Simple questions on Mechanical Vibrations

Question

yung zhen lek 2018-11-13

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https://ww2.mathworks.cn/matlabcentral/answers/429689-simple-questions-on-mechanical-vibrations

回答： Keith Hekman 2020-12-29

For k = 100, c = 2 and m = 1 use Matlab to calculate ωn, ωd and ξ. and Solve the equation of motion for F = F0sin(ωt) where ω = 1 → 20 rad/s and F0 = 10 N and plot the maximum response at steady-state for each frequency.

%Part 2
%Equation of motion
clear all;
clc;
m=1;
c=2;
k=100;
F=0;
Force=[0;0;F];
M=[m 0 0;0 m 0;0 0 m];
K=[2*k -k 0;-k 2*k -k;0 -k k];
C=[2*c c 0;-c 2*c -c;0 -c c];
%Finding values
Z=zeros(3);
I=eye(3);
A=[C M;I Z];
B=[K Z;Z -I];
[V,D]=eig(B,A)
d=diag(D);
r=real(d);
im=imag(d);
wn=abs(d)
wd=im/-1
zeta=sqrt(1-(wd/wn)^2)
%Part 3
%2 equations: (K-Mw^2)a + Cwb=0, -Cwa+(K-Mw^2)=f
F0=10;
f=[0;0;F0];
z=[0;0;0];
w=1:0.1:20;
t=0:0.01:100;
for ii=1:length(w)
    G=K-M.*w(ii)^2;
    H=C.*w(ii);
    T=[G H;-H G];
    constants(:,ii)=T^(-1)*[z;f];
    a(:,ii)= constants(1:3,ii);
    b(:,ii)= constants(4:6,ii);
    x=a(:,ii)*cos(w(ii)*t)+b(:,ii)*sin(w(ii)*t);
    amp(:,ii)=sqrt((a(:,ii)).^2+(b(:,ii)).^2)
end
plot(w,x)