Question for using root function.

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Trong Nhan Tran 2024-5-18

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https://ww2.mathworks.cn/matlabcentral/answers/2120241-question-for-using-root-function

编辑： Trong Nhan Tran 2024-5-20

% 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))

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Torsten 2024-5-19

编辑：Torsten 2024-5-19

在 MATLAB Online 中打开

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

10 9 8 7 6 3720087 w w 2875076127i 13291777051299 w w 1518467207049i 353165987709 w 5 4 3 2 ----------- + -------------- + ----------------- + ----------------- + --------------- + w 34610882040i + 829211728500 w + w 47283750000i + 337500000000 w 50 5000 2500 500 2

% Display the non-zero natural frequencies

disp('Non-zero natural frequencies (Hz):');

Non-zero natural frequencies (Hz):

%disp(root(freqEq))

disp(vpa(root(freqEq)))