Re: normalised mode shapes

prashanth schrieb:
that was fast.. i wont find all these in a textbook.. thanx a ton..
i am going to develop a model specific code because this is my first..
i used matlab..
its very simple to solve the eigen value problem in that.. i just found
out the eigenvalues of the matrix [A]= [K]/[M].. with my bookish
knowledge i am surmising that these values are the square of the
circular frequencies.. i got the eigen vectors too.. but i dunno HOW TO
INTERPRET them!!! and in those eigen vectors i got values ranging from
e-12 to e7.. does this mean that i havent normalised it?

Hello Prashanth,

there are many textbooks where you can find all about this...
Maybe the best one is : Clough: ,,Dynamics of Structures"
For internal usage, I could send you my script of machine dynamics, but it is in german...
I don't know about the syntax in Matlab, but you won't get the eigenvalues by dividing K by M, this operation is only defined for scalars.... As I wrote previosly, you have to get the roots of the characteristic polynom, which is defined by det(K-lambda.M)=0.
These roots, we identify as the squares of our natural (circular) frequencies omega_i...
The eigenvectors p_i you get by: (K-lambda_i.M).p_i=0... the eigenvectors depend linear on each other (as we forced them to be by setting the determinat to zero!!). The eigenvectors you can ,,normalize" to some quantity (e.g. to unity), these eigenvectors represent our mode shapes. The mode shapes show us the ,,eigenform" of our systems as it oscillates in it's specific natural frequency...

What kind of model do you have? Maybe you can send me a sketch of it, so I can help you better...

Regards

Matthias
.

Loading