Abstract
The main objective of this study is to investigate the angular rotation effect of the solid and density of the fluid on the radial vibrations in an unbounded micropolar elastic solid with a fluid-loaded spherical cavity. The micropolar elastic solid is homogeneous and isotropic, but the loaded fluid is homogenous, isotropic, and in viscid. Dispersion relation for radial vibrations of macro-displacements is derived and which is influenced by the loaded fluid and angular rotation of the solid, while the micro-rotational vibrations are not influenced by the loaded fluid and angular rotation. All these results are not obtained in any classical theory of elasticity. Under the MATLAB program, the numerical computations for a particular solid have been performed and have also been shown graphically to understand the effect of angular rotation of the solid and density of the loaded fluid on the behavior of phase velocity and dispersion relation.
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References
Chand D, Sharma JN, Sud SP (1990) Transient generalized magneto-thermo-elastic waves in a rotating half-space. Int J Eng Sci 28(6):547–556
Schoenberg M, Censor D (1973) Elastic waves in rotating media. Quart Appl Math 31(1):115–125
Clarke NS, Burdess JS (1994) Rayleigh waves on a rotating surface. J Appl Mech Trans ASME 61(3):724–726
Destrade M (2004) Surface a acoustic waves in rotating orthorhombic crystals. Proc Royal Soc A Math Phys Eng Sci 460(2042):653–665
Sharma JN, Thakur MD (2006) Effect of rotation on Rayleigh Lamb waves in magneto-thermo elastic media. J Sound Vibr 296(4–5):871–887
Othman MIA, Song Y (2004) Effect of magneto-thermo elastic waves from rotation on plane waves in generalized thermo elasticity with two relaxation times. Int J Solids Struct 41(11–12):2939–2956
Mahmoud SR (2011) Effect of rotation, gravity field and initial stress on generalized magneto-thermo elastic Rayleigh waves in a granualar medium. Appl Math Sci 5(41–44):2013–2032
Somaiah K (2018) Plane wave propagation in a rotating micro-stretch elastic solid in special case. Springer Lecture Notes in Mechanical Engineering, pp 661–672
Eringen AC, Suhubi ES (1964) Non-linear theory of simple micro-elastic solids-I. Int J Eng Sci 2:189–203
Kumar R, Divya, Kumar K (2013) Propagation of wave through cylindrical bore in a swelling porous elastic media. Mater Phys Mech 16:135–143
Srinivas R, Somaiah K (2018) Radial vibrations in unbounded micropolar elastic solid with fluid-loaded spherical cavity. Springer Lecture Notes in Mechanical Engineering, pp 431–438
Deswal S, Kumar R (2010) Wave motion in a viscous fluid filled bore in a micropolar elastic medium with voids. Proc Natl Acad Sci India, Section-A 80:223–234
Ewing WM, Jardetzky WS, Press F (1957) Elastic waves in layered media. The Mac-Graw. Hill Company, New York
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Somaiah, K. (2021). Effect of Rotation and Fluid on Radial Vibrations in a Micropolar Elastic Solid Having a Fluid-Loaded Spherical Cavity. In: Rushi Kumar, B., Sivaraj, R., Prakash, J. (eds) Advances in Fluid Dynamics. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-4308-1_13
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DOI: https://doi.org/10.1007/978-981-15-4308-1_13
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