Flexural vibration in a finite piezoelectric circular solid cylinder of crystal class 6mm is studied for traction-free and electric potential-free boundaries. The solution is obtained in the form of a series, in which the boundary conditions for the shear stresses on curved and plane end surfaces and electric potential on the plane ends are satisfied term-by-term. Remaining other boundary conditions are satisfied by an orthogonalization procedure. The series converges rapidly within a few terms. Numerical computation is carried out for the piezoelectric ceramic PZT4. For various ratios of half-height to radius of the cylinder, the natural frequencies are calculated for the first and second circular modes. The stress distribution over the cylinder for the first circular mode are presented graphically. © 1994.

H. S. Paul

K. Natarajan

Ceramic materials

Computational methods

Convergence of numerical methods

Crystalline materials

Cylinders (shapes)

Electric properties

Mathematical models

Numerical methods

Polynomials

Shear stress

Surfaces

Vibrations (mechanical)

Boundary conditions

CRYSTAL CLASS 6 MM

ELECTRIC POTENTIALS

Flexural Vibrations

MATHEMATICAL SERIES

Natural frequencies

ORTHOGONALIZATION PROCEDURE

PIEZOELECTRIC CERAMIC PZT4

PIEZOELECTRIC CIRCULAR SOLID CYLINDERS

STRESS DISTRIBUTION

Piezoelectric materials

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Flexural vibration in a finite piezoelectric circular cylinder of crystal class 6 mm

International Journal of Engineering Science

In this study, the flexural vibration in a finite piezoelectric circular hollow cylinder belonging to crystal class 6mm is considered. Both the inner and outer curved surfaces and the end plane surfaces are free from traction and electric potential. Solutions for the mechanical displacements and the electric potential are derived in a series form. Boundary conditions on shear stress are satisfied exactly term by term in the series and the remaining boundary conditions are satisfied by an orthogonalization procedure. Numerical analysis is carried out for the piezoelectric ceramic PZT4. The natural frequencies are calculated for the circular modes one and two and presented graphically.

Journal of the Acoustical Society of America

Flexural vibration in a finite piezoelectric hollow cylinder of class 6mm

This paper is concerned with the vibration of a piezoelectic cylinder of arbitrary cross section with a cylindrical cavity of arbitrary shape belonging to class 6. The boundary conditions for the inner and the outer arbitrary surfaces are satisfied by using the Fourier expansion collocation method. The frequency equations for the symmetric and the antisymmetric cases are obtained for the cylinder of general cross section of the inner and the outer boundaries. The analysis of the frequency equations are carried out for the material bone. The longitudinal and flexural vibrations are considered and the numerical results are tabulated. The frequency spectra are also presented. © 1991.

Wave propagation in a piezoelectric bone with a cylindrical cavity of arbitrary shape

The wave propagation in a piezoelectric hollow cylinder of class (6-mm) crystals or ceramics (m) with traction-free surfaces is studied. The frequency equations are obtained subject to various types of electrical boundary conditions and are examined numerically for the piezoceramic material PZT-4; the results are presented graphically as well as in tables. © 1987, Acoustical Society of America. All rights reserved.

Vibrations of a hollow circular cylinder of piezoelectric ceramics

The exact frequency equation for the axisymmetric vibration of a piezoelectric cylinder guided by a thin film of (6 mm) or (oo m) class is obtained. The surface of the cylinder is coated with a perfectly conducting material. The same problem is analyzed by an asymptotic method. The numerical results obtained in the exact method are compared with the solutions of the asymptotic method for 0 < ∊<0.1 (where ∊ is the dimensionless wavenumber). The dispersion curve has been presented graphically and it is compared with the dispersion curve obtained for the vibration of a piezoelectric solid cylinder without a coating. © 1986, Acoustical Society of America. All rights reserved.

Axisymmetric vibration of a piezoelectric solid cylinder guided by a thin film

An asymptotic method due to “Achenbach” is used to analyze the longitudinal and circumferential modes of wave propagation in a piezoelectric solid circular cylinder of crystal class (6 mm) or ceramics (oom). Information obtained in this method is useful for the frequency spectrum at long wavelengths. in this method the displacement components, electric potential, and the frequency are expressed as power series of the dimensionless wavenumber, e = 2ttx radius/wavelength. Substituting these expansions in the field equations and the boundary conditions, a system of coupled second-order inhomogeneous ordinary differential equations with radial coordinate as the independent variable is obtained by collecting the terms of same order em. Integration of such systems of differential equations yields the various terms in the series expansions for the above modes and for the whole range of frequencies, when the real valued dimensionless wavenumber is less than unity (0&lt;e &lt; 1). To test the correctness of the present scheme, the roots of the exact frequency equation are computed and the results thus obtained are compared with the results obtained in the present analysis. © 1982, Acoustical Society of America. All rights reserved.

Asymptotic analysis of the modes of wave propagation in a piezoelectric solid cylinder

Vibrations of Circular Cylindrical Shells of Piezoelectric Silver Iodide Crystals

Journal	International Journal of Engineering Science
ISSN	00207225
Open Access	No