Natural Frequencies and Modes

Natural Frequencies and Modes - CE 573 Structural Dynamics...

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Unformatted text preview: CE 573: Structural Dynamics Example on Natural Frequencies and Modes Given: A two-story building is modeled as a shear-frame structure. Parameters are kg and N/m. 3 35 10 m = × 6 17.5 10 k = × Required: Determine the natural frequencies and natural vibration modes for this building. Solution: 1. Property matrices – use lumped mass approximation. [ ] 3 3 2 70 10 kg. 2 70 10 m M m ⎡ ⎤ × ⎡ ⎤ = = ⎢ ⎥ ⎢ ⎥ × ⎣ ⎦ ⎢ ⎥ ⎣ ⎦ For the stiffness matrix, the bottom stiffness force has a magnitude 1 4 S 1 F kx = , while the top stiffness force has a magnitude 2 2 2 ( ) S 1 F k x x = − . Thus, the stiffness matrix is [ ] 6 6 6 6 6 6 6 4 2 2 6*17.5 10 2*17.5 10 105 10 35 10 N/m = N/m 2 2 2*17.5 10 2*17.5 10 35 10 35 10 k k k K k k ⎡ ⎤ ⎡ + − × − × × − × ⎡ ⎤ = = ⎢ ⎥ ⎢ ⎢ ⎥ − − × × − × × ⎣ ⎦ ⎢ ⎥ ⎢ ⎣ ⎦ ⎣ 6 ⎤ ⎥ ⎥ ⎦ 2. Solving the eigenproblem – first, solve the characteristic equation for the eigenvalues (let 2....
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This note was uploaded on 05/09/2008 for the course CE 573 taught by Professor Whalen during the Fall '05 term at Purdue.

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Natural Frequencies and Modes - CE 573 Structural Dynamics...

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