Підхід до розрахунку гармонічних коливань електропружних циліндрів

Oleksander Ihorovych Bezverkhyi; Liudmyla Oleksandrivna Hryhorieva

doi:10.20535/2523-4455.2018.23.1.64279

Vol. 23 · Issue 1 · 2018 Feb 28, 2018 Acoustical devices and systems

The approach to the calculation of harmonic oscillations of electroelastic cylinders

Oleksander Ihorovych Bezverkhyi Corresponding Національний транспортний університет; National Transport University Ukraine

Liudmyla Oleksandrivna Hryhorieva S. P. Tymoshenko Institute of Mechanics of NAS of Ukraine Ukraine

Pages37-43 PublishedFeb 28, 2018

PDF (Ukrainian)

VOL 23 · ISS 1 · 2018 View issue

Abstract

The paper presents a new approach to the reduction of harmonic equations of electromechanical axially symmetric oscillations in cylindrical system of coordinates to first order ordinary differential equations based on the Hamiltonian formalism by radial coordinate and difference approximations by axial coordinate. Numerical implementation is executed for cylinders with membranes on ends. Integrating of boundary problem is developed by discrete orthogonalization method. Testing of results and comparison with obtained by other authors and other methods results is done. A study of two-dimensional harmonic oscillations of polarized by thickness piezoceramic cylinders at electric load is developed. The dependence of the oscillations nature from the frequency and resonant frequencies for cylinders of different length are defined. The dynamic characteristics of the electromechanical cylinder state at forced oscillations with a frequency close to the first natural frequency are studied. It is established, that with increasing of cylinder length natural frequencies are reduced and the number of resonant frequencies in the considered frequence range increases. Ref. 12, fig. 2.

Keywords

#piezoceramic cylinder #harmonical electrical loads #equations system of Hamiltonian type #electroelastic boundary problem #forced vibrations #natural frequencies #resonance

References

A. M. Bolkisev and N. A. Shulga, “Vyinuzhdennyie kolebaniya pezokeramicheskogo pologo tsilindra (radialnaya polyarizatsiya) [Forced Vibrations of Piezoceramic Hollow Cylinders (radial polarization)],” Pricladnaya Mech. , vol. 21, no. 5, pp. 118–121, 1985.
N. A. Shul’ga and A. M. Bolkisev, Kolebaniya pezoelektricheskikh tel [Vibrations of piezoelectric bodies] . Kyiv: Naukova dumka, 1990.
N. A. Shulga and L. V. Borisenko, “Vibrations of an Axially Polarized Cylinder during Electrical Loading,” Int. Appl. Mech. , vol. 25, no. 11, pp. 1070–1075, 1989, DOI: 10.1007/BF00888988 .
Y. N. Grigorenko, T. I. Efimova, and I. A. Loza, “Free Vibrations of Axially Polarized Piezoceramic Hollow Cylinders of finite Length,” Int. Appl. Mech. , vol. 46, no. 6, pp. 625–634, 2010, DOI: 10.1007/s10778-010-0350-0 .
R. Bansevičius, R. Rimašauskienė, D. Mažeika, and G. Kulvietis, “Analysis of cylindrical piezoelectric actuator used in flow control device,” Mechanika , vol. 17, no. 4, pp. 395–399, 2011, DOI: 10.5755/j01.mech.17.4.568 .
O. V. Korzhyk, O. M. Petrishchev, and N. V. Bogdanova, “Priem zvuka sfericheskim elektrouprugim preobrazovatelem s razreznyimi elektrodami (chast 3) [The trunsducing of sound wave by electroelastics piezo- receiver with dissected electrical electrodes (part 3)],” Electron. Commun. , vol. 20, no. 2 (85), pp. 66–70, 2015, DOI: 10.20535/2312-1807.2015.20.2.47741 .
O. H. Leiko, Z. T. Husak, I. V. Kandrachuk, and M. A. Melnichenko, “Radiation field angled horn antenna with a piezoceramic transducer with radial polarization,” Electron. Commun. , vol. 20, no. 2, pp. 71–78, 2015, DOI: 10.20535/2312-1807.2015.20.2.47742 .
R. V. N. Melnik and K. N. Melnik, “Modelling dynamics of piezoelectric solids in the two-dimensional case,” Appl. Math. Model. , vol. 24, no. 3, pp. 147–163, 2000, DOI: 10.1016/S0307-904X(99)00032-3 .
S. Vidoli and R. C. Batra, “Coupled extensional and torsional deformations of a piezoelectric cylinder,” Smart Mater. Struct. , vol. 10, no. 2, pp. 300–304, 2001, DOI: 10.1088/0964-1726/10/2/315 .
V. M. Shul’ga, “Nonaxisymmetric Electroelastic Vibrations of a Hollow Cylinder with Radial Axis of Physicomechanical Symmetry,” Int. Appl. Mech. , vol. 41, no. 7, pp. 766–769, 2005, DOI: 10.1007/s10778-005-0143-z .
N. A. Shul’ga and L. O. Grigor’eva, “Comparative analysis of the electroelastic thickness vibrations of layers with curved boundaries,” Int. Appl. Mech. , vol. 47, no. 2, pp. 177–185, 2011, DOI: 10.1007/s10778-011-0451-4 .
О. І. Bezverkhyi and L. O. Grigor’eva, “Metod issledovaniya osesimmetrichnyih kolebaniy pezokeramicheskih tel [Research method of axially symmetric oscillations of piezoceramic bodies],” Probl. Comput. Mech. strength Struct. , vol. 24, pp. 5–17, 2015, URL: https://pommk.dp.ua/index.php/journal/article/view/290 .

Next in issue Physical fields of hydroacoustic sonar arrays with baffle and cylindrical piezoceramic radiators with radial polarization

§ 06 — Related

[1] A. M. Bolkisev and N. A. Shulga, “Vyinuzhdennyie kolebaniya pezokeramicheskogo pologo tsilindra (radialnaya polyarizatsiya) [Forced Vibrations of Piezoceramic Hollow Cylinders (radial polarization)],” Pricladnaya Mech. , vol. 21, no. 5, pp. 118–121, 1985.

[2] N. A. Shul’ga and A. M. Bolkisev, Kolebaniya pezoelektricheskikh tel [Vibrations of piezoelectric bodies] . Kyiv: Naukova dumka, 1990.

[3] N. A. Shulga and L. V. Borisenko, “Vibrations of an Axially Polarized Cylinder during Electrical Loading,” Int. Appl. Mech. , vol. 25, no. 11, pp. 1070–1075, 1989, DOI: 10.1007/BF00888988 .

[4] Y. N. Grigorenko, T. I. Efimova, and I. A. Loza, “Free Vibrations of Axially Polarized Piezoceramic Hollow Cylinders of finite Length,” Int. Appl. Mech. , vol. 46, no. 6, pp. 625–634, 2010, DOI: 10.1007/s10778-010-0350-0 .

[5] R. Bansevičius, R. Rimašauskienė, D. Mažeika, and G. Kulvietis, “Analysis of cylindrical piezoelectric actuator used in flow control device,” Mechanika , vol. 17, no. 4, pp. 395–399, 2011, DOI: 10.5755/j01.mech.17.4.568 .

[6] O. V. Korzhyk, O. M. Petrishchev, and N. V. Bogdanova, “Priem zvuka sfericheskim elektrouprugim preobrazovatelem s razreznyimi elektrodami (chast 3) [The trunsducing of sound wave by electroelastics piezo- receiver with dissected electrical electrodes (part 3)],” Electron. Commun. , vol. 20, no. 2 (85), pp. 66–70, 2015, DOI: 10.20535/2312-1807.2015.20.2.47741 .

[7] O. H. Leiko, Z. T. Husak, I. V. Kandrachuk, and M. A. Melnichenko, “Radiation field angled horn antenna with a piezoceramic transducer with radial polarization,” Electron. Commun. , vol. 20, no. 2, pp. 71–78, 2015, DOI: 10.20535/2312-1807.2015.20.2.47742 .

[8] R. V. N. Melnik and K. N. Melnik, “Modelling dynamics of piezoelectric solids in the two-dimensional case,” Appl. Math. Model. , vol. 24, no. 3, pp. 147–163, 2000, DOI: 10.1016/S0307-904X(99)00032-3 .

[9] S. Vidoli and R. C. Batra, “Coupled extensional and torsional deformations of a piezoelectric cylinder,” Smart Mater. Struct. , vol. 10, no. 2, pp. 300–304, 2001, DOI: 10.1088/0964-1726/10/2/315 .

[10] V. M. Shul’ga, “Nonaxisymmetric Electroelastic Vibrations of a Hollow Cylinder with Radial Axis of Physicomechanical Symmetry,” Int. Appl. Mech. , vol. 41, no. 7, pp. 766–769, 2005, DOI: 10.1007/s10778-005-0143-z .

[11] N. A. Shul’ga and L. O. Grigor’eva, “Comparative analysis of the electroelastic thickness vibrations of layers with curved boundaries,” Int. Appl. Mech. , vol. 47, no. 2, pp. 177–185, 2011, DOI: 10.1007/s10778-011-0451-4 .

[12] О. І. Bezverkhyi and L. O. Grigor’eva, “Metod issledovaniya osesimmetrichnyih kolebaniy pezokeramicheskih tel [Research method of axially symmetric oscillations of piezoceramic bodies],” Probl. Comput. Mech. strength Struct. , vol. 24, pp. 5–17, 2015, URL: https://pommk.dp.ua/index.php/journal/article/view/290 .

The approach to the calculation of harmonic oscillations of electroelastic cylinders

Abstract

Keywords

References

Similar articles in this journal

Practical Method of Estimating Safe Sounds for a Person with PTSD

Experimental Study of the Frequency Characteristics of MEMS Microphones for Railway Noise Monitoring

Development of a Bidirectional Road User Warning System Based on the ESP32 Microcontroller

Similar Articles

Similar Articles

Radiation of maximum acoustic power by systems of hydroacoustic cylindrical piezoceramic transducers with circular polarization

Physical fields of hydroacoustic sonar arrays with baffle and cylindrical piezoceramic radiators with radial polarization

Еlectromechanical Sensitivity of Round and Circular Piezoelectric Thin Plates at Mechanical Disturbance

Mechanical fields of the piezoceramic radiator of strength design situated near acoustical baffle

Simulation Modeling of a Filter-Compensating Converter for a Three-Phase Three-Wire Network

Steady-State Analysis of Inverter Working with Varied Load

The laboratory tester of solar cells with dynamic reconfigutration of measuring system

Apparent Power and Efficiency of Three-Phase Four-Wire System

Development of a Bidirectional Road User Warning System Based on the ESP32 Microcontroller

The Process Analysis in Domain of Two Variables