me445_hw3_soln - 1 ME 445 Mechanical Vibrations // Fall...

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Unformatted text preview: 1 ME 445 Mechanical Vibrations // Fall 2009 Homework #3 Solutions Due: 09.11.2009 [4 pts] The natural frequency of the system is computed first. rad/s 83 . 11 75 . 1 245 = = = m k n ω To compute the angular speed, Picture #58 is utilized as shown, Figure 1 Measurement of the angular speed Three spikes are captured covering an angular displacement of about ° = Δ 150 θ . The duration of time between the captured spikes is s 10 14 . 23 ) ms 57 . 11 ( 2 3- × = = Δ T . The angular frequency of rotation is found as, rpm 1080 rad/s 14 . 113 = = Δ Δ = T θ ω The damping effect can be modeled by the aerodynamic drag force induced by the vibration of the plate (see Figure 2). The aerodynamic drag can be expressed as 2 2 1 V A C F d d ρ = , where C d is the drag coefficient, A is the total area of the plate, ρ is the density of air and V is the velocity of the plate. The expression includes square of the velocity, which is a nonlinear term. Energy will be dissipated but this kind of damping is not viscous damping. An equivalent viscous damping dissipated but this kind of damping is not viscous damping....
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me445_hw3_soln - 1 ME 445 Mechanical Vibrations // Fall...

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