130 Nicholas Pomianek et al. domain eigenvalue solvers. These limitations have inspired the recent work of Black et. al. [6], which addresses them by modeling joints as tied contact regions between solid elements. By updating the size of this contact region along with the stiffness and density of the surrounding elements, the global response of a jointed structure was predicted accurately. The present study also uses the idea of defining a ‘virtual material’ [6] but instead uses an approach tailored to situations where a structural prototype is unavailable. This work seeks to develop an accessible and effective framework for joint modeling for use with standard FEA tools that does not require special contact elements or parameters. This work seeks to demonstrate that updating the damping, stiffness, and density characteristics of the elements within an effective joint region (EJR) can create a computationally efficient model that preserves the most important dynamic response features of a joint. Experimental setup The Brake-Reuß standardized test beam (BRB) [7] was used as a case study for this work because of the extensive modal testing data available in the existing literature. The prismatic geometry of the BRB also lends itself well as a best-case-scenario for the modeling approach developed in the following sections. Pictured in Figure 1, the test specimen was manufactured according to the machining specifications outlined in [8] but was made from ASTM A283 steel for material availability reasons. The procedure for assembling the test structure from [8] was followed, where both sides of the BRB are clamped to a flat surface, a shim is inserted in the interface parallel to the bolt axis, and an instrumented torque wrench is used to tighten the bolts to 20 Nm. This assembly procedure is followed during each re-assembly of the system throughout experimentation. The assembled system is suspended using monofilament fishing line to approximate free-free boundary conditions. Fig. 1 Brake-Reuß beam test specimen, dimensions in mm. Modal testing was performed using an aluminum-tipped Bru¨el & Kjær model 8206-002 impact hammer and a Bru¨el & Kjær model 4534-B accelerometer, the placement of the accelerometer and impact hammer target location are shown in Figure 1. Both the accelerometer and impact hammer signals are fed through PCB model 482A21 signal conditioners into a Digilent Analog Discovery 2 digital oscilloscope which records data to a computer running WaveForms software. The system is oriented such that the impact direction is perpendicular to the suspension lines so that they do not add stiffness to the beam. The experimental instrumentation setup is shown in detail in Figure 2.
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