Modal Analysis of Jointed Structures

Abstract Structural systems are often composed of multiple components joined together at localized interfaces. Compared to a corresponding monolithic system these interfaces are designed to have little influence on the load carrying capability of the system, and the resulting change in the overall system mass and stiffness is minimal. Hence, under nominal operating conditions the mode shapes and frequencies of the dominant structural modes are relatively insensitive to the presence of the interfaces. However, the energy dissipation in such systems is strongly dependent on the joints. The microslip that occurs at each interface couples together the structural modes of the system and introduces nonlinear damping into the system, effectively altering the observed damping of the structural modes, which can then significantly alter the amplitude of the response at the resonant modal frequencies. This work develops equations of motion for a jointed structure in terms of the structural modal coordinates and implements a reduced-order description of the microslip that occurs at the interface between components. The interface is incorporated into the modal description of the system through an existing decomposition of a series-series Iwan interface model and a continuum approximation for microslip of an elastic rod. The developed framework is illustrated on several examples, including a discrete three degree-of-freedom system as well as the longitudinal deformation of a continuum beam.

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