Final_exam_2003 - Mechanical Vibrations Final Exam Student...

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Mechanical Vibrations Final Exam Student Name: Instructions : You may use a single 8.5” × 11” piece of notes during the tests. No other materials are allowed. 1. [15 pts] Four accelerometers are evenly spaced, at every 25 [mm], along the machine tool structure shown in Figure 1. Given the experimentally determined mode shapes shown below, which sensor should be moved to adequately measure the first four natural frequencies on each accelerom- eter. Also, sketch the fourth mode shape. U = h ~ U 1 ~ U 2 ~ U 3 ~ U 4 i (1) U = 1 - 0 . 2 0 . 40 - 0 . 2 0 . 60 0 . 80 0 . 01 0 . 20 0 . 25 0 . 40 - 0 . 3 - 0 . 2 0 . 15 0 . 20 0 . 20 0 . 20 (2) Machine Spindle r . . 2 1 Data Acquisition Instrumented Hammer Accelerometers Figure 1: Modal testing schematic. Sensors are placed every 25 [mm] starting from the tool tip (i.e. the tool tip corresponds to x 1 ). 1
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2. [15 pts] Find the damping ratio ( ζ ) and the natural frequency ( ω n ) for the system shown in Figure 2. Also, derive an expression for
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Final_exam_2003 - Mechanical Vibrations Final Exam Student...

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