relationship between natural frequency obtained from continuous and discrete models

[gopi9]

Hi,

I know how to extract the natural frequencies from continuous and discrete model by using eigen-value equations.
This is the continuous model Mx..+Cx.+Kx=F (x. is differentiation of x). The eigenvalue equation for this is (K-1/ω2 M)u=0, 1/ω2 represents frequency.

If we convert that continuous model in to discrete ie., x.=Ax+Bu, Y=Cx+Du. The eigenvalue equation is (A-(abs(λ))I)x=0. here abs(λ) represents natural frequency.

I want to know the relationship(formula) between the natural frequency obtained from continuous model and discrete model.

 

[structSU10]

I don't know of a formula that relates the two. A continuous model is supposed to be more exacty, with essentially infinite degrees of freedom, versus a discrete model which has an accuracy that depends upon the number of discrete points considered.

 

[ishvaaag]

In fact you can see in the Chopra text for dynamics the discretized systems described by your same first equation for the continuous (see the index in the book) (of course in matricial statements). Hence you may be referring to some mathematics to deal with discrete systems of a particular class or in a particular way ... maybe the Bathe text on FEM may have something about that, will try to give a look to it tomorrow.

 

[ishvaaag]

Or it must be just a tricky question, the relation between circular and natural frequency is 2·PI, and if one of them is evaluated in approximation, the relationship must approximate such value;; ω=2·PI·f

I have found nothing in Bathe, Clough and Penzien and some other ... maybe clarifying the context of your question can help a colleague to provide a better answer.