Application of acoustic and electrical methods to study vibrations of an impact oscillator

V. V. Narozhnov

Čelâbinskij fiziko-matematičeskij žurnal, Tome 8 (2023) no. 1, pp. 112-119.

Résumé

The paper presents the results of studying the vibrations of a nonlinear mechanical oscillator with elastic impacts by acoustic and electrical methods. It is shown that multiple impacts of the oscillator with the sample are possible in one period of the driving force. The general picture of nonlinear oscillations is formed as a result of the superposition of oscillator vibrations and elastic waves arising in the sample during impacts.

Détail

Keywords: impact oscillator, forced oscillations, nonlinear dynamics, elastic impact.

Bibliographie

[1] Pust L., Peterka F., Stepan G., Tomlinson G. R., Tondl A., “Nonlinear oscillations in machines and mechanisms theory”, Mechanism and Machine Theory, 34:8 (1999), 1237–1253

[2] Andrianov I. A., van Horssen D. T., “Analytical approximations of the period of a generalized nonlinear van der Pol oscillator”, Journal of Sound and Vibration, 295:3 (2006), 1099–1104

[3] Cveticanin L., “Oscillator with nonlinear elastic and damping force”, Computers and Mathematics with Applications, 62:4 (2011), 1745–1757

[4] Afsharfard A., Farshidianfar A., “Design of nonlinear impact dampers based on acoustic and damping behavior”, International Journal of Mechanical Sciences, 65:1 (2012), 125–133

[5] Akulenko L.D., Nesterov S.V., “Parametric oscillations and the stability of a mechanical system with considerable dissipation”, Journal of Applied Mathematics and Mechanics, 77:2 (2013), 151–158

[6] Rekhviashvili S.Sh., Narozhnov V.V., “Nonlinear dynamics and acoustic signals during elastic impacts of a probe with a solid surface”, News of universities. Applied nonlinear dynamics, 21:6 (2013), 49–57 (In Russ.)

[7] Chillingworth D. R. J., “Single-impact orbits near grazing periodic orbits for an impact oscillator”, Trends in Mathematics, 8 (2017), 37–42

[8] Zeylikovich I.S., Nikitin A.V., Vasilevich A.E., “Excitation and detection of a nonlinear resonance of oscillations of a spring-mass system using electromagnetic induction”, Technical Physics, 65:1 (2020), 1–6

[9] Narozhnov V.V., “Experimental and theoretical investigation of an oscillator with collisions”, Technical Physics, 65:10 (2020), 1600–1604

[10] Costa D., Vaziri V., Kapitaniak M., et al., “Chaos in impact oscillators not in vain: Dynamics of new mass excited oscillator”, Nonlinear Dynamics, 102 (2020), 835–861

[11] Wiercigroch M., Kovacs S., Zhong S., et al., “Versatile mass excited impact oscillator”, Nonlinear Dynamics, 99 (2020), 323–339

[12] Cardoso W. B., Avelar A. T., Bazeia D., “Effects of chaotic perturbations on a nonlinear system undergoing two-soliton collisions”, Nonlinear Dynamics, 106 (2021), 3469–3477

[13] Rekhviashvili S.Sh., Narozhnov V.V., “Stand for the study of metals and alloys viscoelastic properties using the acoustic probe method”, Pat. RF, no. 2552600 (In Russ.)

[14] Khorovits P., Khill U., The art of circuit engineering, Binom Publ, Moscow, 2014 (In Russ.)

[15] Tittse U., Shenk K., Semiconductor circuit design, v. I, DMK Press Publ, Moscow, 2008 (In Russ.)

[16] Narozhnov V.V., “Simulation modeling of a nonlinear oscillator taking into account elastic collisions”, Nonlinear world, 12:11 (2014), 32–36 (In Russ.)