50 A Comparison of Reduced Order Modeling Techniques Used in Dynamic Substructuring 523 Table 50.4 Cylinder-plate-beam test results Mode Frequency (Hz) Damping ratio ( %) Reference Description 1 1 1 NA Rigid translation in X 2 1 1 NA Rigid translation in Y 3 1 1 NA Rigid translation in Z 4 1 1 NA Rigid rotation about X 5 1 1 NA Rigid rotation about Y 6 1 1 NA Rigid rotation about Z 7 116 0.27 5003X+ First bending in the X-Direction 8 153 0.15 5002Z+ First bending in the Z-Direction 9 276 2.37 5002Z+ Internals rotation about Y plus translation in Z 10 282 2.08 5003X+ Internals translation in X and Z 11 300 2.26 5002Z+ Off-axis rotation of internals about Y plus translation in X 12 455 0.32 301Y Axial mode, internals and nose out of phase 13 589 2.09 301Y Internals rotation about Z 14 634 1.96 5002Z+ Internals rotation about X 15 691 1.28 301Y Axial mode, internals and nose in phase 16 742 1.19 3003X+ Suspected foam mode mostly in X 17 761 1.13 3002Z+ Suspected foam mode mostly in Z 18 831 1.00 5002X+ First axial torsion 19 914 0.79 3002Z+ (2,0) ovaling on-axis 20 964 0.22 1301X+ 2nd bending in the X-Direction Fig. 50.9 Configuration of CBP FE model: 1—Beam, 2—Plate, 3—Washer, 4—Cylinder, 5—Ring Table 50.5 Element properties of each component Component Material Material properties 1 Beam 6061 T6 Aluminum ED1.0 107 psi, D0.33, D0.0975lb=in3 2 Plate 6061 T6 Aluminum ED1.0 107 psi, D0.33, D0.0975lb=in3 3 Washer Steel ED3.0 107 psi, D0.29, D0.2800lb=in3 4 Cylinder 6061 T6 Aluminum ED1.0 107 psi, D0.33, D0.0975lb=in3 5 Ring 6061 T6 Aluminum ED1.0 107 psi, D0.33, D0.0975lb=in3 single linear structure by merging the adjacent nodes at the contact points between each component. The element properties of all of the components except the washers are set as 6061 T6 Aluminum, with the material properties listed in Table 50.5. The detailed component name and properties are shown in Table 50.5. Fifteen nodes were selected as the sensor positions and the mesh was constructed such that these corresponded precisely to the actual accelerometer locations. To validate the FE model, the natural frequencies of the cylinder-plate-beam system were examined. Table 50.6 shows the first eleven elastic frequencies of CPB model with the retaining ring on the far left removed. These are compared to the measured natural frequencies of the actual hardware, from a test that was performed before the foam and retaining ring had been installed [6] (Fig. 50.10).
RkJQdWJsaXNoZXIy MTMzNzEzMQ==