Parametric Study on the Sensitivity of Different Properties of Waves Propagating through an Incompressible Medium
This article deals with the study of disturbance that travels through the transversely isotropic medium in the form of waves. The particles of the considered medium have an additional property of small-scale internal rotation along with macroscopic translational deformation. This extra translational...
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| Format: | Article |
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MDPI AG
2023-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/8/1946 |
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| author | Muhammad Aamir Weaam Alhejaili Khalid Lotfy Alaa A. El-Bary Adnan Jahangir |
| author_facet | Muhammad Aamir Weaam Alhejaili Khalid Lotfy Alaa A. El-Bary Adnan Jahangir |
| author_sort | Muhammad Aamir |
| collection | DOAJ |
| description | This article deals with the study of disturbance that travels through the transversely isotropic medium in the form of waves. The particles of the considered medium have an additional property of small-scale internal rotation along with macroscopic translational deformation. This extra translational freedom causes the medium to be micropolar in nature. Along with this, the medium is incompressible, and the dispersion relation of waves propagating through the medium is obtained under specific plan-strain conditions. From the dispersion relation, we can conclude that because of incompressibility, three transverse waves propagate through the medium. The velocity profile, attenuation coefficient, and specific heat loss for these waves are discussed for a particular medium. Later, the special normalized local sensitivity analysis (NLSA) technique is used to depict the effects of parameters on the outcomes of the mathematical model. The obtained results are represented graphically for a particular medium. The proposed model is used to model the mechanical behavior of complex materials with microstructural heterogeneity, such as composites and biological tissues. |
| first_indexed | 2024-03-11T04:46:55Z |
| format | Article |
| id | doaj.art-9f02d623e0a345ae976207a7f1fb7cb2 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T04:46:55Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9f02d623e0a345ae976207a7f1fb7cb22023-11-17T20:18:52ZengMDPI AGMathematics2227-73902023-04-01118194610.3390/math11081946Parametric Study on the Sensitivity of Different Properties of Waves Propagating through an Incompressible MediumMuhammad Aamir0Weaam Alhejaili1Khalid Lotfy2Alaa A. El-Bary3Adnan Jahangir4Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, PakistanDepartment of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, EgyptArab Academy for Science, Technology and Maritime Transport, P.O. Box 1029, Alexandria 5528341, EgyptDepartment of Mathematics, COMSATS University Islamabad, Wah Campus, Wah 47040, PakistanThis article deals with the study of disturbance that travels through the transversely isotropic medium in the form of waves. The particles of the considered medium have an additional property of small-scale internal rotation along with macroscopic translational deformation. This extra translational freedom causes the medium to be micropolar in nature. Along with this, the medium is incompressible, and the dispersion relation of waves propagating through the medium is obtained under specific plan-strain conditions. From the dispersion relation, we can conclude that because of incompressibility, three transverse waves propagate through the medium. The velocity profile, attenuation coefficient, and specific heat loss for these waves are discussed for a particular medium. Later, the special normalized local sensitivity analysis (NLSA) technique is used to depict the effects of parameters on the outcomes of the mathematical model. The obtained results are represented graphically for a particular medium. The proposed model is used to model the mechanical behavior of complex materials with microstructural heterogeneity, such as composites and biological tissues.https://www.mdpi.com/2227-7390/11/8/1946micropolarincompressiblenormalized local sensitivity analysissecular equation |
| spellingShingle | Muhammad Aamir Weaam Alhejaili Khalid Lotfy Alaa A. El-Bary Adnan Jahangir Parametric Study on the Sensitivity of Different Properties of Waves Propagating through an Incompressible Medium Mathematics micropolar incompressible normalized local sensitivity analysis secular equation |
| title | Parametric Study on the Sensitivity of Different Properties of Waves Propagating through an Incompressible Medium |
| title_full | Parametric Study on the Sensitivity of Different Properties of Waves Propagating through an Incompressible Medium |
| title_fullStr | Parametric Study on the Sensitivity of Different Properties of Waves Propagating through an Incompressible Medium |
| title_full_unstemmed | Parametric Study on the Sensitivity of Different Properties of Waves Propagating through an Incompressible Medium |
| title_short | Parametric Study on the Sensitivity of Different Properties of Waves Propagating through an Incompressible Medium |
| title_sort | parametric study on the sensitivity of different properties of waves propagating through an incompressible medium |
| topic | micropolar incompressible normalized local sensitivity analysis secular equation |
| url | https://www.mdpi.com/2227-7390/11/8/1946 |
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