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

Abstract

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.

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

“…These plots are also presented below for some cases, and to evaluate the group velocity, the differentials F k ( , k) and F ( , k) were calculated numerically. The distributions of dispersion curves, phase, and group velocities are presented in the commonly used [18][19][20]23,26,[30][31][32][33]48,54,55] form of dimensionless frequency versus dimensionless wavenumber and dimensionless velocity versus dimensionless frequency, respectively. The angular frequency is normalized in the following way:…”

“…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…”

“…The dynamic behavior of piezoelectric cylinders has been studied from different points of view [37][38][39][40][41][42][43][44][45][46][47][48][49][50]. A modern historical outline of the development of these problems and their applications in electro-mechanical devices can be found in [46,48].…”

“…A modern historical outline of the development of these problems and their applications in electro-mechanical devices can be found in [46,48]. Problems for piezoceramic cylinders with simple geometries were solved with the analytical solutions that satisfy exactly the boundary conditions.…”

Analysis of Axisymmetric and Non-Axisymmetric Wave Propagation in a Homogeneous Piezoelectric Solid Circular Cylinder of Transversely Isotropic Material

“…We seek the solution of the problem (14) -(15) in terms of harmonic travelling waves along z -axis in terms of several displacement and electric potentials first introduced by (Mirsky, 1964) and further used by (Winkel et al 1995) and (Shatalov et al, 2009) After substitution (16) into (14) we obtain the following system of equations: Second equation of system (18) must be compatible with the third and fourth equations of system (17), i.e. we have the following system of equations: …”