Abstract
Non-ideal energy sources are present in several engineering applications where the power source interacts with the dynamics of the structure to which it is coupled. The systems driven by this kind of source present a rich dynamic behavior and some phenomena that can only be observed under non-ideal consideration. The modeling of such systems becomes much more complex due to the interaction between the system and the energy source, requiring an additional equation. The present work proposes a continuous vibration model of a cantilever beam with two unbalanced DC motors. The motors are considered non-ideal energy sources. The advantage of the continuous approach is that the position of the motors can be easily varied. In addition, time–frequency methods are performed in order to characterize and identify the occurrence of the Sommerfeld effect on the non-stationary operation. In order to validate the model, experimental measurements were performed and, subsequently, compared with the numerical results.
Similar content being viewed by others
References
Mereles A, Varanis M, Silva AL, Balthazar JM, Lopes EMO, Bavastri CA (2019) Mathematical modelling of a cantilever beam driven by two unbalanced electric motors. In: Proceedings of the 25th international congress of mechanical engineering, ABCM
Balthazar JM, Mook DT, Weber HI, Brasil RM, Fenili A, Belato D, Felix J (2003) An overview on non-ideal vibrations. Meccanica 38(6):613–621
Kononenko VO (1969) Vibrating systems with a limited power supply. Iliffe, London
Sommerfeld A (1902) Beiträge zum dynamischen ausbau der festigkeitslehe. Physikal Zeitschr 3:266–286
Felix JLP, Balthazar JM, Brasil RM (2005) On saturation control of a non-ideal vibrating portal frame foundation type shear-building. J Vib Control 11(1):121–136
Zhang X, Wen B, Zhao C (2014) Experimental investigation on synchronization of three co-rotating non-identical coupled exciters driven by three motors. J Sound Vib 333(13):2898–2908
Samantaray A, Dasgupta S, Bhattacharyya R (2010) Sommerfeld effect in rotationally symmetric planar dynamical systems. Int J Eng Sci 48(1):21–36
Dimentberg MF (1988) Statistical dynamics of nonlinear and time-varying systems, vol 5. Research Studies Press, Baldock
Evan-Iwanowski R (1976) Resonance oscillations in mechanical systems. North-Holland, Amsterdam
Nayfeh AH, Mook DT (2008) Nonlinear oscillations. Wiley, Hoboken
Cveticanin L, Zukovic M, Balthazar JM (2018) Dynamics of mechanical systems with non-ideal excitation. Springer, Berlin
El-Badawy AA (2007) Behavioral investigation of a nonlinear nonideal vibrating system. J Vib Control 13(2):203–217
Gonçalves P, Silveira M, Junior BP, Balthazar J (2014) The dynamic behavior of a cantilever beam coupled to a non-ideal unbalanced motor through numerical and experimental analysis. J Sound Vib 333(20):5115–5129
Varanis M, Balthazar J, Silva A, Mereles A, Pederiva R (2018) Remarks on the Sommerfeld effect characterization in the wavelet domain. J Vib Control 25:98–108
Brasil R, Balthazar JM (2000) Nonlinear oscillations of a portal frame structure excited by a nonideal motor. In: Proceedings of 2000 2nd international conference on control of oscillations and chaos vol. 2. IEEE, pp 275–278
Tusset AM, Bueno ÁM, dos Santos JPM, Tsuchida M, Balthazar JM (2016) A non-ideally excited pendulum controlled by SDRE technique. J Braz Soc Mech Sci Eng 38(8):2459–2472
Arbex HC, Balthazar JM, de Pontes Junior BR, da Fonseca RMLR, Felix JLP, Tusset AM, Bueno ÁM et al (2015) On nonlinear dynamics behavior and control of a new model of a magnetically levitated vibrating system, excited by an unbalanced dc motor of limited power supply. J Braz Soc Mech Sci Eng 37(4):1139–1150
Hu W-H, Thöns S, Rohrmann RG, Said S, Rücker W (2015) Vibration-based structural health monitoring of a wind turbine system. Part i: resonance phenomenon. Eng Struct 89:260–272
Balthazar JM, Cheshankov BI, Ruschev D, Barbanti L, Weber H (2001) Remarks on the passage through resonance of a vibrating system with two degrees of freedom, excited by a non-ideal energy source. J Sound Vib 239(5):1075–1085
Wauer J, Suherman S (1998) Vibration suppression of rotating shafts passing through resonances by switching shaft stiffness. J Vib Acoust 120(1):170–180
De Souza S, Caldas IL, Viana R, Balthazar JM, Brasil R (2005) Impact dampers for controlling chaos in systems with limited power supply. J Sound Vib 279(3–5):955–967
Felix J, Balthazar JM, Brasil R (2009) A short note on transverse vibrations of a shaft carrying two (or one) disk excited by a nonideal motor. J Comput Nonlinear Dyn 4(1):014501
Balthazar JM, Felix J, Brasil R, Krasnopolskaya T, Shvets AY (2009) Nonlinear interactions in a piezoceramic bar transducer powered by a vacuum tube generated by a nonideal source. J Comput Nonlinear Dyn 4(1):011013
Piccirillo V, Tusset AM, Balthazar JM (2014) Dynamical jump attenuation in a non-ideal system through a magnetorheological damper. J Theor Appl Mech 52(3):595–604
Felix JL, Balthazar JM, Brasil RM (2005) On tuned liquid column dampers mounted on a structural frame under a non-ideal excitation. J Sound Vib 282:1285–1292
de Castro Silva FE, Bavastri CA (2019) A methodology for an optimal design of physical parameters, positions, and viscoelastic materials of simple dynamic absorbers for passive vibration control. J Vib Control 25(6):1133–1147
Bronkhorst KB, Febbo M, Lopes EM, Bavastri CA (2018) Experimental implementation of an optimum viscoelastic vibration absorber for cubic nonlinear systems. Eng Struct 163:323–331
Addison PS (2017) The illustrated wavelet transform handbook: introductory theory and applications in science, engineering, medicine and finance. CRC Press, Boca Raton
Varanis M, Pederiva R (2018) Statements on wavelet packet energy-entropy signatures and filter influence in fault diagnosis of induction motor in non-stationary operations. J Braz Soc Mech Sci Eng 40(2):98
Daubechies I, Lu J, Wu H-T (2011) Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool. Appl Comput Harmon Anal 30(2):243–261
Zhigang C, Xu X, Xiaolei D, Junling Z, Nan Z (2019) Leakage detection in pipelines based on synchrosqueezed wavelet transform. In: 2019 Chinese control and decision conference (CCDC). IEEE, pp 2679–2684
Auger F, Flandrin P, Lin Y-T, McLaughlin S, Meignen S, Oberlin T, Wu H-T (2013) Time-frequency reassignment and synchrosqueezing: an overview. IEEE Signal Process Mag 30(6):32–41
Varanis M, Norenberg JPC, Rocha RT, Oliveira C, Balthazar JM, Tusset ÂM (2020) A comparison of time-frequency methods for nonlinear dynamics and chaos analysis in an energy harvesting model. Braz J Phys 1–10
Wang S, Chen X, Selesnick IW, Guo Y, Tong C, Zhang X (2018) Matching synchrosqueezing transform: a useful tool for characterizing signals with fast varying instantaneous frequency and application to machine fault diagnosis. Mech Syst Signal Process 100:242–288
Mihalec M, Slavič J, Boltežar M (2016) Synchrosqueezed wavelet transform for damping identification. Mech Syst Signal Process 80:324–334
Cao H, Xi S, Chen X, Wang S (2016) Zoom synchrosqueezing transform and iterative demodulation: methods with application. Mech Syst Signal Process 72–73:695–711
Feng Z, Chen X, Liang M (2015) Iterative generalized synchrosqueezing transform for fault diagnosis of wind turbine planetary gearbox under nonstationary conditions. Mech Syst Signal Process 52–53:360–375
Hibbeler RC, Fan SC (2002) Engineering mechanics: dynamics. Prentice Hall, Upper Saddle River
Bisoi A, Samantaray A, Bhattacharyya R (2017) Control strategies for DC motors driving rotor dynamic systems through resonance. J Sound Vib 411:304–327
Wu H-T, Flandrin P, Daubechies I (2011) One or two frequencies? The synchrosqueezing answers. Advn Adapt Data Anal 3(01n02):29–39
Mihalec M, Slavič J, Boltežar M (2016) Synchrosqueezed wavelet transform for damping identification. Mech Syst Signal Process 80:324–334
Perez-Ramirez CA, Amezquita-Sanchez JP, Adeli H, Valtierra-Rodriguez M, Camarena-Martinez D, Romero-Troncoso RJ (2016) New methodology for modal parameters identification of smart civil structures using ambient vibrations and synchrosqueezed wavelet transform. Eng Appl Artif Intell 48:1–12
Oberlin T, Meignen S, Perrier V (2014) The fourier-based synchrosqueezing transform. In: 2014 IEEE international conference on acoustics speech and signal processing (ICASSP). IEEE, pp 315–319
Oliynik P (2016) Development of wireless vibration transducer based on MEMS accelerometer. East Eur J Enterp Technol 3(9):18–24
Author information
Authors and Affiliations
Corresponding author
Additional information
Technical Editor: Thiago Ritto.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Varanis, M., Mereles, A., Silva, A.L. et al. Numerical and experimental investigation of the dynamic behavior of a cantilever beam driven by two non-ideal sources. J Braz. Soc. Mech. Sci. Eng. 42, 516 (2020). https://doi.org/10.1007/s40430-020-02589-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40430-020-02589-8