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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

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# Frequency response function of periodic-stiffness model of system

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