ORIGINAL PAPER
Guided Circumferential Waves in Layered Poroelastic Cylinders
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1
Department of Mathematics, Deccan College of Engineering and Technology, Hyderabad–500 001 (T.S) , India
2
Department of Mechanical Engineering, Deccan College of Engineering and Technology, Hyderabad–500 001 (T.S), India
Online publication date: 2016-12-08
Publication date: 2016-12-01
International Journal of Applied Mechanics and Engineering 2016;21(4):933-950
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ABSTRACT
The present paper investigates the propagation of time harmonic circumferential waves in a two-dimensional hollow poroelastic cylinder with an inner shaft (shaft-bearing assembly). The hollow poroelastic cylinder and inner shaft are assumed to be infinite in axial direction. The outer surface of the cylinder is stress free and at the interface, between the inner shaft and the outer cylinder, it is assumed to be free sliding and the interfacial shear stresses are zero, also the normal stress and radial displacements are continuous. The frequency equation of guided circumferential waves for a permeable and an impermeable surface is obtained. When the angular wave number vanish the frequency equation of guided circumferential waves for a permeable and an impermeable surface degenerates and the dilatational and shear waves are uncoupled. Shear waves are independent of the nature of surface. The frequency equation of a permeable and an impermeable surface for bore-piston assembly is obtained as a particular case of the model under consideration when the outer radius of the hollow poroelastic cylinder tends to infinity. Results of previous studies are obtained as a particular case of the present study. Nondimensional frequency as a function of wave number is presented graphically for two types of models and discussed. Numerical results show that, in general, the first modes are linear for permeable and impermeable surfaces and the frequency of a permeable surface is more than that of an impermeable surface.
REFERENCES (15)
1.
Nagy P.B., Blodgett M. and Godis M. (1994): Weep hole inspection by circumferential creeping waves. – NDT and E., vol.27, pp.131-142.
2.
Christine Valle, Jianmin Qu and Jacobs L.J. (1999): Guided circumferential waves in layered cylinders. – International Journal of Engineering Science, vol.37, pp.1369-1387.
3.
Tajuddin M. and Ahmed Shah S. (2006): Circumferential waves of infinite hollow poroelastic cylinders. – Trans. ASME, J. Appl. Mech., vol.73, pp.705-708.
4.
Tajuddin M. and Ahmed Shah S. (2007): On torsional vibration of infinite hollow poroelastic cylinders. – Journal of Mechanics of Materials and Structures, vol.2, pp.189-200.
5.
Whittier J.S. and Jones J.P. (1967): Axially symmetric wave propagation in a two-layered cylinder. – International Journal of Solids and Structures, vol.3, pp.657-675.
6.
Liu G. and Qu J. (1998): Guided circumferential waves in a circular annulus. – Trans. ASME, J. Appl. Mech., vol.65, pp.424-430.
7.
Malla Reddy P. and Tajuddin M. (2000): Exact analysis of the plane-strain vibrations of thick-walled hollow poroelastic cylinders. – International Journal of Solids and Structures, vol.37, pp.3439-3456.
8.
Towfighi S. Kundu T. and Ehsani M. (2002): Elastic wave propagation in circumferential direction in anisotropic cylindrical curved plates. – Trans. ASME. J. Appl. Mechanics, vol.69, pp.283-291.
9.
Ahmed Shah S. (2011): Flexural wave propagation in coated poroelastic cylinders with reference to fretting fatigue. – Journal of Vibration and Control, vol.17, pp.1049-1064.
10.
Biot M.A. (1956): Theory of propagation of elastic waves in fluid-saturated porous solid. – J. Acoust. Soc. Am., vol.28, pp.168-178.
11.
Viktorov I.A. (1958): Rayleigh-type waves on curved surfaces. – J. Acoust. Soc. Am, vol.4, pp.131-136.
12.
Tajuddin M. and Sarma K.S. (1980): Torsional vibrations of poroelastic cylinders. – Trans. ASME, J. Appl. Mech., vol.47, pp.214-216.
13.
Fatt I. (1959): The Biot-Willis elastic coefficients for a sandstone. – J. Appl. Mech., vol.26, pp.296-297.
14.
Yew C.H. and Jogi P.N. (1976): Study of wave motions in fluid-saturated porous rocks. – J. Acoust. Soc. Am, vol.60, pp.2-8.
15.
Abramowitz A. and Stegun I.A. (1965): Handbook of Mathematical Functions. – National Bureau of Standards, Washington, D.C.