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 (64.87 KiB) Viewed 19 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(xt), and the appropriate boundary conditions for a fixed-free bar. b. 15 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. 15 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), U.(x), and Uz(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). Uo(x) U1(x) U2(x) х 0 5 10 15 20