A 2-DOF linear elastic structure, with mass matrix m = = [4000 5000 kg, and stiffness...

 

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A 2-DOF linear elastic structure, with mass matrix m = = [4000 5000 kg, and stiffness matrix k = 300 -3001 -300 800 103 N/m, external load p = 103 x 30. sin5t N. (10 points) Questions: (1) Determine the vibration modes and natural frequency of the system; (2) Proof the orthogonality features of the vibration modes (3) Suppose the structure's response can be expressed by modal superposition method as v = OY, Y = {}} where is the vibration mode matrix, give the steady state response of the system (hint: (x2) calculate Y, and Y2 first) A 2-DOF linear elastic structure, with mass matrix m = = [4000 5000 kg, and stiffness matrix k = 300 -3001 -300 800 103 N/m, external load p = 103 x 30. sin5t N. (10 points) Questions: (1) Determine the vibration modes and natural frequency of the system; (2) Proof the orthogonality features of the vibration modes (3) Suppose the structure's response can be expressed by modal superposition method as v = OY, Y = {}} where is the vibration mode matrix, give the steady state response of the system (hint: (x2) calculate Y, and Y2 first)