We consider an axisymmetric problem of free longitudinal vibrations of hollow piezoelectric cylinders for some types of boundary conditions on the end faces. The piezoceramic material is polarized in the radial direction. The side faces of a cylinder are covered with short-circuited thin electrodes. The method of solution of the problem is based on the combination of the spline collocation method along the longitudinal coordinate and the step-by-step search method along the radial coordinate. We present results of a numerical analysis of a cylinder of PZT 4 ceramic in a wide range of changes in the geometric parameters of the cylinder.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Ya. I. Burak, O. R. Hachkevych, and R. S. Musii, “Thermoelasticity of electroconductive bodies under the action of pulsed electromagnetic fields,” Mat. Met. Fiz.-Mekh. Polya, 49, No. 1, 75–84 (2006).
O. R. Hachkevych and B. D. Drobenko, “Features of the numerical solution of connected problems of the determination of electromagnetic, thermal, and mechanical fields in deformable thermosensitive electroconductive bodies under quasistationary electromagnetic loads,” Mat. Met. Fiz.-Mekh. Polya, 50, No. 3, 166–177 (2007).
A. Ya. Grigorenko and T. L. Efimova, “Using spline-approximation to solve problems of axisymmetric free vibration of thickwalled orthotropic cylinders,” Prikl. Mekh., 46, No. 10, 74–85 (2008).
A. Ya. Grigorenko and N. P. Yaremchenko, “Stress state of nonthin orthotropic shells with varying thickness and rectangular planform,” Prikl. Mekh., 44, No. 8, 91–102 (2008).
A. Ya. Grigorenko and S. N. Yaremchenko, “Refined analysis of the stress state of orthotropic elliptic cylindrical shells with variable geometrical parameters,” Prikl. Mekh., 44, No. 9, 53–62 (2008).
A. Ya. Grigorenko, T. L. Efimova, and I. A. Loza, “Solution of an axisymmetric problem of free vibrations of piezoceramic hollow cylinders of finite length by the spline collocation method,” Mat. Met. Fiz.-Mekh. Polya, 51, No. 3, 112–120 (2008).
A. Ya. Grigorenko and O. A. Avramenko, “Stress-strain analysis of closed nonthin orthotropic conical shells of varying thickness,” Prikl. Mekh., 44, No. 6, 46–58 (2008).
V. G. Karnaukhov, Ya. V. Tkachenko, and V. F. Zrazhevs’ka, “Investigation of harmonic vibrations of a spherical shell of physically nonlinear piezoelectric material,” Mat. Met. Fiz.-Mekh. Polya, 50, No. 1, 125–129 (2007).
Yu. D. Kovalev and E. N. Stativka, “Bending of a piezoceramic inhomogeneous layer at a sliding fixing of its ends,” Mat. Met. Fiz.-Mekh. Polya, 49, No. 3, 86–95 (2006).
V. N. Lazutkin and A. I. Mikhailov, “Vibrations of piezoceramic cylinders of finite sizes with heightwise polarization,” Akust. Zh., 22, No. 3, 393–399 (1976).
N. A. Shul’ga and L. V. Borisenko, “Vibrations of an axially polarized piezoceramic cylinder during electrical loading,” Prikl. Mekh., 25, No. 11, 15–19 (1989).
N. A. Shul’ga and L. V. Borisenko, “Electroelastic vibrations of sectioned piezoceramic cylinder with axial polarization,” Prikl. Mekh., 26, No. 2, 126–130 (1990).
N. A. Shul’ga, A. Ya. Grigorenko, and I. A. Loza, “Axisymmetric electroelastic waves in a hollow piezoelectric ceramic cylinder,” Prikl. Mekh., 20, No. 1, 26–32 (1984).
M. Hussein and P. R. Heyliger, “Discrete layer analysis of axisymmetric vibrations of laminated piezoelectric cylinders,” J. Sound Vibr., 192, No. 5, 995–1013 (1996).
N. Kharouf and P. R. Heyliger, “Axisymmetric free vibrations of homogeneous and laminated piezoelectric cylinders,” J. Sound Vibr., 174, No. 4, 539–561 (1994).
Author information
Authors and Affiliations
Additional information
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 52, No. 4, pp. 138–144, October–December, 2010.
Rights and permissions
About this article
Cite this article
Loza, I.A. Free vibrations of piezoceramic hollow cylinders with radial polarization. J Math Sci 174, 295–302 (2011). https://doi.org/10.1007/s10958-011-0298-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-011-0298-6