Just stating questions like this makes it obvious this is part of a work assigned to you.
I'll give you something to start with:
The Euler-Bernouilli equation
then take any respectable book in fundamental structural dynamics (which should show more or less every step in great detail for calculating the first eigenvalue (the rest follows easily)
Give it a try and ask more detailed questions if you dont succeed.
Here is a paper that solves a problem by studying the Cantilever Beam. A few pages into this paper, it has the mathmetical expressions for its the first 3 vibration modes and frequencies. cheap web hosting
how about eigen?
how about eigen?
Sounds like homework
Just stating questions like this makes it obvious this is part of a work assigned to you.
I'll give you something to start with:
The Euler-Bernouilli equation
then take any respectable book in fundamental structural dynamics (which should show more or less every step in great detail for calculating the first eigenvalue (the rest follows easily)
Give it a try and ask more detailed questions if you dont succeed.
If you know the natural
If you know the natural frequency and the mass of the load and beam...
k=Wn^2*m (where k=stiffness, Wn=natural frequency, m=total mass)
If the beam's mass is not negligable then the total mass is...
m= m(load)+1/4m(beam)
I'm wondering if this link might help you ;-)
http://www.vibrationdata.com/StructuralDC.htm
Here is a paper that solves a problem by studying the Cantilever Beam. A few pages into this paper, it has the mathmetical expressions for its the first 3 vibration modes and frequencies. cheap web hosting