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.

H. S. Paul

K. Natarajan

article

Crystal Structure

Dielectric constant

ELASTICITY

Electric potential

mathematical analysis

Piezoelectricity

priority journal

system analysis

ULTRASOUND TRANSDUCER

Vibration

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

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

Journal of the Acoustical Society of America

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.

International Journal of Engineering Science

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

Flexural and longitudinal vibrations in an arbitrary shaped pyroelectric infinite cylinder of crystal class 6 with circular cylindrical cavity is considered. The inner and outer surfaces of the cylinder are traction free, earth connected, and thermally insulated. The boundary conditions are satisfied directly at the regular inner surface and the Fourier series collocation method is applied at the outer boundary to satisfy the boundary conditions. A frequency equation has been derived for crystal class 6 for a general cross section. The frequency equation is analyzed numerically for elliptical and cardioidal cross-section cylinders of crystal class 6mm since all the material constants for class 6 are not available. Barium titanate ceramic is taken for numerical calculations. The results are tabulated and are presented graphically. © 1993, Acoustical Society of America. All rights reserved.

Wave propagation in a pyroelectric cylinder of arbitrary cross section with a circular cylindrical cavity

A theoretical study of wave propagation in a piezoelectric cylinder of infinite length of arbitrary cross section with a circular cylindrical cavity of class 6 is investigated. The frequency equations are obtained by using the Fourier expansion collocation method and are analyzed numerically. The frequencies are evaluated for circular, elliptic, and cardioidal sections of bone and are tabulated. A plot of frequency spectrum is also presented for the cardioidal cross-section bar. © 1991, Acoustical Society of America. All rights reserved.

Wave propagation in a piezoelectric human bone of arbitrary cross section with a circular cylindrical cavity

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.

Journal	Journal of the Acoustical Society of America
ISSN	00014966
Open Access	No