AE301WingVibrationLaboratoryManualFull - 1. Wing Vibration...

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1. Wing Vibration 1.1. Purposes Study shed-vortex induced vibration of a low aspect ratio wing. A number of experimental variations are performed to isolate the effect of mass, damping and spring stiffness of the wing. Perform experiments in support of AE/ME455 Mechanical Vibrations, ME324 Dynamics of Mechanical Systems, MA232 Elementary Differential Equations and MA330 Advanced Engineering Mathematics. 1.2. Background The primary goal of vibrations testing is to determine the response of a flexible structure to changing forces or displacements. Aircraft are typically designed using with low- weight in mind. This results in structures that tend to be flexible with accepted higher deflection under static aerodynamic load. To reduce deflections, the wing would need to be made stiffer and this tends to have a weight penalty. A wing on an aircraft experiences changes in atmospheric conditions such as air density, precipitation, drafts, ‘turbulence’, and wakes from other aircraft. These effects amount to a time-varying wing loading. Another effect is seen at high angles of attack either due to a maneuver or when the wing twists along its length relative to a steady fuselage. In this situation, the flow over a high angle of attack wing section will typically generate vortices that grow and shed off into the wake. This creates a specific frequency for loading changes over time. The aerodynamic load is coupled to the wing deflection as the flow is altered due to wing plunging (up and down motion) and angle of attack changes (pitching or twist). The wing may fail if its natural frequency is reached (see links to movies in the Flutter Videos folder). The effect of damping will change the way the wing responds and can protect it by shifting the natural frequency or absorbing energy from the changing load.
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1.2.1. Vibration Effects The wing acts like a cantilevered wing that has time-varying loading along its length. Two vibrations concepts: 1. Natural Frequency and 2. Damping. can be investigated in the design of the wing by using scale models and wind tunnel testing. The theory contains simplifications such as mass lumping, linear elastic behavior and one- dimensional motion. These assumptions along with a momentum change-force balance (or energy equation) yield a second order differential equation of the form (see the lab textbook page 88) where y(t) is the unknown 1D displacement versus time, m is the lumped mass, c is the damping coefficient, k is the elastic spring constant and F is the applied forcing function that might be a sinusoid (vortex shedding) or impulse (gust, bird strike). This differential equation can be solved by numerical means but the parameters m , c and k must be known and are assumed constant over time to ease solution.
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This note was uploaded on 02/07/2011 for the course AE/ME 301 taught by Professor Lafleur during the Spring '11 term at Clarkson University .

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AE301WingVibrationLaboratoryManualFull - 1. Wing Vibration...

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