Free Vibrations in a Rotating Generalized Elastic Hollow Solid Sphere

K Somaiah; K Narasimharao; A Ravi Kumar; R Srinivas

doi:10.17485/IJST/v15i42.1607

Article

Free Vibrations in a Rotating Generalized Elastic Hollow Solid Sphere

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v15i42.1607

Year: 2022, Volume: 15, Issue: 42, Pages: 2252-2258

Original Article

Free Vibrations in a Rotating Generalized Elastic Hollow Solid Sphere

K Somaiah¹, K Narasimharao^2*, A Ravi Kumar³, R Srinivas⁴

¹Department of Mathematics, Kakatiya University, Warangal, 506009, Telangana, India
²Department of Mathematics, Government Degree College for Women, Khammam, 507003,
Telangana, India
³Department of Mathematics, Satavahana University, Karimnagar, 505002, Telangana, India
⁴Information Technology Department, University of Technology and Applied Sciences-Nizwa, 611, Oman

*Corresponding Author
Email: [email protected]

Received Date:03 August 2022, Accepted Date:06 October 2022, Published Date:14 November 2022

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

Abstract

Objective: To investigate the free vibrations in a rotating elastic hollow solid sphere. Method: The method of plane harmonic solution is employed to solve the basic governing equations of rotating elastic solid. Findings: Three types of frequency equations named as coupled frequency (CF) (Radial and tangential) equations, radial frequency (RF) equation and tangential frequency (TF) equations are derived. Novelty: Under the MATLAB program, the numerical computations have been performed for a particular material. Frequency versus angle is shown graphically for rotating and non-rotating material. TF and CF curves are inverse proportional to the angular rotation. Coupled frequencies are slower than the tangential frequencies.

Keywords: Free Vibrations; Rotation; Hollow sphere; Radial frequencies; Tangential frequencies and Coupled Frequencies

References

Lord HW, Shulman Y. A generalized dynamical theory of thermoelasticity. Journal of the Mechanics and Physics of Solids. 1967;15(5):299–309. Available from: https://doi.org/10.1016/0022-5096(67)90024-5
Green AE, Lindsay KA. Thermoelasticity. Journal of Elasticity. 1972;2(1):1–7. Available from: https://doi.org/10.1007/BF00045689
Sharma DK, Thakur D, Walia V, Sarkar N. Fraa vibration analysis of non- local thermo elastic hollow cylinder with diffusion. Journal of Thermal Stresses. 2020;43:981–997. Available from: https://doi.org/10.1080/01495739.2020.1764425
Grigorenko AY, Loza IA. Forced Axisymmetric Vibrations of an Electrically Excited Hollow Sphere Made of a Continuously Inhomogeneous Piezoceramic Material*. International Applied Mechanics. 2020;56(6):674–689. Available from: https://doi.org/10.1007/s10778-021-01044-y
Hamdy M, Youssef. Thermal shock problem of a generalized thermoelastic solid sphere affected by mechanical damage and thermal diffusion. Journal of Engineering and Thermal Sciences. 2021;1(1):1–16. Available from: https://doi.org/10.21595/jets.2021.21934.
Al-Lehaibi EAN. The vibration analysis of a nanobeam due to a ramp-type heating under Moore- Gibson-Thompson theory of thermo-elasticity. Journal of Vibroengineering. 2022;24:394–404. Available from: https://doi.org/10.21595/jve.2021.22231
Sharma DK, HM. Analysis of Free Vibrations of Axisymmetric Functionally Graded Generalized Visco-thermoelastic Cylinder Using Series Solution. Journal of Vibration Engineering & Technologies. 2020;8:783–798. Available from: https://doi.org/10.1007/s42417-019-00178-1
Somaiah K. Effect of Rotation and Fluid on Radial Vibrations in a Micropolar Elastic Solid Having a Fluid-Loaded Spherical Cavity. Advances in Fluid Dynamics. 2021;p. 171–180. Available from: https://doi.org/10.1007/978-981-15-4308-1_13
Somaiah, Chandulal A. Studies of rotation effect on inhomogeneous and attenuation wave propagation in a micropolar elastic solid. AIP Conference Proceedings. 1964;p. 90005–90014. Available from: https://doi.org/10.1063/5.0014536
Eringen AC. Simple microfluids. International Journal of Engineering Science. 1964;2(2):205–217. Available from: https://doi.org/10.1016/0020-7225(64)90005-9
Sharma PK, Kaur D, Sharma JN. Three-dimensional vibration analysis of a thermoelastic cylindrical panel with voids. International Journal of Solids and Structures. 2008;45(18-19):5049–5058. Available from: https://doi.org/10.1016/j.ijsolstr.2008.05.004

Copyright

© 2022 Somaiah 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)