CA-AA242B-Hw2

CA-AA242B-Hw2 - AA 242B: Mechanical Vibrations (Spring...

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Homework #2 Due April 30, 2010 1 Control Tab A control tab of an airplane elevator is hinged about axis A in the elevator (see Figure 1). Its dynamic behavior depends on the moment of inertia I A , and the elastic sti±ness of the control linkage which can be modeled as a torsional spring with a sti±ness coe²cient k θ . Since k θ cannot be measured statically, a resonance test is typically used for that purpose. The elevator is held ³xed, the tab is supported by a spring with a sti±ness coe²cient k 1 , and a harmonic excitation is applied through a spring with a sti±ness coe²cient k 2 , as shown in Figure 1. 1. Explain why the coe²cient k θ cannot be measured by a static test. 2. Find the natural frequency(ies) ω n of the system described above as a function of I A and k θ . 3. Find k θ as a function of the resonance frequency ω r , I A , and other pa- rameters shown in Figure 1. Figure 1: Dynamic testing of a control tab of an airplane elevator.
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CA-AA242B-Hw2 - AA 242B: Mechanical Vibrations (Spring...

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