- #1
marcas3
- 5
- 0
Homework Statement
Hello, I would just like to make sure I am doing the problem correctly. What I have is a cantilever uniform beam that is fixed at one end and free on the other. Basically, it is a wing and I am using a lumped mass approach to find a graphical representation of the wing's displacement when a force is applied at the tip.
Is the script below for MATLAB written correctly? Any advice is greatly appreciated.
Homework Equations
The force at the tip: F=1000*sin(111.5*t)
Also, I am using three masses spaced evenly across the beam which correspond to the beam's length as being 3*l
The Attempt at a Solution
A = 0.09;
l = 2;
I = 2.280*10^(-4);
E = 20.5*10^10;
p = 7.83*10^3;
n3 = 3;
t = 0:.001:10;
F = 1000*sin(111.5*t)';
Bf = [0;0;1]; % Since the force is acting on the wing tip, its on the third mass
flex3 = (l^3)/(E*I)*[1/3 5/6 4/3; 5/6 8/3 14/3; 4/3 14/3 9]; % Flexibility matrix
stif3 = inv(flex3); % Stiffness matrix is inverse of flexibility matrix
mass3 = (p*A*l)/n3*eye(3); % Mass matrix
AA = [zeros(3,3) eye(3,3); -inv(mass3)*stif3 -inv(mass3)*eye(3,3)];
BB = [zeros(3,1); inv(mass3)*Bf];
CC = [0 0 1 0 0 0];
DD = [];
sys_ss = ss(AA,BB,CC,DD)
[y, ti] = lsim(sys_ss, F, t');
plot(ti,y)