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

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