An example about the application of multitone harmonic balance method to Duffing Van Der Pol equation
Example:
Test System
Test parameters
mu=0.5; c11=10^2; c13=5; c13d=0.15; c=1; au0=8*c; au1=10*c; au2=15*c;
%TEST 1--------------------------------------------------------
% input frequency
w1 = 1.3;%rad/s
w2 = 2.7;%rad/s
%TEST 2-------------------------------------------------------
%change frequency
% input frequency
w1 = 10;%rad/s
w2 = 1;%rad/s
%TEST 3-------------------------------------------------------
c=5; % change amplitude
au0=8c;
au1=10c;
au2=15*c;
% input frequency
w1 = 10;%rad/s
w2 = 1;%rad/s
%TEST 4-------------------------------------------------------
Command window output
c=5;
au0=8c;
au1=10c;
au2=15*c;
% input frequency
w1 = 3.2;%rad/s
w2 = 1.8;%rad/s
compute hbe solution:
costhbe =
2.9173e-26
compute numerical solution:
mse_err =
47.3915
mse_err =
9.0363
mse_err =
1.0226e-07
mse_err =
7.0438e-12
Amplitudes of components:
constant :0.37613
0w1+1w2 :0.73122
0w1+2w2 :0.014166
1w1-2w2 :0.0083522
1w1-1w2 :0.018504
1w1+0w2 :0.51892
1w1+1w2 :0.023698
1w1+2w2 :0.014597
2w1-2w2 :0.001303
2w1-1w2 :0.0069842
2w1+0w2 :0.0088012
2w1+1w2 :0.015925
2w1+2w2 :0.019746
Reference studies:
https://link.springer.com/article/10.1007/s11071-008-9390-y
https://link.springer.com/article/10.1007/s11071-010-9688-4