Resonance, Parameter Estimation, and Modal Interactions in a Strongly Nonlinear Benchtop Oscillator

• Published in: Nonlinear dynamics Vol. 40; no. 2; pp. 149 - 167
• Main Authors: Nandakumar, K., Chatterjee, Anindya
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Nature B.V 01.04.2005
• Subjects: Dynamic response; First principles; Forced vibration; Mathematical models; Nonlinearity; Parameter estimation; Qualitative analysis
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-005-4228-3

We study the vibrations of a strongly nonlinear, electromechanically forced, benchtop experimental oscillator. We consciously avoid first-principles derivations of the governing equations, with an eye towards more complex practical applications where such derivations are difficult. Instead, we spend our effort in using simple insights from the subject of nonlinear oscillations to develop a quantitatively accurate model for the single-mode resonant behavior of our oscillator. In particular, we assume an SDOF model for the oscillator; and develop a structure for, and estimate the parameters of, this model. We validate the model thus obtained against experimental free and forced vibration data. We find that, although the qualitative dynamics is simple, some effort in the modeling is needed to quantitatively capture the dynamic response well. We also briefly study the higher dimensional dynamics of the oscillator, and present some experimental results showing modal interactions through a 0:1 internal resonance, which has been studied elsewhere. The novelty here lies in the strong nonlinearity of the slow mode.