Exploiting knowledge of jump-up and jump-down frequencies to determine the parameters of a Duffing oscillator. (English) Zbl 1473.34032
Summary: This work concerns the application of certain non-linear phenomena – jump frequencies in a base-excited Duffing oscillator – to the estimation of the parameters of the system. First, approximate analytical expressions are derived for the relationships between the jump-up and jump-down frequencies, the damping ratio and the cubic stiffness coefficient. Then, experimental results, together with the results of numerical simulations, are presented to show how knowledge of these frequencies can be exploited.
MSC:
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
Keywords:
Duffing oscillator; base excitation; jumps; cubic stiffness coefficient; viscous damping coefficientReferences:
| [1] | Wagg, D.; Neild, S., Nonlinear vibration with control (2015), Springer · Zbl 1315.74002 |
| [2] | (Warminski, J.; Lenci, S.; Cartmell, M. P.; Rega, G.; Wiercigroch, M., Nonlinear dynamic phenomena in mechanics (2012), Springer) |
| [3] | Kovacic, I.; Rand, R., Straight-line backbone curve, Commun Nonlinear Sci Numer Simul, 18, 2281-2288 (2013) · Zbl 1304.34071 |
| [4] | Rice, H. J.; McCraith, J. R., Practical non-linear vibration absorber design, J Sound Vib, 116, 3, 545-559 (1987) |
| [5] | Kovacic, I.; Brennan, M. J.; Waters, T. P., A study of a non-linear vibration isolator with quasi-zero stiffness characteristic, J Sound Vib, 315, 3, 700-711 (2008) |
| [6] | Liu, C.; Jing, X.; Daley, S.; Li, F., Recent advances in micro-vibration isolation, Mech Syst Signal Process, 56-57, 55-80 (2015) |
| [7] | Mann, B. P.; Sims, N. D., Energy harvesting from the nonlinear oscillations of magnetic levitation, J Sound Vib, 319, 1-2, 515-530 (2009) |
| [8] | Ramlan, R.; Brennan, M. J.; Mace, B. R.; Kovacic, I., Potential benefits of a non-linear stiffness in an energy harvesting device, Nonlinear Dyn, 59, 545-558 (2010) · Zbl 1189.70106 |
| [9] | De Paula, A. S.; Inman, D. J.; Savi, M. A., Energy harvesting in a nonlinear piezomagnetoelastic beam subjected to random excitation, Mech Syst Signal Process, 54-55, 405-416 (2015) |
| [11] | Rega, G.; Lenci, S., A global dynamics perspective for system safety from macro- to nanomechanics: analysis, control, and design engineering, ASME. Appl. Mech. Rev., 67, 5, 050802-050802-19 (2015) |
| [12] | Kovacic, I.; Brennan, M. J., The Duffing equation: Nonlinear oscillators and their behaviour (2011), John Wiley & Sons · Zbl 1220.34002 |
| [13] | Brennan, M. J.; Kovacic, I.; Carella, A.; Waters, T. P., On the jump-up and jump-down frequencies of the Duffing oscillator, J Sound Vib, 318, 4-5, 1250-1261 (2008) |
| [15] | Ramlan, R.; Brennan, M. J.; Mace, B.; Kovacic, I.; Burrow, S., On the estimation of linear viscous damping in the Duffing oscillator, (Proceedings of the sixteenth international congress on sound and vibration, vol. 2 (2009), Kraków, Poland), 1088-1095, 5-9 July |
| [16] | Ramlan, R.; Brennan, M. J.; Mace, B. R.; Burrow, S., On the performance of a dual-mode non-linear vibration energy harvesting device, J Intell Mater Syst Struct, 23, 1423-1432 (2012) |
| [17] | Rao, S. S., Mechanical vibrations (1990), Addison-Wesley Pubs · Zbl 0714.73050 |
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