# chap92_add - Example Given a uniform cantilever beam Model...

This preview shows pages 1–6. Sign up to view the full content.

1 Example ± Given a uniform cantilever beam. ± Model the beam with a single finite element . ± Calculate the natural (modal) frequencies and mode shapes. ± Solution: ² Only two unrestrained dof in the system. ² Only the 2x2 lower right portion of the element stiffness and mass matrices will be used. ± From Eqs. 2.3-2 and 9.3-5 (given in the next pages):

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

View Full Document
2 Plane Beam Element: Stiffness matrix = 2 3 6 1 3 2 3 6 3 6 2 2 2 2 L L L L L L L L EI k (SYMMETRIC)
3 Consistent Mass Matrix of a Plane Beam

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

View Full Document
4 Example: The modal frequencies ± Eigenvalues are found by setting determinant to zero ± Expanding the determinant gives the characteristic equation , a quadratic equation in a. Solving we obtain the following two frequencies ± The exact numerical coefficients are 3.516 and 22.03. ± Errors are then 0.5 % and 58 %, respectively.
5 Example (cont.) ± The mode shape corresponding to each frequency is obtained by

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.

## This note was uploaded on 06/06/2011 for the course EAS 4240 taught by Professor Peterifju during the Spring '08 term at University of Florida.

### Page1 / 7

chap92_add - Example Given a uniform cantilever beam Model...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online