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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The development of reduced-order models remains an active research area, despite advances in computational resources. The present work develops a novel order-reduction approach that is designed to incorporate isolated regions that contain, for example, nonlinearitites or accumulating damage. The approach is designed to use global modes of the overall system response, which are then naturally coupled to the response in the isolated region of interest. Two examples are provided to demonstrate both the accuracy and the computational efficiency of the proposed approach. The performance of this approach is compared to the exact response corresponding to a finite element simulation for the chosen problems. In addition, the accuracy and computational efficiency are shown relative to a standard Galerkin reduction based on the linear normal modes. It is found that the proposed reduction offer computational efficiency comparable to a Galerkin reduction, but more accurately represents the response of the system when both are compared to the finite element simulation.

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