Separable equations for a cylindrical anisotropic elastic waveguide

Fraser, W. B.

doi:10.1016/0022-460x(80)90649-5

Cited by 5 publications

(4 citation statements)

References 18 publications

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“…Much later Mirsky (1964) investigated a problem of non-axisymmetric wave propagation in transversely isotropic circular solid and hollow cylinders. Other contributors to the subject were Armenakas and Reitz (1973), Frazer (1980), Nayfeh and Nagy (1995), Berliner and Solecki (1996), Niklasson and Datta (1998), and Honarvar et al (2007), just to name a few. Numerical results for the dispersion of axisymmetric guided waves in a composite cylinder with a transversely isotropic core were presented by Xu and Datta (1991).…”

Section: Introductionmentioning

confidence: 99%

Analysis of non-axisymmetric wave propagation in a homogeneous piezoelectric solid circular cylinder of transversely isotropic material

Shatalov¹,

Every²,

Yenwong-Fai³

2009

International Journal of Solids and Structures

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a b s t r a c tA study concerning the propagation of free non-axisymmetric waves in a homogeneous piezoelectric cylinder of transversely isotropic material with axial polarization is carried out on the basis of the linear theory of elasticity and linear electro-mechanical coupling. The solution of the three dimensional equations of motion and quasi-electrostatic equation is given in terms of seven mechanical and three electric potentials. The characteristic equations are obtained by the application of the mechanical and two types of electric boundary conditions at the surface of the piezoelectric cylinder. A novel method of displaying dispersion curves is described in the paper and the resulting dispersion curves are presented for propagating and evanescent waves for PZT-4 and PZT-7A piezoelectric ceramics for circumferential wave numbers m = 1, 2, and 3. It is observed that the dispersion curves are sensitive to the type of the imposed boundary conditions as well as to the measure of the electro-mechanical coupling of the material.

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Section: Introductionmentioning

confidence: 99%

Analysis of non-axisymmetric wave propagation in a homogeneous piezoelectric solid circular cylinder of transversely isotropic material

Shatalov¹,

Every²,

Yenwong-Fai³

2009

International Journal of Solids and Structures

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“…For instance, Fraser type biorthogonality relations 25,26 do not seem to exist in case of general anisotropic materials. Up to the author's knowledge, Fraser's relation has only been extended to particular anisotropy having at least one plane of elastic symmetry 22,27 .…”

Section: B Forced Responsementioning

confidence: 99%

Investigation of the interwire energy transfer of elastic guided waves inside prestressed cables

Treyssède¹

2016

The Journal of the Acoustical Society of America

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Elastic guided waves are of interest for the non-destructive evaluation of cables. Cables are most often multi-wire structures, and understanding wave propagation requires numerical models accounting for the helical geometry of individual wires, the interwire contact mechanisms and the effects of prestress. In this paper, a modal approach based on a so-called semi-analytical finite element method and taking advantage of a biorthogonality relation is proposed in order to calculate the forced response under excitation of a cable, multi-wired, twisted, and prestressed. The main goal of this paper is to investigate how the energy transfers from a given wire, directly excited, to the other wires in order to identify some localization of energy inside the active wire as the waves propagate along the waveguide. The power flow of the excited field is theoretically derived and an energy transfer parameter is proposed to evaluate the level of energy localization inside a given wire. Numerical results obtained for different polarizations of excitation, central and peripheral, highlight how the energy may localize, spread, or strongly change in the cross-section as waves travel along the axis. In particular, a compressional mode localized inside the central wire is found, with little dispersion and significant excitability.

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“…Rosenfeld and Keller (1974) found asymptotic expansions for both long and short high-frequency waves propagating in elastic rods of arbitrary cross-section. Fraser (1980) used the method of eigenfunction expansion to separate the equations of motion for a cylindrical anisotropic waveguide. Berliner and Solecki (1996) studied the wave propagation in fluid-loaded transversely isotropic cylinders.…”

Section: Introductionmentioning

confidence: 99%

Elastic waves in piezoceramic cylinders of sector cross-section

Puzyrev¹

2010

International Journal of Solids and Structures

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a b s t r a c tThe propagation of elastic waves in piezoceramic cylindrical waveguides of circular cross-sections with sector cut is investigated on the basis of the linear theory of electroelasticity. Dispersion functions are obtained from boundary conditions in an analytical form of functional determinants for each value of the generalized wave number. A selected set of numerical results including real, imaginary and complex branches of full dispersion spectrums with various symmetry of wave movements is presented to describe the essential characteristics of the waves. Leading effects of spectrums transformation by change of waveguide's angular measure are enlightened, and wave asymptotic behavior is analyzed. The variation of the cross-section is considered as a mechanism to control the dispersion characteristics of waveguides.

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Separable equations for a cylindrical anisotropic elastic waveguide

Cited by 5 publications

References 18 publications

Analysis of non-axisymmetric wave propagation in a homogeneous piezoelectric solid circular cylinder of transversely isotropic material

Analysis of non-axisymmetric wave propagation in a homogeneous piezoelectric solid circular cylinder of transversely isotropic material

Investigation of the interwire energy transfer of elastic guided waves inside prestressed cables

Elastic waves in piezoceramic cylinders of sector cross-section

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