Bending waves in beams with shear... derivation

[NS4U]

I'm looking for a text that talks about solving for bending wave propagation in a beam that also includes shear deformation. I've found a few that talk about writing the wave equation... but I'm looking for something that actually solves the Diff. Eq to get the stead state response.

Any suggestions?

 

[electricpete]

"Advanced Engineering Dynamics" by Harrison and Nettleton
ISBN 0 340 64571 7
ISBN 0 470 23592 6

Section 6.12 derives the "Timoshekno Beam Equation" for waves in a uniform beam, including shear deformation energy and rotary inertia. They use Hamilton's principle for this derivation.

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[electricpete]

Sorry - I didn't read the question closely. This reference derives the equation but doesn't apply it.

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[NS4U]

That may still be helpful.

Thanks!