1.) 175 points) A rocket is clamped the launch pad like a vertical fixed-free beam (cantilever beam) as shown in the ill

[answerhappygod]

1 175 Points A Rocket Is Clamped The Launch Pad Like A Vertical Fixed Free Beam Cantilever Beam As Shown In The Ill 1 (64.82 KiB) Viewed 13 times

1.) 175 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: miem, m2 = 0.5m, m -0.25m. ka = k, k2 = 2k, k) = 2k. C1 = 0, C2 = 0, Cu = 0, F = 0, F2=0, F = 0. m3 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. A zu C. (20 points] Using A = 12(1-DI = 0, derive the Characteristic Determinant of the system. (Hint) it will be a 3 by 3 matrix in terms of a, where a = mo?/k. No need to compute the characteristic polynomial or its roots. d. (20 points) Given the first natural frequencies 01 = 0.73 (k/m)/2, and recalling that 2 = 1/w?, use the Characteristic Equation and the system of 3-equations and 3-unknowns to calculate the associated first mode shape vector X(1) mi e. [10 points) Given the following 3 mode shape vectors, neatly and accurately plot each of the mode shapes based on the Eigenvectors. You can use the same graph for all three plots. (Note) vectors written in transposed notation. x(1) = (1.00, 1.23, 1.04}" X (1) X(2) = (1.00, -0.05, -2.61}" X2) X(B) = (1.00, -8.19, 12.58}" X (3)