Bending Vibrations of Bimorph Piezoceramic Plates of Noncanonical Shape
- 5 Downloads
The superposition method is used to develop an effective method for analytical solution of the problem of the harmonic bending vibrations of parallelogram-shaped bimorph piezoceramic plates. The reduction of infinite series allows deriving a finite-dimensional system of algebraic equations by satisfying given boundary conditions by minimizing the standard deviation and using the collocation method.
Keywordsbending vibrations piezoceramic plates of noncanonical shape superposition method collocation method standard deviation reduction method natural frequency spectrum
Unable to display preview. Download preview PDF.
- 1.M. Ya. Bornyak and B. Soltannia, “Projection method of solving the problem of the natural vibrations of a clamped plate,” Akust. Visn., 12, No. 1, 11–18 (2009).Google Scholar
- 4.V. V. Meleshko and S. O. Papkov, “Bending vibrations of simply supported elastic rectangular plates: from Khladni (1809) and Ritz (1909) to today,” Akust. Visn., 12, No. 4, 34–51 (2009).Google Scholar
- 5.V. T. Grinchenko, A. F. Ulitko, and N. A. Shul’ga, Electroelasticity, Vol. 5 of the five-volume series Mechanics of Coupled Fields in Structural Members [in Russian], Naukova Dumka, Kyiv (1989).Google Scholar
- 6.W. P. Mason, Piezoelectric Crystals and Their Application to Ultrasonics, Van Nostrand, New York (1950).Google Scholar
- 8.P. Shakeri Mobarakeh, V. T. Grinchenko, V. V. Popov, B. Soltannia, and G. M. Zrazhevsky, “Modern methods for numerical-analytical solution of boundary-value problems in noncanonical domains,” Mat. Metody Fiz.-Mekh. Polya, 60, No. 4, 75–89 (2017).Google Scholar
- 9.P. Shakeri Mobarakeh and G. M. Zrazhevs’ky, “Galerkin’s algorithm in the method of partial domains of solving boundary problems,” Visn. Kyiv. Univ., Ser. Fiz. Mat. Nauky, No. 1, 75–82 (2014).Google Scholar
- 11.M. Hajikhani, B. Soltannia, A. R. Oskouei, and M. Ahmadi, “Monitoring of delamination in composites by use of acoustic emission,” in: Proc. 3rd Condition Monitoring &Fault Diagnosis Conf., Tehran, Iran (2009).Google Scholar
- 12.A. W. Leissa and M. S. Qatu, Vibrations of Continuous Systems, McGraw-Hill, New York (2011).Google Scholar
- 15.P. Shakeri Mobarakeh, V. T. Grinchenko, H. Ahmadi, and B. Soltannia, “The amplitude-frequency characteristics of piezoceramic plates depending on the shape of the boundaries,” in: Proc. 7th Int. Conf. on Acoustics and Vibration (ISAV2017), Tehran, Iran (2017).Google Scholar
- 16.P. Shakeri Mobarakeh, V. T. Grinchenko, S. Iranpour Mobarakeh, and B. Soltannia, “Influence of acoustic screen on directional characteristics of cylindrical radiator,” in: Proc. 5th Int. Conf. on Acoustics and Vibration (ISAV2015), Tehran, Iran (2015).Google Scholar
- 19.P. Shakeri Mobarakeh, V. T. Grinchenko, and G. M. Zrazhevsky, “A numerical-analytical method for solving boundary-value problem of elliptical type for a parallelogram shaped plate,” Bulletin of T. Shevchenko Nat. Univ. of Kyiv, Ser.: Phys.-Math., Special issue, 297–304 (2015).Google Scholar