Eigendata problem

[heitor]

Hello.

In a model have a fixed-free beam that supports a reservatory at the free side.
If I could evaluate the first frequency of the system (beam+reservatory) by using only the eigenvalues and eigenvectors of the beam, it would save me a lot of time since the reservatory can work with several loads. Do you think it is raisonable?

Thank you!

 

[tomirvine]

I assume that the reservatory could be modeled as a point mass.

Vibration textbooks have natural frequency formulas for a fixed-free beam with a point mass on the free end. (I can send the formulas to you via Email if you do not have a textbook.)

The fundamental mode shape could be assumed as that for a fixed-free beam, as a first approximation.

A more sophisticated analysis could be done with the Rayleigh-Ritz method, or the finite element method.

Tom Irvine
Email: tomirvine@aol.com

http://www.vibrationdata.com

 

[hacksaw]

Sturm-Liouville insures that you can expand the solution of the problem you describe. It doesn't tell you how fast the solution converges however.

The Rayleigh-Ritz method is fine as long as you are seeking information about the the lowest order mode.