Natural Frequencies and Modes

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

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

## This note was uploaded on 05/09/2008 for the course CE 573 taught by Professor Whalen during the Fall '05 term at Purdue.

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online