Numerical solution of the problem of propagation of forced electroelasticity waves in a solid piezoceramic cylinde
DOI:
https://doi.org/10.15407/dopovidi2022.04.033Keywords:
forced wave propagation, axisymmetric problem, piezoelectric solid cylinder, numerical method, nonhomogeneous material, kinematic characteristicsAbstract
The propagation of forced axisymmetric waves in a solid homogeneous and inhomogeneous piezoceramic cylinder with axial polarization based on the linear theory of elasticity and the linear electromechanical coupling is investigated. A mechanical load to the lateral surface of the cylinder is applied and it is free of the electrodes. The case of the continuously inhomogeneous piezoceramic cylinder material is considered. The boundary conditions at singular point of a solid piezoceramic cylinder are formulated. The discretely continual analytical numerically approach to solve of the problems of the forced wave propagation in the piezoceramic solid cylindrical bodies is proposed. The three-dimensional problem of the theory of electroelasticity in the partial derivatives (by presenting components of the elasticity tensor, component of displacement vectors, electrical induction and electrostatic potential by running waves in the axial direction) is reduced to the boundary value problems for the system of the ordinary differential equations. The оne-dimensional problem is solved by a stable method of discrete orthogonalization. The kinematic analysis of the propagation of forced electroelastic waves in a solid piezoceramic homogeneous and inhomogeneous cylinder is carried out
Downloads
References
Dai, H. -I., Hong, L., Fu, Y. -M. & Xiao, X. (2010). Analytical solution for electromagnetothermoelastic behavior of a functionally graded piezoelectric hollow cylinder. Appl. Math. Model., 34, No. 2, pp. 343-357. https: //doi. org/10. 1016/j. apm. 2009. 04. 008
Grigorenko, A. Y. & Loza, I. A. (2017). Axisymmetric Acoustoelectric Waves in a Hollow Cylinder Made of a Continuously Inhomogeneous Piezoelectric Material. Int. Appl. Mech., 53, No. 4, pp. 374-380. https: //doi. org/10. 1007/s10778-017-0821-7
Grigorenko, A. Y. & Loza, I. A. (2017). Propagation of axisymmetric electroelastic waves in a hollow layered cylinder under mechanical excitation. Int. Appl. Mech., 53, No. 5, pp. 562-567. https: //doi. org/10. 1007/ s10778-017-0837-z
Grigorenko, A. Y, Müller, W. H., Grigorenko, Y. M. & Vlaikov, G. G. (2016). Recent developments inanisotropic heterogeneous shell theory. In: General theory and applications of classical theory. Vol. I. Berlin: Springer.
Grigorenko A. Ya., Müller, W. H. & Loza, I. A. (2021). Selected Problems in the Elastodynamics of Piezoceramic Bodies. Springer.
Grigorenko, Ya. M., Grigorenko, A. Ya. & Rozhok, L. S. (2006). Solving the Stress Problem for Solid Cylinders with Different End Conditions. Int. Appl. Mech., 42, No. 6, pp. 629-635. https: //doi. org/10. 1007/s10778-006-0130-z
Han, X. & Liu, G. -R. (2003). Elastic waves in a functionally graded piezoelectric cylinder. Smart. Mater. Struct., 12, No. 6, pp. 962-971. https: //doi. org/10. 1088/0964-1726/12/6/014
Puzyrev, V. & Storozhev, V. I. (2011). Wave propagation in axially polarized piezoelectric hollowcylinder of sector cross section. J. Sound. Vib., 330, Is. 18-19, pp. 4508-4518.
Paul, H. S. (1962). Torsional vibration of a circular cylinder of piezoelectric β-quartz. Arch. Mech. Stosow., 14, No. 5, pp. 127-134.
Puzyrev, V. (2010). Elastic waves in piezoceramic cylinders of sector cross-section. Int. J. Solids. Struct., 47, Is. 16, рр. 2115-2122. https: //doi. org/10. 1016/j. ijsolstr. 2010. 04. 011
Shatalov, M. Y., Every, A. G. & Yenwong-Faia, A. S. (2009). Analysis of non-axisymmetric wave propagation in a homogeneous piezoelectric solid circular cylinder of transversely isotropic material. Int. J. Solids. Struct., 46, No. 3–4, pp. 837-850. https: //doi. org/10. 1016/j. ijsolstr. 2008. 09. 022
Shul’ga, N. A. (2002. ) Propagation of harmonic waves in anisotropic piezoelectric cylinders. Homogeneous piezoceramic waveguides. Int. Appl. Mech., 38, pp. 1440-1458. https: //doi. org/10. 1023/A: 1023205707153
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Reports of the National Academy of Sciences of Ukraine
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
