Frequency response function of periodic-stiffness model of system

  • #1
Hi,
I'm analyzing a 3 dof undamped system with discrete springs and masses. Three of the springs have time-dependent stiffness, following periodic law (with period T), they are modulated at the same frequency but with a phase difference of 120 deg one from the other.
So this is my system:

(M * d^2x/dt^2) + K(t)*x = f(t)

with:
- M diagonal mass matrix (3x3), constant

- x=[x1;x2;x3] displacements vector (3x1)

- f(t)= f0*[sen(w*t);0;0] forcing vector (3x1) acting only on the first dof

- K(t) symmetric stiffness matrix:

> k11= ko + 2*kc/cos(30) + km*(cos(wm*t));
> k22= ko + 2*kc/cos(30) + km*(cos(wm*t + 2*pi/3));
> k33= ko + 2*kc/cos(30) + km*(cos(wm*t + 4*pi/3));

> k(i,k)= -kc/cos(30) for i~=k

wm = modulation frequency
ko, kc = constants


How can I calculate the frf for this system in order to obtain output amplitude at the second and third dof?
Any help is very appreciated!!!
Have a nice day.

Paolo
 

Answers and Replies

  • #2
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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

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