132 N. A. Bari et al. Rather than full-scale testing, the behavior of the complete structure is commonly inferred from test results obtained from experiments on a scaled model of the entire structure or testing of a critical component of the structure [6]. One approach to characterizing a system’s dynamic response is pseudo-dynamic testing (PsD), in which only a vital element of the entire structure (typically a complex, difficult to model component) is tested physically while the remainder of the structure is modeled numerically [7, 12, 13]. With PsD methods, the physical element is excited statically under loading conditions and not by dynamic excitations, such as ground acceleration, which leads to several experimental inaccuracies. Recent technological advances in signal processing have allowed for full-scale structural testing to be performed on components of interest, with the remainder of the structure being numerically modeled. Hybrid Substructuring (HS) is a recently developed technique to investigate the dynamic behavior of structural systems [1, 2]. These advances have led to a new, innovative approach to computing displacement, velocity, and acceleration of components under dynamic excitation during experimental settings [8]. This testing technique, referred to as Real-Time Hybrid Substructuring (RTHS), is widely used for performance evaluations of structural systems subjected to dynamic loading [5]. RTHS is similar to the PsD testing method; however, with RTHS, both physical and numerical substructure partitions are simultaneously integrated into a realtime loop while the physical structure is dynamically excited [3]. Once the theoretical model is validated as an accurate mathematical representation of the structure, HS is typically the simplest method of the two to perform because no transfer system or real-time control loop algorithm is required. Both HS and RTHS are methods that rely heavily on a numerical model of a substructure to represent the dynamic response of the complete system accurately. Consequently, these approaches permit for impacts of uncertainties in the system, such as those due to jointed connections, to be incorporated into the numerical substructure as probabilistic variables. This paper aims to quantify a system’s uncertainties by incorporating experimental data with an optimization algorithm to find probabilistic values of uncertain parameters so that system uncertainty may be propagated into a hybrid substructuring scheme. The methodology will be demonstrated through an analysis of the bolted joints uncertainties in the Box and Removable Component (BARC) test structure. 12.2 Experimental Procedure 12.2.1 Test Component The Box Assembly with Removable Component (BARC) test structure, developed at Sandia National Laboratories and Kansas City National Security Campus for the Boundary Condition Round Robin Challenge [11], was used in this study. This structure was explicitly designed as a standard system for researchers to integrate into a testbed when designing environmental shock and vibration tests, focusing on the issue of uncertain boundary conditions [10, 11]. The BARC consists of two substructures. The base substructure is a cut box frame and the removable component is a beam, with the two substructures connected by two C-channels. The BARC substructures are aluminum 6061 and the C-channels are aluminum 6063. The cut box substructure is 3 (7.62 cm) wide and 6 (15.24 cm) tall with a top cut of 0.5 (1.27 cm) and thickness of 0.25 (0.635 cm). The removable component is 1 (2.54 cm) wide and 5 (12.7 cm) long with a thickness of 0.125 (0.3175 cm). C-clamps are 1 (2.54 cm) wide and 2 (5.08 cm) tall. The BARC was assembled onto the shaker table using four button cap screws with its flat faces normal to the direction of motion. The four mounting screws were hand tightened until secure. Then they were tightened using a socket wrench. The C-channel brackets were attached to the box frame using eight stainless steel socket cap screws, which were each torqued to 20 in-lbs [9]. The beam was then attached using two hex bolts, which were each torqued to 50 in-lbs. Although the specified assembly configuration is asymmetric, the BARC was assembled symmetrically for the results presented in this paper, as illustrated in Fig. 12.1. 12.2.2 Experimental Setup The BARC was instrumented with eight single-axis accelerometers measuring along the axis of excitation, two on each leg of the box and two on each C-channel. A bi-axial accelerometer was placed at the center of the removable component measuring acceleration vertically as well as in the direction of excitation. Locations of the accelerometers are illustrated in Fig. 12.2. Accelerometers were also placed at the base of the shaker table to measure the input acceleration and controlling the excitation. Due to hardware constraints the tests were run using two data acquisition systems with limited channels. Two
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