Identification of multiple local nonlinear attachments using a single measurement case

Abstract This research focuses on the construction of representative mathematical models for the dynamics of multiple local nonlinear attachments installed on the same primary structure. Specifically, the applicability of the recently developed characteristic nonlinear system identification (CNSI) to multiple attachments and attachments tuned to modes higher than the first linear mode of the primary structure is investigated. The CNSI procedure is a data-driven approach that produces a mathematical model for the dynamics of local nonlinear attachments directly from experimental measurements with the only knowledge of the mass of the attachment and the general frequency content required. The applicability of the CNSI method for multiple attachments is demonstrated using a two-story tower with one local nonlinear attachment installed on each floor in two configurations. In the first configuration, both attachments are tuned to interact with the first mode of the tower. In the second configuration, the linear stiffness of the attachment installed on the first floor is increased, such that it interacts with the second mode instead of the first. The resulting models are numerically integrated, and the resulting displacements are directly compared with the experimental measurements. This comparison provides validation of the success and strength of the CNSI method for identifying multiple nonlinear attachments using a single measurement case. The method is particularly suitable for transient response data, and it is unlikely that the method would work with harmonic and random excitation responses. The method also might not be ideal for systems having inflexible impacts or asymmetric restoring forces.

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