539.3
537.226.86
534.1

п’єзоелектричні резонатори
втрати енергії
коефіцієнти зв’язку
циліндричні оболонки
piezoelectric resonators
energy losses
coupling factors
cylindrical shells

Статтю присвячено аналізу проблеми вимушених коливань п’єзокерамічних циліндричних оболонок у вигляді коротких і високих кілець з радіальною поляризацією. Паралельно наведено просту ітераційну експериментально-обчислювальну методику визначення компонентів втрат енергії та коефіцієнтів зв’язку, яку ілюстровано розрахунками адмітансу коротких і високих кілець. Показано, що адмітанс, імпеданс і фазові кути не залежать від умов електричного навантаження, проте миттєва потужність дуже чутлива до режиму. Цей факт пояснює, чому режим заданої сталої напруги супроводжується значною нелінійністю, а в режимі заданого сталого струму такої нелінійності немає. Також досліджено напружений стан кілець. Встановлено, що чим більше відношення висоти до середнього діаметра кільця, тим вищий рівень крайової моди і тим сильніше розподіл головних напружень відрізняється від косинусоїди. В дуже коротких кільцях крайова мода не реєструється.
This paper is devoted to the analysis of the forced vibrations problem for piezoceramic cylindrical shells in the form of short and high rings with radial polarization. Simultaneously a new simple technique for an experimental-computational determination of energy losses components as well as coupling factors is presented. An iterative determination process is illustrated by admittance calculations in resonance–anti-resonance frequency bands for strong modes. It is shown that the admittance, impedance, phase shifts are independent on exciting electric conditions. Sample power, sample voltage and sample current are very sensitive to loading circumstances. When vibrations of the piezoelectric sample are excited by the constant voltage, the instantaneous power in sample increases at resonance frequency in many times in respect to far-resonant frequencies case. And when vibrations of the piezoelectric sample are excited by the constant current, the instantaneous power in sample decreases at resonance frequency in that ratio. The instantaneous power reaches maximum value at resonances for the constant sample voltage and at anti-resonances for the constant sample current. This fact explains why the constant voltage regime is surrounded by significant nonlinearity but in the constant currant regime such phenomenon is absent. The stress state of rings was investigated too. Verification of vibration modes was made using the method of piezotransformer transducer. This method enables to determine the distribution of internal stresses for piezoceramic elements from measurements of the surface distribution of charges. For this purpose a number of small electrode-transducers have been divided in an exterior electrode coating of the cylindrical surface. Its potentials and charges are proportional to the sum of principal stresses. It was established that the greater the ratio of height to the middle diameter of the ring, the higher the level of edge mode and the more the distribution of main stresses is different from the cosine function. In a very short rings edge mode is not registered.

1. Uchino, K. Loss mechanisms in piezoelectrics: how to measure different losses separately [Text] / K. Uchino, S. Hirose // IEEE Trans. Ultrason. Ferroelectr. Freq. Control. – 2001. – 48, No. 1. – P. 307–321.
2. Ural, S. O. Development of a high power piezoelectric characterization system and its application for resonance/antiresonance mode characterization [Text] / S. O. Ural, S. Tunodemir, Yu. Zhuang, K. Uchino //Jpn. J. Appl. Phys. – 2009. – 48, No. 5R. – 056509.
3. Uchino, K. Loss mechanisms and high power piezoelectrics [Text] / K. Uchino, J. H. Zheng, Y. H. Chen et al. // J. Mat. Sci. – 2006. – 41. – P. 217–228.
4. Shul’ga, N. A. The vibrations of piezoelectric bodies [Text] / N. A. Shul’ga, A. M. Bolkisev. – Kiev: Naukova Dumka. – 1990. – 228 p.
5. Shul’ga, M. О. Resonance electromechanical vibrations of piezoelectric plates [Text] / M. О. Shul’ga, V. L. Karlash. – Kyiv: Naukova Dumka, 2008. – 270 p.
6. Karlash, V. L. Resonant electromechanical vibrations of piezoelectric plates [Text] / V. L. Karlash // Int. Appl. Mech. – 2005. – 41, No. 7. – P. 709–747.
7. Karlash, V. L. Longitudinal and lateral vibrations of a plate piezoceramic transformer [Text] / V. L. Karlash // Ukr. J. Phys. – 2006. – 51, No. 10. – P. 985–991.
8. Glozman, I. A. Piezoceramics [Text] / I. A. Glozman. – Moscow: Energiya, 1972. – 288 p.
9. Jaffe, B. Piezoelectric ceramics [Text] / B. Jaffe, W. R. Cook, H. Jaffe. – Academic Press: London, 1971. – 142 p.
10. Karlash, V. L. Energy losses in piezoceramic resonators and its influence on vibrations’ characteristics [Text] / V. L. Karlash // Electronics and communication. – 2013. – 19, No. 2(79). – P. 82–94.
11. Karlash, V. L. Methods of determination of coupling factors and energy losses at piezoceramics resonator’s vibrations [Text] / V. L. Karlash // Acoustic bulletin. – 2012. – 15, No. 4. – P. 24–38.
12. Shul’ga, M. О. Amplitude-phase characteristics of radial vibrations of thin piezoceramics disk near resonances [Text] / M. О. Shul’ga, V. L. Karlash // Reports of the National Academy of Sciences of Ukraine. – 2013, No. 9. – P. 80–86.
13. Shul’ga, M. О. Measurement of piezoceramic elements admittance in Mason’s four-pole and its variants [Text] / M. О. Shul’ga, V. L. Karlash // Proc. ІУ Int. Sci. -tech. Conf. «Sensors, devices and systems» – 2008. – Cherkasy. – Gurzuf, 2008. – P. 54–56.
14. Karlash, V. L. Particularities of amplitude-frequency characteristics of admittance of thin piezoceramic half-disk [Text] / V. L. Karlash // Int. Appl. Mech. – 2009. – 45, No. 10. – P. 1120–1126.
15. Drumheller, D. S. Dynamic shell theory for ferroelectrics ceramics [Text] / D. S. Drumheller, A. Kalnins // J. Acoust. Soc. Am. – 1970. – 47. – Р. 1343–1353.

1. Uchino, K. Loss mechanisms in piezoelectrics: how to measure different losses separately [Text] / K. Uchino, S. Hirose // IEEE Trans. Ultrason. Ferroelectr. Freq. Control. – 2001. – 48, No. 1. – P. 307–321.
2. Ural, S. O. Development of a high power piezoelectric characterization system and its application for resonance/antiresonance mode characterization [Text] / S. O. Ural, S. Tunodemir, Yu. Zhuang, K. Uchino //Jpn. J. Appl. Phys. – 2009. – 48, No. 5R. – 056509.
3. Uchino, K. Loss mechanisms and high power piezoelectrics [Text] / K. Uchino, J. H. Zheng, Y. H. Chen et al. // J. Mat. Sci. – 2006. – 41. – P. 217–228.
4. Shul’ga, N. A. The vibrations of piezoelectric bodies [Text] / N. A. Shul’ga, A. M. Bolkisev. – Kiev: Naukova Dumka. – 1990. – 228 p.
5. Shul’ga, M. O. Resonance electromechanical vibrations of piezoelectric plates [Text] / M. O. Shul’ga, V. L. Karlash. – Kyiv: Naukova Dumka, 2008. – 270 p.
6. Karlash, V. L. Resonant electromechanical vibrations of piezoelectric plates [Text] / V. L. Karlash // Int. Appl. Mech. – 2005. – 41, No. 7. – P. 709–747.
7. Karlash, V. L. Longitudinal and lateral vibrations of a plate piezoceramic transformer [Text] / V. L. Karlash // Ukr. J. Phys. – 2006. – 51, No. 10. – P. 985–991.
8. Glozman, I. A. Piezoceramics [Text] / I. A. Glozman. – Moscow: Energiya, 1972. – 288 p.
9. Jaffe, B. Piezoelectric ceramics [Text] / B. Jaffe, W. R. Cook, H. Jaffe. – Academic Press: London, 1971. – 142 p.
10. Karlash, V. L. Energy losses in piezoceramic resonators and its influence on vibrations’ characteristics [Text] / V. L. Karlash // Electronics and communication. – 2013. – 19, No. 2(79). – P. 82–94.
11. Karlash, V. L. Methods of determination of coupling factors and energy losses at piezoceramics resonator’s vibrations [Text] / V. L. Karlash // Acoustic bulletin. – 2012. – 15, No. 4. – P. 24–38.
12. Shul’ga, M. O. Amplitude-phase characteristics of radial vibrations of thin piezoceramics disk near resonances [Text] / M. O. Shul’ga, V. L. Karlash // Reports of the National Academy of Sciences of Ukraine. – 2013, No. 9. – P. 80–86.
13. Shulga, M. O. Measurement of piezoceramic elements admittance in Masons four-pole and its variants [Text] / M. O. Shulga, V. L. Karlash // Proc. IU Int. Sci. -tech. Conf. "Sensors, devices and systems" – 2008. – Cherkasy. – Gurzuf, 2008. – P. 54–56.
14. Karlash, V. L. Particularities of amplitude-frequency characteristics of admittance of thin piezoceramic half-disk [Text] / V. L. Karlash // Int. Appl. Mech. – 2009. – 45, No. 10. – P. 1120–1126.
15. Drumheller, D. S. Dynamic shell theory for ferroelectrics ceramics [Text] / D. S. Drumheller, A. Kalnins // J. Acoust. Soc. Am. – 1970. – 47. – R. 1343–1353.