24 B. Moldenhauer et al. dynamics of the internal shaker components and the linear stiffness and damping characteristics of the joints between the test fixture and the shaker, removing the need to accurately model them analytically. Also, by using FEMs of the fixture and potential test article, many different test configurations can be quickly simulated, avoiding costly prototyping and testing. Previously, this method was successfully applied to a relatively simple setup as a proof of concept [4]. This research explores a more complicated structure that provides valuable insight into how this framework can be applied to a real test scenario with dynamically complex subcomponents. This paper is divided into several sections, starting with a summary of dynamic substructuring and the theory behind the TSM. Following this, the various subsystems that will be utilized in the substructuring process are introduced and described. The work done to create accurate FEMs of the fixture and test article is then presented. After which, the test procedure implemented to acquire and process experimental data is defined. With all the necessary information to perform the TSM substructuring, the resultant experimental/analytical shaker model is evaluated relative to experimental truth data. Conclusions are then stated pertaining to the accuracy and capability of implementing the TSM to efficiently model electrodynamic shakers with complex fixtures and test articles. 3.2 Theory 3.2.1 Dynamic Substructuring Modeling and analyzing system dynamics becomes increasingly difficult as the size and complexity of the structure grows. Large FEMs can require an unreasonable amount of time and computational power to directly solve, and as the assembly becomes larger and more complicated it becomes more difficult to design and perform an experiment that can capture all of the modes of interest. However, these difficulties can be somewhat alleviated by dividing the structure into smaller, more manageable subcomponents that can be analyzed individually in whatever domain is most appropriate, e.g. experimental or analytical. When one of the components is experimental, the methods used to combine experimental and numerical models to predict the response of the coupled system are termed experimental dynamic substructuring [5, 6]. Experimental dynamic substructuring methods are divided into two groups: Frequency-Based Substructuring (FBS) and Component Mode Synthesis (CMS) [7]. FBS uses the frequency response functions (FRFs) of the subcomponents to predict the response of the assembled system. CMS, also known as Modal Substructuring, combines the subcomponent equations of motion in modal coordinates to build the equation of motion of the assembled system. The CMS methods differ from each other in which component’s modes are chosen to represent the subcomponent. It is imperative that the component modes of the individual subcomponents form an adequate basis to represent the motion of the coupled assembly. In the research presented herein, this is achieved using the Transmission Simulator Method. 3.2.2 Transmission Simulator Method The Transmission Simulator Method (TSM), as proposed by Allen, Mayes, et al. [2, 3, 8], allows for experimental and analytical models to be coupled together through a common subcomponent that is present in both. This component, referred to as the Transmission Simulator (TS), acts as a distributed interface between the experimental and analytical subsystems, allowing their coupling constraints to be satisfied by the modal dynamics of the TS, as opposed to the more difficult process of enforcing compatibility in all six physical degrees of freedom at each point on the surface of the interface. Also, the TS effectively mass-loads the interface between the other subsystems and simulates the forces that would act there in the assembled structure. In practice, an experimental model is obtained by performing a modal test on some physical system that includes the TS. By decoupling a FEM of the TS from this model, the physical presence of the TS is removed, while the dynamics of a loaded interface are left on the physical component model. If this same process is carried out on a FEM that includes the TS and a third subcomponent, an analytical model of that subcomponent with a mass loaded interface is produced. The experimental and analytical models with mass loaded interfaces can then be coupled together with CMS, yielding a hybrid experimental/analytical model of the assembled structure. This research applies the TSM to create a model of a floor-mounted electromagnetic shaker that has a three-sided half cube mounted on the armature, and a cantilever beam attached to the half cube. The shaker with the half cube is the experimental subsystem, the half cube is the TS and represents a shaker fixture, and the beam represents a prospective test article and, together with the half cube, is the analytical subsystem. Figure 3.1 displays a schematic of the effective process that will be
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