Title Nonlinear Vibrations of Piezoceramic Disk

Year 2020, Volume: 22 Issue: 64, 209 - 217, 24.01.2020

Gözde Sarı , Yasemin Nur Aydın

https://doi.org/10.21205/deufmd.2020226421

Abstract

Nonlinear vibration analysis of
piezo disc which is forced directly by piezo electrical effect is studied. Piezoceramic
disc consists of brass disc and piezo layer. The piezoceramic disk is attached
to the ground by an elastic foundation. The effect of nonlinearity occurs with
the effect of elastic foundation. In this article, the equation of motion with
cubic nonlinearity is proposed for the nonlinear vibrations of the piezoceramic
disc. In order to obtain the phase modulation and frequency response functions
of the cubic nonlinear equation, multi-scales method is applied in the
equation. The analytically derived frequency response curve is confirmed by
experimental data of the harmonic forced disk with piezoelectric effect. The
experimentally obtained frequency response curves of the piezoceramic disk
forced by the piezoelectric effect are obtained directly in the first mode. The
results are as follows; It is found that as the amplitude of the force
increased, minor decreases in nonlinear resonance frequency are observed. It is
observed that nonlinear behavior is of softening type. It is observed that the
experimental model is compatible with the experimental results.

Keywords

piezoceramic disk, nonlinear vibration, experimental analysis, multiple scales method

Piezo Seramik Diskin Nonlineer Titreşimleri

Abstract

Piezo elektriksel etki ile direkt
olarak zorlanan piezo diskin nonlineer titreşim analizi çalışılmıştır. Piezoseramik
disk; pirinç disk ve piezo tabakadan oluşmaktadır. Piezoseramik disk elastik
yatak ile yere bağlanmıştır. Nonlineerlik etkisi elastik yatak etkisi ile  ortaya çıkmaktadır.  Bu makalede piezoseramik diskin nonlineer
titreşimleri için kübik nonlineeriteye sahip hareket denklemi önerilmiştir.
Kübik nonlineer denklemin faz modülasyon ve frekans cevap fonksiyonlarını elde
etmek için denklemde çok ölçekli metot uygulanmıştır. Analitik olarak türetilen
frekans cevap eğrisi, piezo elektriksel etki ile harmonik olarak zorlanan
diskin deneysel verileriyle doğrulanmıştır. Piezoelektriksel etki ile zorlanan
piezoseramik diskin deneysel olarak elde edilen frekans cevap eğrileri; direkt
olarak birinci modda elde edilmiştir. 
Sonuçlar şöyledir; zorlama genliği arttıkça nonlineer rezonans
frekansında minör azalmalar olduğu tespit edilmiştir. Nonlineer davranışın
yumuşatıcı tipte olduğu gözlenmiştir. Deneysel sonuçlarla teorik modelin uyumlu
olduğu gözlemlenmektedir. 

Keywords

piezoseramik disk, nonlineer titreşim, deneysel analiz, çok ölçekli metot

References

• [1] Rupitsch, S.J. 2019. Piezoelectric sensors and actuators - fundamentals and applications, Springer, Berlin, 559.
• [2] Wu, X., Lin, J., Kato, S., Zhang, K., Ren, T. and Liu, L., 2008. A frequency adjustable vibration energy harvester, Proceeding of PowerMEMS 2008, 9-12 Kasım, Japan, 245–8.
• [3] Leland, E.S., Wright, P.K., 2006. Resonance tuning of piezoelectric vibration energy scavenging generators using compressive axial preload, Smart Material and Structure, Cilt. 15 s. 1413, DOI:10.1088/0964-1726/15/5/030.
• [4] Hu, H., Xue, H. and Hu, Y., 2007. A spiral-shaped harvester with an improved harvesting element and an adaptive storage circuit, IEEE transactions on ultrasonics, ferroelectrics, and frequency control, Cilt 54 s. 1177–87, DOI: 1177–87, 10.1109/TUFFC.2007.371.
• [5] Ramlan, R., Brennan, M. J., Mace, B. R. and Kovacic, I., 2009. Potential benefits of a non-linear stiffness in an energy harvesting device, Nonlinear Dynamics, Cilt 59 s. 545–58, DOI: 10.1007/s11071-009-9561-5.
• [6] Cottone, F., Vocca, H. and Gammaitoni, L., 2009. Nonlinear energy harvesting ,Physical Review Letters 102 080601, DOI: https://doi.org/10.1103/PhysRevLett.102.080601.
• [7] Mann, B. P. and Sims, N. D., 2010. On the performance and resonant frequency of electromagnetic induction energy harvesters, Journal of Sound and Vibration, Cilt. 329 s. 1348–61, DOI: 10.1016/j.jsv.2009.11.008.
• [8] Stanton, S. C., McGehee, C. C. and Mann, B. P., 2010. Nonlinear dynamics for broadband energy harvesting: investigation of a bistable piezoelectric inertial generator, Physica D: Nonlinear Phenomena Cilt. 239 s. 640–53, DOI:10.1016/j.physd.2010.01.019.
• [9] Tvedt, L. G. W., Nguyen, D. S. and Halvorsen, E., 2010. Nonlinear behavior of an electrostatic energy harvester under wideand narrowband excitation Journal of Microelectromechanical Systtems, Cilt. 19 s. 305–16, DOI: 10.1109/JMEMS.2009.2039017.
• [10] Nguyen, D. S., Halvorsen, E., Jensen, G. U. and Vogl, A., 2010. Fabrication and characterization of a wideband MEMS energy harvester utilizing nonlinear springs, Journal of Micromechanical Microengineering, Cilt. 20 125009 11 s., DOI:https://doi.org/10.1088/0960-1317/20/12/125009.
• [11] Yang, B., Liu, J., Tang, G., Luo, J., Yang, C., and Li, Y., A, 2011. Generator with nonlinear spring oscillator to provide vibrations of multi-frequency, Applied Physics Letters, Cilt. 99 223505 3 s., DOI: 10.1063/1.3664223.
• [12] Patel, V.K., Reed, F.K., Kisne, R., Peng, C., Moghaddam, S., Momen, A. M., 2018. Novel Experimental Study of Fabric Drying Using Direct Contact Ultrasonic Vibration, Journal of Thermal Science and Engineering Applications, Cilt. 11(2), 021008 10s., DOI: 10.1115/1.4041596.
• [13] Dupuis, E. D., Momen, A.M., Patel, V.K., Shahab, S., 2019. Electroelastic Investigation of Drying Rate in The Direct Contact Ultrasonic Fabric Dewatering Process, Applied Energy Cilt. 235, (1) s. 451-462, DOI:https://doi.org/10.1016/j.apenergy.2018.10.100.
• [14] Arafa, M., Baz, A., 2004. On the nonlinear behavior of piezoelectric actuators, Journal of vibration and control, Cilt. 10, s. 387-398, DOI:https://doi.org/10.1177/1077546304033365.
• [15] Uzun, Y., Kurt, E.H., Kurt, H., 2015. Explorations of displacement and velocity nonlinearities and theireffects to power of a magnetically-excited piezoelectric pendulum, Department, Sensors and Actuators A, Cilt. 224 s. 119–130, DOI:https://doi.org/10.1016/j.sna.2015.01.033.
• [16] James, A. J., Vukasinovic, B., Smith, M. K. and Glezer, A., 2003. Vibration-induced drop atomization and bursting, Journal of Fluid Mechanics, Cilt. 476 s. 1-28, DOI:https://doi.org/10.1017/S0022112002002835.
• [17] Nayfeh, A.H., 1973. Perturbation Methods, A. Wiley Interscience, Jhn Wiley & Sons, New York, 1973.
• [18] Nayfeh, A.H. 1881, Introduction to Perturbation Techniques, New York, Wiley, 1981.
• [19] Nayfeh, A.H., Nayfeh J.F. and Mook, D.T., 1995, Nonlinear Oscillations, New York, Wiley, 1995.
• [20] (Erişim tarihi: 13.06.2019) https://www.murata.com/en-eu/products/sound/diaphragm/7bbww