Parametric Study on the Sensitivity of Different Properties of Waves Propagating through an Incompressible Medium

Muhammad Aamir, Weaam Alhejaili, Khalid Lotfy, Alaa A. El-Bary and Adnan Jahangir
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Muhammad Aamir: Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan
Weaam Alhejaili: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Khalid Lotfy: Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
Alaa A. El-Bary: Arab Academy for Science, Technology and Maritime Transport, P.O. Box 1029, Alexandria 5528341, Egypt
Adnan Jahangir: Department of Mathematics, COMSATS University Islamabad, Wah Campus, Wah 47040, Pakistan

Mathematics, 2023, vol. 11, issue 8, 1-13

Abstract: 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.

Keywords: micropolar; incompressible; normalized local sensitivity analysis; secular equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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