71 Expansion of Nonlinear System Response Using Linear Transformation. . . 765 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (sec) MAC - 15 DOF a Space vs. Test - Single Beam with Conical Spring Contact 1 2 3 4 5 6 7 8 9 101112131415 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 DOF TRAC - 15 DOF a Space vs. Test - Single Beam with Conical Spring Contact Fig. 71.23 MAC (top) and TRAC (bottom) comparisons between 15 DOF ‘a’ space model and test for transient portion of time response (0–0.2 s) – single beam with conical spring contact For this experimental case, good correlation was observed between the experimentally measured and analytically predicted displacement responses for a single beam with conical spring contact. Although small discrepancies were observed between the analytical and test results, the predicted results were considered to provide a sufficient level of correlation to describe the nonlinear behavior of the tested system. This case also further demonstrates the proposed methodology for use in applications where experimental data is available for comparison with the analytical models being used in forced nonlinear response simulations. Again note that the expansion of this nonlinear response was achieved using the modes of the originally uncoupled linear component beam model. The expansion process did not distort the data of the separate systems or any perturbation of the combined system because a sufficient number of modes have been used to span the space of the system in all of its various configurations. As a result, measurements that are difficult to make experimentally can be accurately obtained by expansion at a fraction of the time required to measure every single location.
RkJQdWJsaXNoZXIy MTMzNzEzMQ==