Abstract
Abstract The development of nonlinear modal analysis so far has focused on structures with smooth nonlinearities. However, nonsmooth nonlinearities, which are, for instance, caused by contact interactions are highly relevant in practical applications. This paper proposes a novel numerical approach along with a method for the measurement of nonlinear modes of structures with nonsmooth contact nonlinearities. The proposed numerical method combines the shooting method and the harmonic balance method, yielding a mixed time-frequency domain representation of the system, allowing for an efficient treatment of the nonsmooth contact law within the numerical approach. Moreover, the mass of the system is redistributed such that the contact nodes are massless. Thereby, the dynamic contact problem can be reduced to a quasi-static contact problem. A salient feature of this numerical approach is that the contact problems are solved without the need for any contact parameters, such as penalty or restitution coefficients. Furthermore, the conservative nature of the contact law incorporated in this formulation allows for the calculation of nonlinear modes as periodic solutions of conservative systems. The experimental method relies on a nonlinear phase resonance approach. Hitherto, phase resonance methods have exclusively been applied to systems with smooth nonlinearities. In this study, an automated nonlinear phase resonance approach with phase-controlled excitation is used, providing a robust experimental procedure, which facilitates the treatment of strong nonsmooth nonlinearities, e.g., caused by unilateral constraints inducing impacts. The numerical and experimental methods are demonstrated by an application to a benchmark structure consisting of a beam with one-sided support leading to impacts. It is shown that the numerical method can be applied without the need for any nonlinear system identification effort and the results agree well with the measured nonlinear modes.
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