Question for using root function.
显示 更早的评论
% Using the MATLAB function “roots” for find non-zero natural frequencies
% define symbolic variable w
syms w;
% Given parameters
m1 = 1.8; m2 = 6.3; m3 = 5.4; m4 = 22.5; m5 = 54;
c2 = 10; c3 = 0.5; c4 = 1.50; c5 = 1.1;
k2 = 100000; k3 = 50; k4 = 75; k5 = 10;
% Set up system matrices
% mass matrix
M = diag([m1, m2, m3, m4, m5]);
% damping matrix
C = [c2 -c2 0 0 0;
-c2 c2+c3 -c3 0 0;
0 -c3 c3+c4 -c4 0;
0 0 -c4 c4+c5 -c5;
0 0 0 -c5 c5];
% stiffness matrix
K = [k2 -k2 0 0 0;
-k2 k2+k3 -k3 0 0;
0 -k3 k3+k4 -k4 0;
0 0 -k4 k4+k5 -k5;
0 0 0 -k5 k5];
% Calculate frequency equation
Zw = w^2*M + 1i*w*C + K; % impedance matrix
freqEq = det(Zw); % take determinant to get frequency equation
pretty(simplify(freqEq)); % display simplified frequency equation
% Display the non-zero natural frequencies
disp('Non-zero natural frequencies (Hz):');
disp(root(freqEq))
11 个评论
John D'Errico
2024-5-18
编辑：John D'Errico
2024-5-18
Please stop posting the same question multiple times. If you want to expand on a question, then do so by editing the question, or by adding a comment. I closed the last question as a duplicate. In fact, since this is now at least the third time you asked this question...
Trong Nhan Tran
2024-5-18
Torsten
2024-5-18
disp(vpa(root(freqEq)))
instead of
disp(root(freqEq))
Trong Nhan Tran
2024-5-19
If you use the code from above, you won't get this error (at least if you work with MATLAB R2024a).
syms w
% Given parameters
m1 = 1.8; m2 = 6.3; m3 = 5.4; m4 = 22.5; m5 = 54;
c2 = 10; c3 = 0.5; c4 = 1.50; c5 = 1.1;
k2 = 100000; k3 = 50; k4 = 75; k5 = 10;
% Set up system matrices
% mass matrix
M = diag([m1, m2, m3, m4, m5]);
% damping matrix
C = [c2 -c2 0 0 0;
-c2 c2+c3 -c3 0 0;
0 -c3 c3+c4 -c4 0;
0 0 -c4 c4+c5 -c5;
0 0 0 -c5 c5];
% stiffness matrix
K = [k2 -k2 0 0 0;
-k2 k2+k3 -k3 0 0;
0 -k3 k3+k4 -k4 0;
0 0 -k4 k4+k5 -k5;
0 0 0 -k5 k5];
% Calculate frequency equation
Zw = w^2*M + 1i*w*C + K; % impedance matrix
freqEq = det(Zw); % take determinant to get frequency equation
pretty(simplify(freqEq)); % display simplified frequency equation
% Display the non-zero natural frequencies
disp('Non-zero natural frequencies (Hz):');
%disp(root(freqEq))
disp(vpa(root(freqEq)))
Trong Nhan Tran
2024-5-19
编辑：Trong Nhan Tran
2024-5-20
I don't have experience with the physical background of your equations.
Just solving your system for omega gives a similar result as yours - only the 1i's are missing.
syms w
% Given parameters
m1 = 1.8; m2 = 6.3; m3 = 5.4; m4 = 22.5; m5 = 54;
c2 = 10; c3 = 0.5; c4 = 1.50; c5 = 1.1;
k2 = 100000; k3 = 50; k4 = 75; k5 = 10;
M1 = [-k2, k2, 0, 0, 0;k2, -k3-c3-k2, k3+c3, 0, 0;0, k3, -k4-c4-k3, k4+c4, 0;0, 0, k4, -k5-c5-k4, k5+c5;0, 0, 0, k5, -k5];
M2 = [-c2, c2, 0, 0, 0;c2, -c2, 0, 0, 0;0, c3, -c3, 0, 0;0, 0, c4, -c4, 0;0, 0, 0, c5, -c5];
M3 = diag([m1,m2,m3,m4,m5]);
M = M1+w*M2+w^2*M3;
vpa(root(det(M)==0))
Trong Nhan Tran
2024-5-19
Torsten
2024-5-19
I just wrote your system of equations in matrix form
M(w)*[X1;X2;X3;X4;X5] = 0
and determined the values of w for which the equation has a nontrivial solution.
Trong Nhan Tran
2024-5-19
Write your equations (1)-(5) as
M1*[X1;X2;X3;X4;X5] + w*M2*[X1;X2;X3;X4;X5] + w^2*M3*[X1;X2;X3;X4;X5] = 0
and you will see that my M1, M2 and M3 matrices are correct to reproduce your system.
But as I said: I don't know if this is how "natural frequencies" are defined.
回答（0 个）
类别
在 帮助中心 和 File Exchange 中查找有关 Linear Algebra 的更多信息
2024-5-18
2024-5-20
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
Translated by 
