Propagation of Elastic Waves along a Cylindrical Rod of Micropolar Elastic Solid with Stretch under Impedance Boundary Conditions

G Rajkumar; K Somaiah; K Narasimharao; B Venkateswararao

doi:10.17485/IJST/v17i15.322

Article

Propagation of Elastic Waves along a Cylindrical Rod of Micropolar Elastic Solid with Stretch under Impedance Boundary Conditions

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v17i15.322

Year: 2024, Volume: 17, Issue: 15, Pages: 1566-1576

Original Article

Propagation of Elastic Waves along a Cylindrical Rod of Micropolar Elastic Solid with Stretch under Impedance Boundary Conditions

G Rajkumar^1*, K Somaiah¹, K Narasimharao², B Venkateswararao³

¹Department of Mathematics, Kakatiya University, Warangal, 506009, Telangana, India
²Department of Mathematics, Government Degree College for Women, Khammam, 507003, Telangana, India
³Department of Mathematics, SR & BGNR Government Arts & Science College (A), Khammam, 507003, Telangana, India

*Corresponding Author
Email: [email protected]

Received Date:05 February 2024, Accepted Date:19 March 2024, Published Date:13 April 2024

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objective: The objective of this article is to derive the dispersion relations of elastic waves along a cylindrical rod of homogeneous, isotropic micropolar elastic solid with stretch under impedance boundary conditions. Method: The basic equations and constitutive relations are converted into cylindrical coordinates and solved by adopting the method of plane harmonic solution. Findings: Displacements, micro rotations, and micro stretch relations are derived analytically. The dispersion relations pertaining to elastic waves with using impedance boundary conditions also derived analytically and these relations are compared with the results of Tomar. Novelty: With the use of the MATLAB program, the effects of impedance parameters, micropolarity and stretch are discussed for a particular model. The speed of the elastic wave is proportional to the ratio of the impedance parameter in microstretch elastic solids, but there is no significant effect of the impedance ratio in micropolar elastic solids.

Keywords: Elastic Waves, Cylindrical rod, Micropolarity, Micro stretch, Impedance Boundary Conditions

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Copyright

© 2024 Rajkumar et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)