2.) [25 points) As before, a rocket is clamped on the launch pad like a vertical fixed-free beam (cantilever beam) as sh

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2 25 Points As Before A Rocket Is Clamped On The Launch Pad Like A Vertical Fixed Free Beam Cantilever Beam As Sh 1 (66.33 KiB) Viewed 14 times

2.) [25 points) As before, a rocket is clamped on the launch pad like a vertical fixed-free beam (cantilever beam) as shown in the illustration. Analyze the structure to determine its longitudinal (long-axis/vertical) vibration characteristics. This time, consider the rocket to be a continuous system. a. [5 points) For the longitudinal vibration in a bar write down the free-vibration equation, the equation for the wave speed "c", the general harmonic solution for the longitudinal displacement u(x,t), and the appropriate boundary conditions for a fixed-free bar. b. [5 points) Apply the boundary conditions to the general equation for longitudinal vibration to determine the values of the coefficient A and the frequency equation associated with the coefficient B. C. [5 points) Since the frequency equation can only be zero when the harmonic function (in this case cosine) is equal to zero, use the fact that cos((2n+1)/2) = 0 to write the general natural frequency equation, and then write the specific equation for the first 3 natural frequencies where n=0,1, and 2. d. [5 points) For each of the first three natural frequencies, write down the associated Mode Shape equations for U.(x), where n = 0, 1, and 2. e. [5 points) Assuming Co = 2.6137, C1 = 1.0827, and C2 = 1.0827, and the length of the rocket is l = 20 meters, use the 3 mode shape equations to compute the deflection of the rocket at x = 0,5, 10, 15, and 20 meters along it length. Create a table of these values with columns x, Uo(x), U1(x), and U2(x), and rows for x = 0,5, 10, 15, and 20. Plots these 3 curves neatly on one clear large graph. [hint: just plot the longitudinal deflections as transverse magnitudes in the plot). = Uox) U(x) U2(x) х 0 5 10 15 20