327d60b DE-627 ger DE-627 rakwb eng QA1-939 Uma Bharti verfasserin aut The Behavior of Shear Waves in the Composite Multi-Material Structure with the Periodic Asymmetric Surfaces 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The behavior of surface horizontally polarized shear waves (SH waves) in the composite multi-material structure with a periodic irregular surface and interface is investigated analytically in the present study. To unravel the enshrouded features of the SH-wave propagation in a multi-layer structure, we consider a model of three distinct composite materials. In the schematic of the problem, the guiding layer (M-I) contains fluid-saturated porous materials of finite thickness, the intermediate layer (M-II) contains fiber-reinforced composites, and the substrate contains the functionally graded orthotropic materials (M-III). The free surface of M-I and the upper interface of the medium are considered to be irregular on a periodic basis, but the interface of M-II and M-III is supposed to be regular. The dispersion relation is obtained analytically and demonstrated graphically for the phase velocity versus the wave number to analyze the propagation behavior of the SH-wave propagation in the proposed structure. The acquired results resemble the typical Love wave results, confirming the validity of the present work. The current work provides a comprehensive evaluation of the impact of regular and irregular boundaries of the composite materials on the phase velocity of the SH waves. It is notable that the behavior of the reinforced parameters, initial stress, and porosity on the phase velocity is consistent in both scenarios. More than the irregularity of the free surface, the periodic irregularity of the interface had an impact on the phase velocity. The obtained results are useful to understand the compositions of the materials on the mountain surface. shear waves porous material orthotropic material reinforced material periodic irregularity initial stress Mathematics Pramod Kumar Vaishnav verfasserin aut Shao-Wen Yao verfasserin aut Hijaz Ahmad verfasserin aut In Symmetry MDPI AG, 2009 15(2023), 2, p 491 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:15 year:2023 number:2, p 491 https://doi.org/10.3390/sym15020491 kostenfrei https://doaj.org/article/6573085eda494f0a9927acd95327d60b kostenfrei https://www.mdpi.com/2073-8994/15/2/491 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 15 2023 2, p 491 |
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10.3390/sym15020491 doi (DE-627)DOAJ079962327 (DE-599)DOAJ6573085eda494f0a9927acd95327d60b DE-627 ger DE-627 rakwb eng QA1-939 Uma Bharti verfasserin aut The Behavior of Shear Waves in the Composite Multi-Material Structure with the Periodic Asymmetric Surfaces 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The behavior of surface horizontally polarized shear waves (SH waves) in the composite multi-material structure with a periodic irregular surface and interface is investigated analytically in the present study. To unravel the enshrouded features of the SH-wave propagation in a multi-layer structure, we consider a model of three distinct composite materials. In the schematic of the problem, the guiding layer (M-I) contains fluid-saturated porous materials of finite thickness, the intermediate layer (M-II) contains fiber-reinforced composites, and the substrate contains the functionally graded orthotropic materials (M-III). The free surface of M-I and the upper interface of the medium are considered to be irregular on a periodic basis, but the interface of M-II and M-III is supposed to be regular. The dispersion relation is obtained analytically and demonstrated graphically for the phase velocity versus the wave number to analyze the propagation behavior of the SH-wave propagation in the proposed structure. The acquired results resemble the typical Love wave results, confirming the validity of the present work. The current work provides a comprehensive evaluation of the impact of regular and irregular boundaries of the composite materials on the phase velocity of the SH waves. It is notable that the behavior of the reinforced parameters, initial stress, and porosity on the phase velocity is consistent in both scenarios. More than the irregularity of the free surface, the periodic irregularity of the interface had an impact on the phase velocity. The obtained results are useful to understand the compositions of the materials on the mountain surface. shear waves porous material orthotropic material reinforced material periodic irregularity initial stress Mathematics Pramod Kumar Vaishnav verfasserin aut Shao-Wen Yao verfasserin aut Hijaz Ahmad verfasserin aut In Symmetry MDPI AG, 2009 15(2023), 2, p 491 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:15 year:2023 number:2, p 491 https://doi.org/10.3390/sym15020491 kostenfrei https://doaj.org/article/6573085eda494f0a9927acd95327d60b kostenfrei https://www.mdpi.com/2073-8994/15/2/491 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 15 2023 2, p 491 |
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10.3390/sym15020491 doi (DE-627)DOAJ079962327 (DE-599)DOAJ6573085eda494f0a9927acd95327d60b DE-627 ger DE-627 rakwb eng QA1-939 Uma Bharti verfasserin aut The Behavior of Shear Waves in the Composite Multi-Material Structure with the Periodic Asymmetric Surfaces 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The behavior of surface horizontally polarized shear waves (SH waves) in the composite multi-material structure with a periodic irregular surface and interface is investigated analytically in the present study. To unravel the enshrouded features of the SH-wave propagation in a multi-layer structure, we consider a model of three distinct composite materials. In the schematic of the problem, the guiding layer (M-I) contains fluid-saturated porous materials of finite thickness, the intermediate layer (M-II) contains fiber-reinforced composites, and the substrate contains the functionally graded orthotropic materials (M-III). The free surface of M-I and the upper interface of the medium are considered to be irregular on a periodic basis, but the interface of M-II and M-III is supposed to be regular. The dispersion relation is obtained analytically and demonstrated graphically for the phase velocity versus the wave number to analyze the propagation behavior of the SH-wave propagation in the proposed structure. The acquired results resemble the typical Love wave results, confirming the validity of the present work. The current work provides a comprehensive evaluation of the impact of regular and irregular boundaries of the composite materials on the phase velocity of the SH waves. It is notable that the behavior of the reinforced parameters, initial stress, and porosity on the phase velocity is consistent in both scenarios. More than the irregularity of the free surface, the periodic irregularity of the interface had an impact on the phase velocity. The obtained results are useful to understand the compositions of the materials on the mountain surface. shear waves porous material orthotropic material reinforced material periodic irregularity initial stress Mathematics Pramod Kumar Vaishnav verfasserin aut Shao-Wen Yao verfasserin aut Hijaz Ahmad verfasserin aut In Symmetry MDPI AG, 2009 15(2023), 2, p 491 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:15 year:2023 number:2, p 491 https://doi.org/10.3390/sym15020491 kostenfrei https://doaj.org/article/6573085eda494f0a9927acd95327d60b kostenfrei https://www.mdpi.com/2073-8994/15/2/491 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 15 2023 2, p 491 |
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10.3390/sym15020491 doi (DE-627)DOAJ079962327 (DE-599)DOAJ6573085eda494f0a9927acd95327d60b DE-627 ger DE-627 rakwb eng QA1-939 Uma Bharti verfasserin aut The Behavior of Shear Waves in the Composite Multi-Material Structure with the Periodic Asymmetric Surfaces 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The behavior of surface horizontally polarized shear waves (SH waves) in the composite multi-material structure with a periodic irregular surface and interface is investigated analytically in the present study. To unravel the enshrouded features of the SH-wave propagation in a multi-layer structure, we consider a model of three distinct composite materials. In the schematic of the problem, the guiding layer (M-I) contains fluid-saturated porous materials of finite thickness, the intermediate layer (M-II) contains fiber-reinforced composites, and the substrate contains the functionally graded orthotropic materials (M-III). The free surface of M-I and the upper interface of the medium are considered to be irregular on a periodic basis, but the interface of M-II and M-III is supposed to be regular. The dispersion relation is obtained analytically and demonstrated graphically for the phase velocity versus the wave number to analyze the propagation behavior of the SH-wave propagation in the proposed structure. The acquired results resemble the typical Love wave results, confirming the validity of the present work. The current work provides a comprehensive evaluation of the impact of regular and irregular boundaries of the composite materials on the phase velocity of the SH waves. It is notable that the behavior of the reinforced parameters, initial stress, and porosity on the phase velocity is consistent in both scenarios. More than the irregularity of the free surface, the periodic irregularity of the interface had an impact on the phase velocity. The obtained results are useful to understand the compositions of the materials on the mountain surface. shear waves porous material orthotropic material reinforced material periodic irregularity initial stress Mathematics Pramod Kumar Vaishnav verfasserin aut Shao-Wen Yao verfasserin aut Hijaz Ahmad verfasserin aut In Symmetry MDPI AG, 2009 15(2023), 2, p 491 (DE-627)610604112 (DE-600)2518382-5 20738994 nnns volume:15 year:2023 number:2, p 491 https://doi.org/10.3390/sym15020491 kostenfrei https://doaj.org/article/6573085eda494f0a9927acd95327d60b kostenfrei https://www.mdpi.com/2073-8994/15/2/491 kostenfrei https://doaj.org/toc/2073-8994 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 15 2023 2, p 491 |
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The behavior of surface horizontally polarized shear waves (SH waves) in the composite multi-material structure with a periodic irregular surface and interface is investigated analytically in the present study. To unravel the enshrouded features of the SH-wave propagation in a multi-layer structure, we consider a model of three distinct composite materials. In the schematic of the problem, the guiding layer (M-I) contains fluid-saturated porous materials of finite thickness, the intermediate layer (M-II) contains fiber-reinforced composites, and the substrate contains the functionally graded orthotropic materials (M-III). The free surface of M-I and the upper interface of the medium are considered to be irregular on a periodic basis, but the interface of M-II and M-III is supposed to be regular. The dispersion relation is obtained analytically and demonstrated graphically for the phase velocity versus the wave number to analyze the propagation behavior of the SH-wave propagation in the proposed structure. The acquired results resemble the typical Love wave results, confirming the validity of the present work. The current work provides a comprehensive evaluation of the impact of regular and irregular boundaries of the composite materials on the phase velocity of the SH waves. It is notable that the behavior of the reinforced parameters, initial stress, and porosity on the phase velocity is consistent in both scenarios. More than the irregularity of the free surface, the periodic irregularity of the interface had an impact on the phase velocity. The obtained results are useful to understand the compositions of the materials on the mountain surface. |
abstractGer |
The behavior of surface horizontally polarized shear waves (SH waves) in the composite multi-material structure with a periodic irregular surface and interface is investigated analytically in the present study. To unravel the enshrouded features of the SH-wave propagation in a multi-layer structure, we consider a model of three distinct composite materials. In the schematic of the problem, the guiding layer (M-I) contains fluid-saturated porous materials of finite thickness, the intermediate layer (M-II) contains fiber-reinforced composites, and the substrate contains the functionally graded orthotropic materials (M-III). The free surface of M-I and the upper interface of the medium are considered to be irregular on a periodic basis, but the interface of M-II and M-III is supposed to be regular. The dispersion relation is obtained analytically and demonstrated graphically for the phase velocity versus the wave number to analyze the propagation behavior of the SH-wave propagation in the proposed structure. The acquired results resemble the typical Love wave results, confirming the validity of the present work. The current work provides a comprehensive evaluation of the impact of regular and irregular boundaries of the composite materials on the phase velocity of the SH waves. It is notable that the behavior of the reinforced parameters, initial stress, and porosity on the phase velocity is consistent in both scenarios. More than the irregularity of the free surface, the periodic irregularity of the interface had an impact on the phase velocity. The obtained results are useful to understand the compositions of the materials on the mountain surface. |
abstract_unstemmed |
The behavior of surface horizontally polarized shear waves (SH waves) in the composite multi-material structure with a periodic irregular surface and interface is investigated analytically in the present study. To unravel the enshrouded features of the SH-wave propagation in a multi-layer structure, we consider a model of three distinct composite materials. In the schematic of the problem, the guiding layer (M-I) contains fluid-saturated porous materials of finite thickness, the intermediate layer (M-II) contains fiber-reinforced composites, and the substrate contains the functionally graded orthotropic materials (M-III). The free surface of M-I and the upper interface of the medium are considered to be irregular on a periodic basis, but the interface of M-II and M-III is supposed to be regular. The dispersion relation is obtained analytically and demonstrated graphically for the phase velocity versus the wave number to analyze the propagation behavior of the SH-wave propagation in the proposed structure. The acquired results resemble the typical Love wave results, confirming the validity of the present work. The current work provides a comprehensive evaluation of the impact of regular and irregular boundaries of the composite materials on the phase velocity of the SH waves. It is notable that the behavior of the reinforced parameters, initial stress, and porosity on the phase velocity is consistent in both scenarios. More than the irregularity of the free surface, the periodic irregularity of the interface had an impact on the phase velocity. The obtained results are useful to understand the compositions of the materials on the mountain surface. |
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The current work provides a comprehensive evaluation of the impact of regular and irregular boundaries of the composite materials on the phase velocity of the SH waves. It is notable that the behavior of the reinforced parameters, initial stress, and porosity on the phase velocity is consistent in both scenarios. More than the irregularity of the free surface, the periodic irregularity of the interface had an impact on the phase velocity. 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