400 D. DiMaio the assumption that the nonlinearities induced by friction joints are mode dependant. For instance, mode 4 (T2) shows an increase in accelerance peak level with an increasing vibration level, whereas mode 8 (T4) shows the opposite. The type of nonlinear behaviour shown by the former mode has been widely observed in bolted structure dynamics [2]. 35.6 Nonlinear Dynamic Investigation Using Strain Analysis So far, the nonlinear analysis has been performed using classic modal testing tools, that is to say, mainly based on FRFs generated using a single output response. Most nonlinear vibration analysis are based on those methods. The vibration nonlinearity induced by friction joints is mode dependant as the stress field in the vicinity of the joint is specific to each mode. From the linear FE modal analysis, an assumption has been made that the torsional modes are the most likely to show microslip behaviour in the contact interface as the shear stress is important as well as its surface area. The bending modes are more likely to show a joint separation behaviour as the normal stress along the joint line is more important than torsional modes. Those assumptions need to be validated by experimental data as well as further numerical analysis based on strain/stress outputs instead of acceleration in a single point. 35.6.1 Experimental Strain Measurements 35.6.1.1 Strain Gages Setup It has been seen in Sect. 35.4 that the critical stress, likely to lead to nonlinear behaviours, are located both at the contact interface (especially the shear stress components) and on the bottom surface of the structure along the joint line for the normal stress components. However, the contact interface strain/stress components are not measurable with the common strain measurement techniques. Strain gauges were planned at locations on the casing of the test structure and in order to keep the generation data sensible four points were selected. Two measurement points were selected at the edge and two at the middle of the test structure. Each pair were displaced to be one on the short and one on the long flange, as shown in Fig. 35.17. This layout was planned to capture possible changes across the flange for an excitation given at the shorter component. It was possible to measure xx, zz and xz (plane stress). However, for the case of interest, xx, which could induce a partial separation of the bolted joint, and xz, which was related to the friction behaviour of the bolted joint (even though it is not located at the joint interface, it could give a good insight), were relevant to the test. Now, in terms of strain components (the measurable quantity), the Hooke strain–stress relationship for plane stress gives: xx D E 1 2 . xx C zz/ (35.3) xz D E 1 2 .1 / xy (35.4) Then, xx, zz and xz are required to get the stress components of interest. This is possible to measure those strain components with three components gages or so called rosettes [17]. The 45ı rosettes gages were carefully attached on the casing surface, Fig. 35.17 Measurement points for the strain gauges
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