Modal Analysis with Galerkin's Method

Modal analysis for a 2DOF suspension system with Galerkin's method over "ne" individual elements

The purpose of this program is to perform modal analysis for a two-degrees of freedom tractor suspension system. Galerkin's method over "ne" individual elements of time domain [t1,t2], was used to numerically solve the two uncoupled resulting 2nd-oder ODEs.

Original suspension model:
M*d2x+B*dx+K*x=0, t1<t<t2
where x=[xs,xw]
BC:
xs(t1 )=xs1 , xs(t2 )=xs2,
xw(t1 )=xw1 , xw (t2)=xw2

Modal equations:
d2(Etta1)+Bg_diag(1,1)*d(Etta1)+(Omega1^2)*(Etta1)=0
d2(Etta2)+Bg_diag(2,2)*d(Etta2)+(Omega2^2)*(Etta2)=0
Boundary conditions in modal coordinates:
Etta1=Fi1'*M*xs
Etta2=Fi2'*M*xs
BC=[Etta1 Etta2]

The output of this program:
1- The solution of Etta1(t), Etta1'(t), Etta1"(t)
2- The solution of Etta2(t), Etta2'(t), Etta2"(t)