Publications

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This work extends recent methods to calculate dynamic substructuring predictions of a weakly nonlinear structure using nonlinear pseudo-modal models. In previous works, constitutive joint models (such as the modal Iwan element) were used to capture the nonlinearity of each subcomponent on a mode-by-mode basis. This work uses simpler polynomial stiffness and damping elements to capture nonlinear dynamics from more diverse jointed connections including large continuous interfaces. The proposed method requires that the modes of the system remain distinct and uncoupled in the amplitude range of interest. A windowed sinusoidal loading is used to excite each experimental subcomponent mode in order to identify the nonlinear pseudo-modal models. This allows for a higher modal amplitude to be achieved when fitting these models and extends the applicable amplitude range of this method. Once subcomponent modal models have been experimentally extracted for each mode, the Transmission Simulator method is implemented to assemble the subcomponent models into a nonlinear assembled prediction. Numerical integration methods are used to evaluate this prediction compared to a truth test of the nonlinear assembly.

In a companion paper (Roettgen, D.R., et al.: Substructuring of a nonlinear beam using modal Iwan framework, Part 1: nonlinear modal model identification. Presented at the international modal analysis conference XXXV, Garden Grove, 2017), “Substructuring of a nonlinear beam using modal Iwan framework, Part I: Nonlinear Modal Model Identification”, nonlinear modal models are constructed for an experimental substructure that represent the dynamics using a set of uncoupled weakly nonlinear modes. This assumes that the linear modes of the structure remain uncoupled so that the nonlinearity can be described in a mode by mode fashion. These nonlinear modal models can be used to simulate the response of the experimental system. This paper demonstrates the use of these models to represent a substructure in an experimental-analytical substructuring prediction. The authors utilize the transmission simulator method on the experimentally derived models to generate predictions of a modified Brake-Reuss Beam system. The substructuring predictions are then compared to a truth test data set to validate the method. To further understand the limitations of the method and its sensitivity to measurement noise, the modal substructuring approach is also simulated on a finite element model of the beam that contains three discrete nonlinear elements to represent the joint.

This work uses a method whereby weak nonlinearity in a substructure, as typically arises due to microslip in bolted interfaces, can be captured and modeled on a mode-by-mode basis. The method relies on the fact that the modes of a weakly nonlinear structure tend to remain uncoupled so long as their natural frequencies are distinct and higher harmonics generated by the nonlinearity do not produce significant response in other modes. A single degree-of-freedom (DOF) system with an Iwan joint, which is known as a modal Iwan model, effectively captures the way in which the stiffness and damping depend on amplitude for each mode. This work presents the experiments used to generate these modal Iwan models. In a companion paper this model is assembled to another component using dynamic substructuring techniques to estimate the amplitude dependent frequency and damping of the full assembly.

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