Frequency response based identification of nonlinear oscillators

Abstract

Experimental modal analysis is commonly used to identify models for the vibratory behavior of structures. This is done by conducting a set of experiments to obtain the structure’s governing equations and information in the form of eigenfrequencies, mode shapes, and damping. However, linearity of the test structure is assumed within this identification procedure. Hence, as it stands, experimental modal analysis is not readily applicable to build models when nonlinearities are present through, for example, friction, (electro-) magnetic fields, or large deformations. To identify governing equations for such systems, a robust and systematic identification procedure is proposed in this article. The identification routine is formulated in the frequency domain, and a noise reduction scheme and a simplification routine are employed to obtain sparse and robust models. The identification procedure is implemented in an automated script (FrID), which is applied to forced response measurements stemming from structures with magnets, clamps, and bolted joints as well as systems with multiple active modes and internal resonances. The identified governing equations accurately fit the experimentally obtained frequency response measurements and can also be utilized to extrapolate the response for different forcing amplitudes. Moreover, nonlinear modes of the underlying conservative system can be computed from the identified governing equations.