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Joints and fasteners often have a significant effect on the dynamical behaviour of assembled mechanical structures and the analytical prediction of structural responses therefore depends upon the accuracy of joint modelling. Detailed constitutive models that fully describe the behaviour of frictional interfaces are often unduly complicated; in which case simpler phenomenological models having parameters identified from vibration tests may be preferable. Unfortunately the direct measurement of forces transmitted between two contacting surfaces and their relative displacements are not possible in practice and it is therefore necessary to rely on measurements remote from joints. In this paper, the parameters of an assumed nonlinear joint model are identified by force-state mapping from time-domain acceleration records in response to single-frequency excitation close to the first natural frequency. The problem of lack of accessibility for measurement at the joint is overcome by casting the governing equation of the system in modal coordinates so that modal parameters are identified to represent the nonlinear behaviour of the joint. A particular result from the experimental programme is the identification of viscous damping coefficients dependent upon displacement amplitude. The significance of this result is that the complex phenomenon of energy dissipation in lap joints can be represented by a simple analytical model capable of producing accurate results.

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This paper proposes an optimization-based framework to determine the type of nonlinear model present and identify its parameters. The objective in this optimization problem is to identify the parameters of a nonlinear model by minimizing the differences between the experimental and analytical responses at the measured coordinates of the nonlinear structure. The application of the method is demonstrated on a clamped beam subjected to a nonlinear electromagnetic force. In the proposed method, the assumption is that the form of nonlinear force is not known. For this reason, one may assume that any nonlinear force can be described using a Taylor series expansion. In this paper, four different possible nonlinear forms are assumed to model the electromagnetic force. The parameters of these four nonlinear models are identified from experimental data obtained from a series of stepped-sine vibration tests with constant acceleration base excitation. It is found that a nonlinear model consisting of linear damping and linear, quadratic, cubic, and fifth order stiffness provides excellent agreement between the predicted responses and the corresponding measured responses. It is also shown that adding a quadratic nonlinear damping does not lead to a significant improvement in the results.