Abstract In standard design practice, it is often necessary to assemble engineered structures from individually manufactured parts. Ideally, the assembled system should perform as if the connections between the components were perfect, that is, as if the system were a single monolithic piece. However, the fasteners used in those connections, such as mechanical lap joints, are imperfect and highly nonlinear. In particular, these jointed connections dissipate energy, often through friction over highly localized microscale regions near connection points, and are known to exhibit history dependent, or hysteretic behavior. As a result, while mechanical joints are one of the most common elements in structural dynamics problems, their presence implies that assembled structural systems are difficult to model and analyze. Through rigorous experimental, analytical, and numerical work over the past century, researchers from several different disciplines have developed numerous damping models that give rise to the dynamical behavior attributed to joints. The present work seeks to review, compare, and contrast several linear and nonlinear damping models that are known to be relevant to modeling assembled structural systems. These models are presented and categorized to place them in the proper historical and mathematical context as well as presenting numerous examples of their applications. General properties of hysteretic friction damping models are also studied and compared analytically. Connections are drawn between the different models so as to not only identify differences between models, but also highlight commonalities not normally seen to be in association.

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Switched reluctance motors (SRM) are characterized by rotor/stator pole pairs, in which the wound field coils in the stator poles induce magnetic reluctance in the rotor poles to create torque. However, noise development during motor operation is a key issue for this class of motors and much of the work to understand the acoustics and vibrations of these systems is limited to comparing experimental measurements with high-performance, multiphysics simulations. This work focuses on mathematical analysis of these systems through reduced-order modeling using both numerical and analytical methods, and the results are compared against experimental measurements of a typical SRM. To describe the underlying response of the experimental system, a circular shell model is developed for the stator, and electromagnetic finite element analysis is utilized to develop a physically motivated forcing profile for the experimental system. A numerical simulation model is then constructed by applying the calculated electromagnetic forces to the stator, and effective system parameters are determined by calibrating the numerical model to match experimental measurements. An analytical approximation is then derived by leveraging disparate timescales in the problem, and it is shown that the analytical solution accurately recovers the numerical and experimental results while also providing insight into the underlying physics of the experimental system.

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