# Modal analysis for a CANTILEVER BEAM

## Main Question or Discussion Point

Hi there,

I am a beginner and I need to do analytical derivation of a beam and model it in matlab.

the beam is cantilever and it is excited at its cantilever end

any hints to start?

Cheers

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Mech_Engineer
Gold Member
Have you learned how to derive the equations of state for a beam through multiple integrations of its loading or shear force diagrams?

Have you learned how to derive the equations of state for a beam through multiple integrations of its loading or shear force diagrams?
nto really! would u recommend a book please? thanks

[Vibration analysis] Timoskenko beam Vs.Euler-bernoulli beam ?

Hello,

I am looking for explanations and detailed studies or even brief ones about the differences in Vibration analysis and dynamic studies as well as static analysis between

Timoskenko beam and .Euler-bernoulli beam

when should i use Euler-bernoulli beam?

Thanks

Mech_Engineer
Gold Member

Anyway, they are two approximations that take into account a different depth of effects in the beam...

http://en.wikipedia.org/wiki/Timoshenko_beam_theory

http://en.wikipedia.org/wiki/Euler-Bernoulli_beam_equation

Timoshenko theory takes into account shear deformation, rotational inertia, and other effects while Euler-Bernoulli is a simple but effective theory that is easier to understand an solve for, but may be less accurate depending on the complex loading, geometry, or deflection of the beam.

In any case, it is necessary that a certain degree of "engineering discretion" is used to decide which theory is best for your application and how improtant and accurate a result will be.

Have you learned how to derive the equations of state for a beam through multiple integrations of its loading or shear force diagrams?
am not quite sue what you mean here ?!

Mech_Engineer