Effect of Rotation and Fluid on Radial Vibrations in a Micropolar Elastic Solid Having a Fluid-Loaded Spherical Cavity

Radial Vibrations in Unbounded Micropolar Elastic Solid with Fluid Loaded Spherical Cavity

Lecture Notes in Mechanical Engineering - Applications of Fluid Dynamics ◽

10.1007/978-981-10-5329-0_31 ◽

2017 ◽

pp. 431-438

Author(s):

R. Srinivas ◽

K. Somaiah

Keyword(s):

Spherical Cavity ◽

Elastic Solid ◽

Radial Vibrations

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On generalized thermoelastic disturbances in an elastic solid with a spherical cavity

Journal of Applied Mathematics and Stochastic Analysis ◽

10.1155/s1048953391000187 ◽

1991 ◽

Vol 4 (3) ◽

pp. 225-240 ◽

Cited By ~ 6

Author(s):

Basudeb Mukhopadhyay ◽

Rasajit Bera ◽

Lokenath Debnath

Keyword(s):

Laplace Transform ◽

Classical Theory ◽

Spherical Cavity ◽

Dynamic Pressure ◽

Elastic Solid ◽

Dynamical Theory ◽

The Laplace Transform ◽

Generalized Thermoelastic ◽

Short Time ◽

The Waves

In this paper, a generalized dynamical theory of thermoelasticity is employed to study disturbances in an infinite elastic solid containing a spherical cavity which is subjected to step rise in temperature in its inner boundary and an impulsive dynamic pressure on its surface. The problem is solved by the use of the Laplace transform on time. The short time approximations for the stress, displacement and temperature are obtained to examine their discontinuities at the respective wavefronts. It is shown that the instantaneous change in pressure and temperature at the cavity wall gives rise to elastic and thermal disturbances which travel with finite velocities v1 and v2(>v1) respectively. The stress, displacement and temperature are found to experience discontinuities at the respective wavefronts. One of the significant findings of the present analysis is that there is no diffusive nature of the waves as found in classical theory.

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Radial vibrations of an infinite medium with a spherical cavity

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/bf01601167 ◽

1963 ◽

Vol 14 (6) ◽

pp. 745-748 ◽

Cited By ~ 2

Author(s):

Václav Vodička

Keyword(s):

Spherical Cavity ◽

Infinite Medium ◽

Radial Vibrations

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Stress amplification in three-dimensional narrow zones created by cavities

Theoretical and Applied Mechanics ◽

10.2298/tam1201071s ◽

2012 ◽

Vol 39 (1) ◽

pp. 71-97

Author(s):

Stavros Syngellakis

Keyword(s):

Spherical Cavity ◽

Exact Analytical Solution ◽

Three Dimensional ◽

Elastic Solid ◽

Bending Moments ◽

Series Solutions ◽

Minimum Thickness ◽

Narrow Region ◽

Stress Amplification ◽

Radial Tension

The paper is concerned with a particular case of stress amplification arising from the proximity of a spherical cavity to the boundary of a loaded elastic solid. The performed approximate analysis yields distributions of stresses and displacements in the narrow region formed between a spherical cavity and the faces of a thin flat layer subjected to a far field uniform radial tension. The narrow region is modelled as a circular plate of non-uniform thickness undergoing coupled membrane and flexural deformation. Series solutions are obtained for both membrane forces and bending moments leading to estimates for the stress concentration factor at minimum thickness. These predictions are found consistent with those obtained from both the exact analytical solution and finite element modelling of the problem. Cross-validated results from the two latter methods also provide trends for the stress amplification due to the narrowness of the region.

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