Question

I. (20%) A frame structure with lumped mass is shown below: 3m L/2 m El El It can be shown that the stiffness and mass matrices of the framed structure with respect to the coordinates u and u2 can be obtained as: 4 01 [A]=7713 41 [M-m and L424J (a) Determine the natural frequencies and modal vectors of the structural system. (b) Assume the first modal vector is estimated as迪 . Use this modal vector to estimate the natural frequency of the structure.

Please provide a clear step by step solution.

Answer 1

[好 E131 5 L 5 L 5L 5L -36 E ↑ SEI SL 25 L 3ソ 65 EL [뿡

let 2 (트)"。。 ht 8m2 til 35 1 36 m2.5 439/E で7m mL 82 474 ,. m L a, , 3,176 mL 5L Sl -36 ET 5l

E1 Asbune -%27 korn Equation o 713 ED -36 5L EJレ 4 2 /2 -36 asfume

0.736? Kom En the matsin om 48E1 5L -36E 5L -36E1 5 t 5t L36 E 5L 5L 씐부.ne...-0 36E1 2EJ 3E1 5ml SoLm 36LE The Syslem platfaj hreueng ω.1 be became legs on 02, the 书me tu:‘d of the buildint asti be more.

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