Measurement of multivalued response curves of a strongly nonlinear system by exploiting exciter dynamics

Abstract

A strongly nonlinear system often has multiple solutions under harmonic excitation. However, measuring all of these multiple responses in structural dynamics is challenging because often one solution is unstable and difficult to obtain. The standard stepped sine approach is to fix the harmonic excitation force amplitude, and step the excitation frequency up or down. This leads to the well-known jump phenomenon, and captures at most two stable solutions. Alternatively, the excitation frequency can be fixed and the amplitude swept up or down, although this also leads to jumps in the response. Recently, experimental continuation methods have successfully measured all solutions, including the unstable solutions, via active control. This paper takes a different approach and exploits the dynamics of the electromagnetic exciter to both stabilize the unstable solution, and also to track the solutions continuously, without any jumps. This is achieved by monotonically increasing or decreasing the voltage applied to the exciter at a fixed frequency, and using the force drop-out phenomenon through the resonance to control the force applied to the structure. In these tests, the input voltage then defines the continuation parameter, rather than force amplitude or frequency in the standard tests. The obvious advantage of this method is that there is no feedback control of the excitation and it is easy to implement. A strongly nonlinear single degree of freedom system is used to demonstrate this method.