32 Nonlinear System Identification of Mechanical Interfaces Based on Wave Scattering 335 the first layer, and the system parameters can be identified by matching the PP model predictions with data taken from experimentally measured strains. In the next section, we apply the PP model to identification of the nonlinear interfaces of two SHBP experiments: one with a prestressed clearance interface and one with a prestressed frictional interface. 32.3 Nonlinear System Identification 32.3.1 Preloaded Clearance Interface The first system we study is a SHPB system composed of two hardened AISI 1566 steel bars . D7.8g=cm3, ED210GPa, D0.29/ with a prestressed clearance interface and is depicted in Fig. 32.2. The incident bar had length of 96 in. (244 cm) and a step up in diameter from 1.25 in. (3.2 cm) to 1.5 in. (3.8 cm) at the midpoint, and was supported by a backstop placed at the midpoint. The backstop also served to support the static axial preload that was applied to the system. The transmission bar had a length of 48 in. (122 cm) and a diameter of 1.5 in. (3.8 cm), and was supported by two bushing supports. Additionally, the right end was attached to a hydraulic press, which provided the static axial preload on the system. The bars were not match finished, thus the contact area is relatively small with low preload and fully closed with high preload. Uniaxial semiconductor strain gages were placed diametrically opposed at four locations, two before and two after the interface. The strains were measured for 10 ms at a sampling rate of 2.5 MHz. A standard modal impact hammer was used to apply the impulsive force at the left boundary of the incident bar. All experiments were conducted by the Air Force Research Laboratory at Eglin Air Force Base, FL and are fully documented in [6, 7]. For the system identification discussed herein, a 100 lb preload case (minimal contact) and a 4000 lb preload case (maximum contact) are chosen. A qualitative analysis revealed that an additional tensile wave followed the compressive wave to the interface. This additional tensile wave is either due to the externally applied load or is a result of the compression between the step up in diameter and the backstop. As the purpose of this research is to identify the nonlinear interface and not the interaction at the backstop, the superposition of the compressive wave and the tensile wave is used as the input force to the PP model. Since some contact exists at low preload, the interface is modeled as two springs in series: one depending on the preload and one independent of the preload K.z, P/ D 1 k1.P/ C 1 k2 1 z, (32.9) where Pis the preload on the system, k1 is the stiffness that depends on the preload, andk2 is the stiffness independent of the preload. The system parameters are identified using MATLAB’s patternsearch optimization algorithm with the objective of maximizing the R-squared value between the experimentally measured waves and the predicted PP model waves for the first three measurement locations. The optimization was run simultaneously for both preload cases in order to accurately identify the constant stiffness term, but was only run up to a dimensionless time of 2.5 as secondary effects are dominant after this time. The optimized dimensionless stiffness values are found to be a b Fig. 32.2 The preload interface bar: (a) experimental setup and (b) static dynamic loading. Reprinted with permission from [7]
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