1 / 56

# Dynamic Response of MDOF Structures - PowerPoint PPT Presentation

Dynamic Response of MDOF Structures. Equilibrium of forces condition gives the equations of motions:. Example : 2-DOF, identical mass & stiffness Free vibration. How do we solve this set of coupled equations?. By observation, the solution should be harmonic.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Dynamic Response of MDOF Structures' - kasen

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Dynamic Response of MDOF Structures

Example motions:: 2-DOF, identical mass & stiffness Free vibration

How do we solve this set of coupled equations?

Substituting into the equations of motion:

Need to find non-trivial solution  coefficient matrix has to be singular

Natural frequencies motions:of the 2-DOF system.

1 motions:

2

Example motions:: 5-DOF, identical mass & stiffness Free vibration

Scaling the Modeshapes motions:

• Arbitrary Set one modeshape coefficient equal to unity (ex: coeff. at roof level = 1.0) Mass normalized

Forced Vibration motions:

modal representation

Premultiply by

MDOF Examples motions:

find modes motions: