Investigating reflection phenomenon of plane waves in a fractional order thermoelastic rotating medium using nonlocal theory
Within the framework of fractional-order thermoelasticity, the propagation of elastic waves in non-local isotropic rotating medium has been considered. The frequency dispersion relation is derived by solving the governing equations in the x y -plane for the given problem. Three coupled quasi-waves h...
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| Published in | Mechanics of time-dependent materials Vol. 28; no. 3; pp. 1375 - 1393 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Dordrecht
Springer Netherlands
01.09.2024
Springer Nature B.V |
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| ISSN | 1385-2000 1573-2738 |
| DOI | 10.1007/s11043-024-09709-0 |
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| Abstract | Within the framework of fractional-order thermoelasticity, the propagation of elastic waves in non-local isotropic rotating medium has been considered. The frequency dispersion relation is derived by solving the governing equations in the
x
y
-plane for the given problem. Three coupled quasi-waves have been seen to move through this kind of medium at different rates. The Helmholtz decomposition theorem has been used to decompose the system into longitudinal and transverse components. Analytical computations are made for the waves’ related amplitude ratios and their speed. The amplitude ratios for the reflected waves are computed with the help of suitable boundary conditions. The impact of fractional order, rotational frequency, and non-local parameters on propagation speed and amplitude ratios has been studied and the same has been plotted graphically. In the absence of rotation, the prior findings mentioned in the literature are obtained as a specific case. |
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| AbstractList | Within the framework of fractional-order thermoelasticity, the propagation of elastic waves in non-local isotropic rotating medium has been considered. The frequency dispersion relation is derived by solving the governing equations in the
x
y
-plane for the given problem. Three coupled quasi-waves have been seen to move through this kind of medium at different rates. The Helmholtz decomposition theorem has been used to decompose the system into longitudinal and transverse components. Analytical computations are made for the waves’ related amplitude ratios and their speed. The amplitude ratios for the reflected waves are computed with the help of suitable boundary conditions. The impact of fractional order, rotational frequency, and non-local parameters on propagation speed and amplitude ratios has been studied and the same has been plotted graphically. In the absence of rotation, the prior findings mentioned in the literature are obtained as a specific case. Within the framework of fractional-order thermoelasticity, the propagation of elastic waves in non-local isotropic rotating medium has been considered. The frequency dispersion relation is derived by solving the governing equations in the xy-plane for the given problem. Three coupled quasi-waves have been seen to move through this kind of medium at different rates. The Helmholtz decomposition theorem has been used to decompose the system into longitudinal and transverse components. Analytical computations are made for the waves’ related amplitude ratios and their speed. The amplitude ratios for the reflected waves are computed with the help of suitable boundary conditions. The impact of fractional order, rotational frequency, and non-local parameters on propagation speed and amplitude ratios has been studied and the same has been plotted graphically. In the absence of rotation, the prior findings mentioned in the literature are obtained as a specific case. |
| Author | Azhar, Ehtsham Ali, Hashmat Jamal, Muhammad Bibi, Farhat |
| Author_xml | – sequence: 1 givenname: Muhammad surname: Jamal fullname: Jamal, Muhammad organization: Department of Mathematics, PMAS Arid Agricultural University – sequence: 2 givenname: Farhat surname: Bibi fullname: Bibi, Farhat email: farhatnaz6464@gmail.com organization: Department of Mathematics, PMAS Arid Agricultural University – sequence: 3 givenname: Ehtsham surname: Azhar fullname: Azhar, Ehtsham organization: Department of Mathematics, PMAS Arid Agricultural University – sequence: 4 givenname: Hashmat surname: Ali fullname: Ali, Hashmat organization: Department of Mathematics, PMAS Arid Agricultural University |
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| Snippet | Within the framework of fractional-order thermoelasticity, the propagation of elastic waves in non-local isotropic rotating medium has been considered. The... |
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| SubjectTerms | Amplitudes Boundary conditions Characterization and Evaluation of Materials Classical Mechanics Decomposition Elastic waves Engineering Plane waves Polymer Sciences Reflected waves Rotation Solid Mechanics Thermoelasticity Wave propagation Wave reflection |
| Title | Investigating reflection phenomenon of plane waves in a fractional order thermoelastic rotating medium using nonlocal theory |
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