Comparative Analysis of Two Methods Used for the Investigation of Harmonic Vibrations of Piezoceramic Cylinders
- 14 Downloads
We study steady-state axisymmetric vibrations of finite-length piezoceramic cylinders subjected to electric loading. A key system of equations is constructed as result of the reduction of the system of equations of electroelasticity in a cylindrical coordinate system to a system of Hamilton-type equations or by using the conditions of stationarity of the functional of Hamilton–Ostrogradskii principle. In the first case, the transition to ordinary differential equations is performed by using finite-difference expressions. In the second case, it is necessary to use spline approximations of the first-order. For the solution of the obtained boundary-value problems, we apply the method of discrete orthogonalization. The results obtained by using the indicated methods are compared. The dependence of vibrations on the frequency of loading is analyzed for a radially polarized cylinder. The resonance frequencies are determined.
Unable to display preview. Download preview PDF.
- 1.O. I. Bezverkhyi, “On one method of investigation of axisymmetric harmonic vibrations in electroelasticity,” Zbirn. Nauk. Prats. Dnipr. Derzh. Tekh. Univ. Tekh. Nauk., Issue 1, 130–135 (2014).Google Scholar
- 2.O. I. Bezverkhyi, “On one method of investigation of axisymmetric vibrations of piezoceramic bodies,” in: Actual Problems of Mechanics of Deformable Solids. Proc. of the VII Internat. Sci. Conf. [in Russian], Donetsk Nat. Univ., Donetsk (2013), Vol. 1, pp. 65–69.Google Scholar
- 3.A. M. Bolkisev and N. A. Shul’ga, “Forced vibrations of piezoceramic hollow cylinder (radial polarization),” Prikl. Mekh., 21, No. 5, 118–121 (1985).Google Scholar
- 4.A. Ya. Grigorenko, T. L. Efimova, and I. A. Loza, “Free vibrations of axially polarized piezoceramic hollow cylinders of finite length,” Prikl. Mekh., 46, No. 6, 17–26 (2010); English translation: Int. Appl. Mech., 46, No. 6, 625–633 (2010).Google Scholar
- 5.Yu. S. Zav’yalov, B. I. Kvasov, and V. L. Miroshnichenko, Methods of Spline Functions [in Russian], Nauka, Moscow (1980).Google Scholar
- 6.V. Z. Parton and B. A. Kudryavtsev, Electromagnetoelasticity of Piezoelectric and Conducting Bodies [in Russian], Nauka, Moscow (1988).Google Scholar
- 7.V. M. Shul’ga, “Nonaxisymmetric electroelastic vibrations of a hollow cylinder with radial axis of physicomechanical symmetry,” Prikl. Mekh., 41, No. 7, 68–72 (2005); English translation: Int. Appl. Mech., 41, No. 7, 766–769 (2005).Google Scholar
- 8.N. A. Shul’ga and A. M. Bolkisev, Vibrations of Piezoelectric Bodies [in Russian], Naukova Dumka, Kiev (1990).Google Scholar
- 9.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); English translation: Sov. Appl. Mech., 25, No. 11, 1070–1074 (1989).Google Scholar
- 10.M. O. Shulga and V. L. Karlash, Resonance Electromechanical Vibrations of Piezoelectric Plates [in Ukrainian], Naukova Dumka, Kiev (2008).Google Scholar
- 12.M. O. Shulga and L. O. Grigoryeva, “Electromechanical unstationary thickness vibrations of piezoceramic transformers at electric excitation,” in: A. L. Galloway (editor), Mechanical Vibrations: Types, Testing and Analysis, Nova Sci. Publ., New York (2011), p. 179–204.Google Scholar