A 2DOF system, shown in the figure, has m1=5 kg, m2=10 kg, k1=
1500+n N/m, n=15 and k2= 6500 N/m.
Do the following and check your answers using the below Matlab
code:
1- Check is it correct to use the mass and stiffness matrices
[m] and [k] mentioned in the code.
2- Find the two natural frequencies (Eigen frequencies),
3- Find the Modal vectors (Eigen vectors)
4- Find the Mode shapes
MATLAB code:
clc;
m1 = ;
m2 = ;
k1= ;
k2 = ;
m = [m1 0; 0 m2]; %mass matrix [m]
k = [(k1 + k2) -k2; -k2 k2]; %stiffness matrix [k]
eigsort(k,m);
function [u,wn]=eigsort(k,m)
Omega=sqrt(eig(k,m));
[vtem,~]=eig(k,m);
[wn,isort]=sort(Omega);
il=length(wn);
for i=1:il
v(:,i)=vtem(:,isort(i));
end
disp("The natural frequencies are (rad/sec)")
wn
disp("\nThe eigenvectors of the system are")
v
disp("Ratios of eigenvectors are:\n")
A1_A2_1 = v(1,1)/v(2,1)
A1_A2_2 = v(1,2)/v(2,2)
figure(1)
plot([0,1,2,3], [0,A1_A2_1,1,0],'b-s', 'LineWidth',2,
'MarkerSize',10);
hold on;
plot([0,1,2,3], [0,-A1_A2_2,-1,0],'r-s', 'LineWidth',2,
'MarkerSize',10);
hold off; ylabel('Eigne Vector Ratio'); xlabel('Mass Number');
xticks([1 2]);
legend('Mode 1', 'Mode 2')
end
- Mechanical Vibrations A 2dof System Shown In The Figure Has M1 5 Kg M2 10 Kg K1 1500 N N M N 15 And K2 6500 N M 1 (27.7 KiB) Viewed 30 times