Jointed interfaces are sources of the greatest amount of uncertainty in the dynamics of a structural assembly. In practice, jointed connections introduce nonlinearity into a system, which is often manifested as a softening response in frequency response, exhibiting amplitude dependent damping and stiffness. Additionally, standard joints are highly susceptible to unrepeatability and variability that make meaningful prediction of the performance of a system prohibitively difficult. This high degree of uncertainty in joint structure predictions is partly due to the physical design of the interface. This paper experimentally assesses the influence of the interface geometry on both the nonlinear and uncertain aspects of jointed connections. The considered structure is the Brake-Reuß beam, which possesses a lap joint with three bolted connections, and can exhibit several different interface configurations. Five configurations with different contact areas are tested, identified, and compared, namely joints with complete contact in the interface, contact only under the pressure cones, contact under an area twice that of the pressure cones, contact only away from the pressure cones and Hertzian contact. The contact only under the pressure cone and Hertzian contact are found to behave linearly in the range of excitation used in this work. The contact area twice that of the pressure cone behaves between the complete contact and contact only under the pressure cone cases.

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Two key properties of a vibrating structure are the frequencies at which it resonates and its ability to absorb energy. For a linear structure, these properties are characterised by the natural frequencies and the damping ratios. For nonlinear systems, such properties may not exist and equivalents must be sought. A method of measuring equivalent properties has been developed for nonlinear systems by examining the decaying vibration time history following excitation of the system. In a first stage, the time history is filtered to separate out a frequency range of interest. In the second stage, which is the main concern of this paper, instantaneous values of natural frequencies and damping ratios are extracted from the decaying time history by means of a curve fitting process. The curve fitting involves finding four parameters two of which are the instantaneous natural frequency and damping ratio and two more which account for the amplitude and phase. The curve fitting is a minimisation process which is divided into two stages. For each minimisation step, the amplitude and phase are extracted first. It is shown that this may be done in a one-step process. Next the frequency and damping are determined. This is found to be a straightforward although more difficult process. The key to simplifying the problem is to recast the model in a favourable form that reduces the curve fitting process from one of finding four parameters to finding just two. The procedure is found to be robust and capable of detailed investigation.

The dynamics of structures built-up from components connected by bolted joints are not well understood. Experiments were conducted with bolted joints in a shear configuration in which instantaneous vibration frequencies and damping could be measured. A system with bolted joints was excited and the free vibration decay measured. As the vibration decays, the damping decreases and the frequencies increase. This suggests a new interpretation for the contact patch in a bolted joint, involving bound, slipping and alternating regions. The changing size of the bound region controls the instantaneous frequencies and the relative displacement inside the slipping region and the alternating region controls the damping behaviour. Shims of different lengths enabled the behaviour of the contact patch to be investigated. A clear trend exists between the length of the shims and the non-linear dynamic behaviour. The introduction of multiple shims did not increase the damping or alter the dynamic nonlinear behaviour. The introduction of grease into the bolted joint increased the damping but oil did not. The vibration measurements enable the size of the contact patch to be estimated.