Wave propagation in a transversely isotropic solid cylinder of arbitrary cross-sections immersed in fluid

Ponnusamy, P.; Rajagopal, Manikanda

doi:10.1016/j.euromechsol.2009.09.002

Cited by 9 publications

(9 citation statements)

References 19 publications

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“…In order to solve the system of partial differential equations (1), we use wave potentials method, which was introduced by Buchwald [52] and later has been used by many other authors [19,26,33,35,48]. These potential functions ψ j are related to displacement components as…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…In the past decades, the problem of elastic wave propagation in noncircular finite and infinite cylinders and related problems has received a great deal of attention [25][26][27][28][29][30][31][32][33][34][35][36]. At the same time, active use of piezoelectric devices in various applications has been continuously increasing, stirring up the interest in modeling of dynamic behavior of piezoelectric components, in particular, of cylindrical geometry.…”

Section: Introductionmentioning

confidence: 99%

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Controlling the dynamic behavior of piezoceramic cylinders by cross-section geometry

2012

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This paper focuses on the possibilities of controlling the dispersion spectra and wave characteristics of cylindrical waveguides by changing their geometry and electro-elastic properties. We consider cylinders with classical circular and hollow cross-sections, and waveguides that have sector cut of arbitrary angular measure in the cross-section. Numerical results are presented for the cylinders of all studied types with different boundary conditions. It is shown that the required wave characteristics can be obtained by a variation of the cross-section geometry of the waveguides.

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Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Controlling the dynamic behavior of piezoceramic cylinders by cross-section geometry

2012

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“…For a tetragonal elastic body, Piola stress tensor components are given in terms of five independent elastic constants as follows [3,4]: t rr = c 11 ∂u r ∂r + c 12 u r r + c 13 ∂u z ∂z , t uu = c 12 ∂u r ∂r + c 11 u r r + c 13 ∂u z ∂z ,…”

Section: Formulation Of the Problem And Basic Equationsmentioning

confidence: 99%

“…With the advancement of space research, it has become necessary to obtain a deep insight in the behavior of materials, especially of the anisotropic ones that are so frequently used in missiles and other allied systems. Without taking into the consideration the effect of the magnetic field, the analysis of longitudinal wave propagation in an anisotropic and homogeneous circular cylindrical shell, according to the theory of elasticity, has been done by many authors [1–7]. Moreover, the propagation of harmonic waves, in circular cylinders that are made of isotropic or anisotropic materials, has been investigated and evaluated numerically, on the basis of the theory of elasticity, by Mirsky [8], Tsai [9] and White and Tongtaow [10].…”

Section: Introductionmentioning

confidence: 99%

A mathematical model for longitudinal wave propagation in a magnetoelastic hollow circular cylinder of anisotropic material under the influence of initial hydrostatic stress

Abd-alla

Alshaikh

Giorgio

et al. 2015

Mathematics and Mechanics of Solids

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In this paper, we built a mathematical model to study the influence of the initial stress on propagation of longitudinal waves in a hollow infinite circular cylinder in the presence of an axial initial magnetic field. The elastic cylinder is assumed to be made of a tetragonal system material. The problem is described by the equations of elasticity, taking into account the effect of the initial stress and the electro-magnetic equations of Maxwell. This requires the solution of the equations of motion in cylindrical coordinates with the z-axis directed along the axis of the cylinder. The displacement components will be obtained by founding the analytical solutions of the motion's equations. The frequency equations have been obtained in the form of a determinant involving Bessel functions. The roots of the frequency equation give the values of the characteristic circular frequency parameters of the first three modes for various geometries when the initial hydrostatic stress is compression or tension. These roots, which correspond to various modes, are numerically calculated and presented graphically. This study shows that waves in a solid body propagating under the influence of an initial stress can differ significantly from those propagating in the absence of the initial stress. The results of this research are used in analyzing the relationship between magnetic field, the initial stress and the frequency equation and could lead to discussions for using the magnetic field and the initial stress in ultrasound imaging.

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“…Guided waves in a transversely isotropic cylinder immersed in a fluid was analyzed by Ahmad [26]. Ponnusamy [27] and later with Rajagopal [28] have studied, the wave propagation in a generalized thermo elastic solid cylinder of arbitrary cross-section and in a homogeneous transversely isotropic thermo elastic solid cylinder of arbitrary cross-sections respectively using the Fourier expansion collocation method.…”

Section: Introductionmentioning

confidence: 99%

Wave propagation in a transversely isotropic solid cylinder of arbitrary cross-sections immersed in fluid

Cited by 9 publications

References 19 publications

Controlling the dynamic behavior of piezoceramic cylinders by cross-section geometry

Controlling the dynamic behavior of piezoceramic cylinders by cross-section geometry

A mathematical model for longitudinal wave propagation in a magnetoelastic hollow circular cylinder of anisotropic material under the influence of initial hydrostatic stress

Wave propagation in a piezoelectric solid bar of circular cross-section immersed in fluid

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