Free vibrations of axially polarized piezoceramic hollow cylinders of finite length

The problem of the free axisymmetric vibrations of longitudinally polarized piezoceramic hollow cylinders is solved by a numerical analytic method. The spline-collocation method with respect to the longitudinal coordinate is used to reduce the original problem of electroelasticity to an eigenvalue boundary-value problem for ordinary differential equations with respect to the radial coordinate. This problem is solved by the stable discrete-orthogonalization and incremental search methods. Numerical results are presented and the natural frequencies of the cylinders are analyzed for a wide range of their geometric characteristics     

Free nonaxisymmetric vibrations of radially polarized hollow piezoceramic cylinders of finite length

The three-dimensional problem of free nonaxisymmetric vibrations of hollow piezoceramic cylinders with axial polarization is considered. An efficient numerical analytic method to solve boundary-value problems is proposed. The original three-dimensional problem of electroelasticity is reduced to a two-dimensional problem by representing the displacement components as standing circumferential waves. Spline collocation with respect to the axial coordinate is used to reduce this two-dimensional problem to an eigenvalue boundary-value problem with respect to the radial coordinate. This problem is solved by the stable discrete-orthogonalization and incremental-search methods. Numerical results are presented and the natural frequencies of the cylinders are analyzed in a wide range of their geometric characteristics     

Elastic waves in piezoceramic cylinders of sector cross-section

The 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.     

Vibrations of an axially polarized piezoceramic cylinder during electrical loading

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 25, No. 11, pp. 15–19, November, 1989.     

Generalized Bleustein-Gulyaev type waves in layered porous piezoceramic structure

The propagation of a Bleustein-Gulyaev (B-G) type wave in a structure consisting of multiple layers and a half-space of porous piezoelectric materials is theoretically studied. The solutions of the problem in terms of the mechanical displacements and electric potential functions are obtained for each layer and the half-space. The dispersion equation is obtained for electrically open and shorted boundary conditions by use of the transfer matrix method. A peculiar kind of B-G waves is investigated, which can propagate only in the layer over the half-space. The relationship between the piezoelectric constants and the dielectric constants is found for the existence of a peculiar kind of propagation modes. The numerical results in terms of the phase velocity and the electromechanical coupling factor with different thicknesses of the layer stack are presented.     

Stress state of layered hollow cylinders with irregularly shaped cross-section

The stress state of longitudinally corrugated layered hollow orthotropic elliptic cylinders is determined using discrete Fourier series for different geometrical parameters. The results obtained are presented in the form of plots and tables and analyzed     

Radially polarized functionally graded piezoelectric hollow cylinders as sensors and actuators

An axisymmetric electroelastic problem of hollow radially polarized piezoceramic cylinders made of functionally graded (FG) materials is analyzed. For the material properties of power-law profile, a closed-form solution is derived. For a general gradient variation, an analytic approach is suggested, which reduces the problem to a Fredholm integral equation. Solving the resulting equation, the response of the electroelastic field can be determined. No severe limitation is required for varying material properties in this method. Numerical results of a cylindrical FG piezoelectric tube with PZT-5H as the inner surface ceramic are evaluated, and the distribution of the radial and circumferential stresses as well as the electric potential for piezoelectric sensors and actuators are presented graphically under electric and mechanical stimuli, respectively. Our results indicate that the electroelastic response in an FG piezoceramic tube with material properties decreasing when the radius increases becomes more obvious than that with material properties increasing. Moreover, the gradient index strongly affects the stress distribution and electric response. The obtained results are helpful for the design of annular cylindrical FG piezoelectric sensors/actuators.     

Numerical solution to the initial-boundary-value problem of electroelasticity for a radially polarized hollow piezoceramic cylinder

The paper proposes and analyzes different approaches to constructing numerical schemes to solve the nonstationary vibration problem for a radially polarized piezoelectric hollow cylinder with different electric boundary conditions under mechanical loading. It is established that when the cylinder is subjected to internal pressure, the radial displacements are similar and the longitudinal displacements substantially different in cylinders with electroded and nonelectroded surfaces __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 12, pp. 67–75, December, 2006.     

Nonaxisymmetric vibrations of radially polarized hollow cylinders made of functionally gradient piezoelectric materials

The nonaxisymmetric problem of natural vibrations of radially polarized hollow cylinders made of functionally gradient piezoelectric materials is solved. The properties of the material change continuously along a radial coordinate according to an exponential law. The lateral surfaces of the cylinder are free of external tractions and short circuited by electrodes. After separation of variables and representation of the components of the displacement vector in the form of standing circumferential waves, the initially three-dimensional problem is reduced to a two-dimensional partial differential equation problem. By using the method of spline-collocations with respect to a longitudinal coordinate, this two-dimensional problem is reduced to a boundary-value problem for the eigenvalues expressed in terms of ordinary differential equations. This problem is solved by the stable discrete-orthogonalization technique in combination with a step-by-step search method with respect to the radial coordinate. Results were obtained numerically and subsequently analyzed in this paper.     

Axisymmetric waves in a fluid-filled,hollow, elastic cylinder surrounded by a fluid

The laws of propagation of axisymmetric normal modes in a hollow cylinder filled with and surrounded by fluid media are investigated. Dispersion curves are plotted, exhibiting functional relations between the complex propagation constant and the dimensionless frequency. Distinctive attributes of the dispersion curves and the energy characteristics of the investigated waveguide structure are analyzed.Institute of Hydromechanics, National Academy of Sciences of Ukraine, Kiev. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 9, pp. 15–23, September, 1994.     

Turbulent boundary layers on axially inclined cylinders. Part 1. Surface-pressure/velocity correlations

The boundary layer on a cylinder with its axis at small inclinations of 0–6° to the freestream (an idealisation of `streamers' used in underwater seismic surveys) has been studied experimentally by measurements involving surface pressure fluctuations and their correlation with the axial velocity. There is no evidence of vortex shedding at Reynolds numbers typical of streamers at operating conditions. The behaviour of the wall-pressure field is substantially altered by small incidence: correlation length scales decrease on the upstream side, but remain relatively unaltered on the downstream side. Attention is also paid to the axisymmetry of the flow by reference to axial velocity statistics of up to fourth order. Received: 10 June 2000/Accepted: 4 July 2001