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# SolSec1_5 - Problems and Solutions Section 1.5(1.66 through...

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Problems and Solutions Section 1.5 (1.66 through 1.74) 1.66 A helicopter landing gear consists of a metal framework rather than the coil spring based suspension system used in a fixed-wing aircraft. The vibration of the frame in the vertical direction can be modeled by a spring made of a slender bar as illustrated in Figure 1.21, where the helicopter is modeled as ground. Here l = 0.4 m, E = 20 × 10 10 N/m 2 , and m = 100 kg. Calculate the cross-sectional area that should be used if the natural frequency is to be f n = 500 Hz. Solution: From Figure 1.21 ! n = k m = EA lm (1) and n = 500 Hz 2 " rad 1 cycle # \$ % = 3142 rad/s Solving (1) for A yields: A = n 2 lm E = 3142 ( ) 2 .4 ( ) 100 ( ) 20 " 10 10 A = 0.0019 m 2 = 19cm 2

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1.67 The frequency of oscillation of a person on a diving board can be modeled as the transverse vibration of a beam as indicated in Figure 1.24. Let m be the mass of the diver ( m = 100 kg) and l = 1 m. If the diver wishes to oscillate at 3 Hz, what value of EI should the diving board material have? Solution: From Figure 1.24, ! n 2 = 3 EI ml 3 and n = 3 Hz 2 " rad 1 cycle # \$ % = 6 rad/s Solving for EI EI = n 2 ml 3 3 = 6 ( ) 2 100 ( ) 1 ( ) 3 3 = 11843.5 Nm 2 1.68 Consider the spring system of Figure 1.29. Let k 1 = k 5 = k 2 =100 N/m, k 3 = 50 N/m, and k 4 = 1 N/m. What is the equivalent stiffness?
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SolSec1_5 - Problems and Solutions Section 1.5(1.66 through...

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