- Mi M2 M3 1 75 Points A Rocket Is Clamped The Launch Pad Like A Vertical Fixed Free Beam Cantilever Beam As Shown 1 (13.21 KiB) Viewed 10 times
- Mi M2 M3 1 75 Points A Rocket Is Clamped The Launch Pad Like A Vertical Fixed Free Beam Cantilever Beam As Shown 2 (55.29 KiB) Viewed 10 times
1.) (75 points) A rocket is clamped 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. Consider the rocket to be a multi-degree of freedom system with three (3) degrees of freedom. Assume the following: mi=m, m2 = 0.5m, ma = 0.25m. kı =k, k= 2k, k3 = 2k. C1 = 0, C2 = 0, C3 = 0. F1 = 0, F2 = 0, F3 = 0. a a. (5 points) Create a diagram of the physical system with all associated mass, stiffness, damping, external force, and displacement elements. b. (20 points) Starting with the assumed values, write down the mass matrix [m] and the stiffness matrix [k]. Using the flexibility influence coefficients from example 6.5 compute the influence matrix (a). Use [m] and [al, compute the Dynamical Matrix [D] for the system. No need to write the (c) matrix. C. (20 points] Using A = 12)-[D]1 = 0, derive the Characteristic Determinant of the system. (Hint) it will be a 3 by 3 matrix in terms of a, where a = m 02/k. No need to compute the characteristic polynomial or its roots.