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Journal ArticleDOI

Wave propagation in a hollow pyroelectric circular cylinder of crystal class 6

01 Mar 1991-Acta Mechanica (Springer)-Vol. 87, Iss: 1, pp 37-46

Abstract: Flexural and longitudinal wave propagation in a hollow pyroelectric cylinder of crystal class 6 are considered. The frequency equation has been derived for two different cases. Case (i) is for a hollow cylinder whose inner and outer surfaces are traction free, completely coated with electrode which are shorted and thermally insulated. Case (ii) is for a hollow cylinder whose inner surface is clamped, completely coated with electrode which are shorted and thermally insulated while the outer surface is same as in case (i). The frequency equation has been analyzed numerically for Barium titanate ceramic. The results are tabulated and the dispersion curves are presented.
Topics: Longitudinal wave (50%)
Citations
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Journal ArticleDOI
J. S. Yang1, Romesh C. Batra2Institutions (2)
Abstract: We study the effect of heat conduction on the shift in the frequencies of a freely vibrating linear piezoelectric body by using two perturbation methods. In one method a small parameter that is associated with the thermal conductivity is employed, and in the other the small parameter involves the thermocoupling constants. In each case it is shown that the first-order effect on frequencies is to shift them by a small imaginary number thereby signifying that the effect of energy dissipation due to heat conduction is to reduce the amplitude of vibration.

41 citations


Journal ArticleDOI
Abstract: The propagation of Lamb waves in a homogeneous, transversely isotropic, piezothermoelastic plate subjected to charge- and stress-free, thermally insulated or isothermal boundary conditions, is investigated. Secular equations for the plate in closed form and isolated mathematical conditions for symmetric and antisymmetric wave mode propagation in completely separate terms are derived. It is shown that motion of purely transverse (SH) mode gets decoupled from rest of the motion and remains unaffected due to piezoelectric, pyroelectric and thermal effects. At short wavelength limits, the secular equations for symmetric and skew symmetric waves reduce to Rayleigh surface wave frequency equation, because a finite plate in such situation behaves like a semi-infinite medium. The amplitudes of dilatation, temperature change and electrical potential have also been computed during the symmetric and skew symmetric mode of vibrations of the plate. Finally, numerical solution of various secular equations and other relevant relations is carried out for cadmium-selenide (6 mm class) material. The dispersion curves, attenuation coefficients and amplitudes of dilatation, temperature change and electrical potential for symmetric and antisymmetric wave modes are presented graphically in order to illustrate and compare the analytical results. The theory and numerical computations are found to be in close agreement. The various wave characteristics are found to be more stable and realistic in the presence of piezoelectric and pyroelectric effects than in the absence of such effects, thereby making such materials more viable for practical applications and use.

37 citations


Journal ArticleDOI
Abstract: By virtue of the separation of variables technique, the piezothermoelastic axisymmetric dynamic problem of a pyroelectric hollow cylinder is transformed to a second kind of Volterra integral equation about a function with respect to time, which can be solved successfully by means of the interpolation method. Then the solution of displacements, stresses, electric displacements, and electric potential are obtained. The present method is suitable for a pyroelectric hollow cylinder with an arbitrary thickness subjected to arbitrary thermal loads. Numerical results are presented.

27 citations


Journal ArticleDOI
J. N. Sharma1, Vishal Walia1Institutions (1)
Abstract: The present paper is devoted to extend the study on propagation of Rayleigh surface waves in homogeneous, transversely isotropic, piezothermoelastic semi-space subjected to stress free, open or closed circuit, thermally insulated/isothermal boundary conditions, in the context of non-classical (generalized) theories of thermoelasticity. Secular equations for surface wave propagation in the considered media are derived from a coupled system of governing partial differential equations of linear generalized piezothermoelasticity. The surface amplitudes, specific loss factor, and surface particle motion are also investigated. The surface particle paths during the motion are found to be elliptical which degenerate into straight lines in case there is no phase difference between horizontal and vertical components of surface displacements. The results in the context of coupled theory of thermoelasticity can be obtained from the present analysis by setting thermal relaxation parameters equal to zero. Finally, in order to illustrate and verify the analytical developments, the numerical solution of secular equations, specific loss factor, eccentricities, and inclination of particle paths with wave normal is carried out for cadmium-selenide (6 mm class) material with the help of Descartes’ algorithm and functional iteration method. The computer simulated results are then presented graphically in order to illustrate and compare them in the context of coupled and generalized theories of thermoelasticity.

25 citations


Journal ArticleDOI
Hanfeng Ding1, H. M. Wang1, Weiqiu Chen1Institutions (1)
TL;DR: The piezothermoelastic axisymmetric plane strain dynamic problem of a special non-homogeneous pyroelectric hollow cylinder is transformed to a Volterra integral equation of the second kind about a function with respect to time, which can be solved successfully by means of the interpolation method.
Abstract: By virtue of the introduction of a dependant variable and the separation of variables technique, the piezothermoelastic axisymmetric plane strain dynamic problem of a special non-homogeneous pyroelectric hollow cylinder is transformed to a Volterra integral equation of the second kind about a function with respect to time, which can be solved successfully by means of the interpolation method. Then the solutions of displacements, stresses, electric displacements and electric potential are obtained. The present method is suitable for a non-homogeneous pyroelectric hollow cylinder with an arbitrary thickness subjected to arbitrary axisymmetric thermal loads. Numerical results are presented graphically.

19 citations


References
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Journal ArticleDOI

2,573 citations


Journal ArticleDOI
Raymond D. Mindlin1Institutions (1)
Abstract: A system of two-dimensional equations is derived for high frequency motions of crystal plates accounting for coupling of mechanical, electrical and thermal fields.

316 citations


"Wave propagation in a hollow pyroel..." refers background in this paper

  • ...Mindlin [ 7 ] discussed the high frequency equations of crystal plates....

    [...]


Book ChapterDOI
01 Jan 1989-

124 citations


Journal ArticleDOI
Abstract: Solutions for the flexural and axisymmetric vibrations of piezoelectric cylindrical shells of the crystal class 6mm are investigated. Applying suitable mechanical and electrical boundary conditions, the frequency equations have been obtained.

65 citations


"Wave propagation in a hollow pyroel..." refers background in this paper

  • ...Paul [ 2 ] discussed the flexural and axisymmetrie vibrations of piezoelectric circular eylindrieal shell....

    [...]


Journal ArticleDOI
Abstract: This paper is concerned with the steady−state radial−shear vibrations of an axially polarized piezoelectric ceramic tube of infinite length, whose cylindrical surfaces are either traction−free or subjected to a relative displacement. Open− and short−circuit resonant frequency equations are formulated and the deviation between frequency pairs examined numerically. Fundamental resonant frequency curves are given for traction−free PZT−4 cylinders having arbitrary geometry, which approach the infinite plate solutions for large radius/thickness ratios. The theory is applied to the vibrations of annular accelerometers operating in the radial−shear mode.Subject Classification: 40.26.

55 citations


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