An Experimental Method for the Phase Controlled Frequency Response Measurement of Nonlinear Vibration Systems

Experimental determination of frequency response function of nonlinear systems is difficult when there exists more than one solution branch. Depending on the system at hand, various types of jump phenomena can be observed and in the example of the well-known Duffing-oscillator, it is not possible to experimentally determine the unstable solution branch if the system is excited by a harmonic force. In the present paper we investigate the Duffing-oscillator and present a method, which allows to reformulate the equation of motion of the system with force-excitation in the form of an equivalent self-excited system. Considering the phase between force and response as the input variable, it is possible to evaluate the frequency of the systems vibration for any given phase shift. In the same way the corresponding response amplitude is determined. An experimental set-up is presented, which is used to validate the performance of the method. Measurements of the backbone curve are performed and discussed on the background of theoretical predictions. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)