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clear all;
clc;
close all;

%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% MODAL ANALYSIS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear all;
clc


k1 = 0.5e9;
k2 = 1e9;

M1 = 65040;
M2 = 62080;

%Assumed modal damping:
z1= 0.001;                    
z2= 0.1;
%
%Define effective mass and stiffness matrices:
M=[M1,0;0,M2];
K=[k1+k2,-k2;-k2,k2];
%
[V,D]=eig(inv(M)*K);
Nat_freq=sqrt(D);               %Natural frequencies in rad/s
Nat_freq_Hz=Nat_freq/(2*pi)     %Natural frequencies in Hz

Nat_freq_Hz = 2×2

30.0725 0 0 9.3732

%
%Vnorm - normalised modal matrix   
Normal_modes=[V(:,1)/V(1,1) V(:,2)/V(2 ,2)];
Vnorm_columns=[V(:,1)/V(1,1) V(:,2)/V(1,2)]; 

%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% GENERATE FORCE (Square Pulses) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
N=1024;
%fs=400      %Sample rate (samples/s)
fs=1000;
f_Nyquist=fs/2      %Nyquist frequency

f_Nyquist = 500

df=fs/N             %Frequency resolution

df = 0.9766

dt=1/fs             %Time increment of samples

dt = 1.0000e-03

%Tlength=dt*(N-1)   %Simulation duration in s
Tlength= 40.96;     %Duration of simulation(s)[40.96]
t=0:dt:Tlength;     %time array with increment dt
Ndata=length(t)     %Data length over the duration of simulation

Ndata = 40961

%
%======= Generation of random excitation ========

%%%CHANGE TO YOUR DATA
F0=25e3          %Amplitude of sinusoidal excitation 

F0 = 25000

Force=0.5*F0*(square(t.*(pi),5)+1); %Zero mean with amplitude F0
Force=Force';
%======= End of random signal generation =======
%  
figure(1)     
plot(t,Force,'b')  %Plot 'Force' time history
grid
xlabel('Time(s)')
ylabel('Force(N)')
title('Excitation force time history')
legend('Random signal')

%
%Show frequency domain features of the excitation
fft_force=fft(Force,N);   %FFT of 'Force'
fft_force=fft_force';  %Change from row vector to column vector
freq=0:df:df*(N-1);  %Generate a frequency array with increment df
%
figure(2)
plot(freq,db(abs(fft_force)),'r')  %Plot mag of 'fft_force' on db scale
grid on
xlabel('Frequency(Hz)')
ylabel('Magnitude of fft force')
title('Magnitude of FFT of the excitation force')

%
%Right-Hand-Side(RHS) force vector of EoM:
%NB: One row for one EoM
F=[zeros(1,Ndata);Force']; %F size is 2xNdata

%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  SUPERPOSITION METHOD %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Defines the normal mode matrix from the Modal Analysis results
%============================   Begin [4]  =============================
disp('Normal modes from modal analysis are used below')

Normal modes from modal analysis are used below

X1=Vnorm_columns(:,1);        
X2=Vnorm_columns(:,2);  
disp('Modal matrix X:')

Modal matrix X:

X=[X1 X2]   %Form modal matrix for subsequent solution

X = 2×2

1.0000 1.0000 -0.8221 1.2744

%Modal mass and stiffness matrices
disp('Modal mass matrix Mg:')

Modal mass matrix Mg:

Mg=X'*M*X;
disp('Modal stiffness matrix Kg:')

Modal stiffness matrix Kg:

Kg=X'*K*X;
%
%Modal force vector for Ndata time steps (Ndata columns)
Fg=X'*F;    %A 4xNdata matrix with one row for one mode of de-coupled EoMs



%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% NUMERICAL METHOD %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Part 6 solves the de-coupled SDOF EoM for each mode
%============================   Begin [6]  =============================
Tspan=[0 Tlength];
q0=[0;0];
%
%NB: The user function file 'Example1_AnyInput.m' should be located in the 
%same folder.
%
%Solving the 1st mode
mq=Mg(1,1);
kq=Kg(1,1);
cq = 2*z1*Nat_freq(1,1)*Mg(1,1);
fq=Fg(1,:);
[T1 Q1]=ode45(@(t,y) Example1_AnyInput(t,y,mq,kq,cq,fq,dt),Tspan,q0);

Unrecognized function or variable 'Example1_AnyInput'.

Error in solution (line 116)
[T1 Q1]=ode45(@(t,y) Example1_AnyInput(t,y,mq,kq,cq,fq,dt),Tspan,q0);

Error in odearguments (line 90)
f0 = feval(ode,t0,y0,args{:}); % ODE15I sets args{1} to yp0.

Error in ode45 (line 106)
odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

%
%Solving the 2nd mode
mq=Mg(2,2);
kq=Kg(2,2);
cq = 2*z2*Nat_freq(2,2)*Mg(2,2);
fq=Fg(2,:);
[T2 Q2]=ode45(@(t,y) Example1_AnyInput(t,y,mq,kq,cq,fq,dt),Tspan,q0);
%
%Below change the response output from 'ode45' with variable-stepsize into
%fixed stepsize with time array 't' using interpolation function 'PCHIP'
Q1N=interp1(T1,Q1,t,'PCHIP'); 
Q2N=interp1(T2,Q2,t,'PCHIP');


%plots the modal co-ordinate time history for each mode

figure(31)
plot(t,Q1N(:,1))
grid on
xlabel('Time(s)')
ylabel('Displacement q1')
title('1st modal co-ordinate time history')
%
figure(32)
plot(t,Q2N(:,1))
grid on
xlabel('Time(s)')
ylabel('Displacement q2')
title('2nd modal co-ordinate time history')


% Applies modal superposition transformation: x=X*q

x_rows=X*[Q1N(:,1)';Q2N(:,1)'];   % Real Displacement
x_dot =X*[Q1N(:,2)';Q2N(:,2)'];   % Velocity

%NB: dimensions in above multiplication X(2x2)*Q(2xNdata)-> x(2xNdata)
x=x_rows';       %Transpose to put each displacement history as a column


figure(41)
plot(t,x(:,1))
grid on
xlabel('Time(s)')
ylabel('Displacement x1(m)')
title('m1 displacement response')

%
figure(42)
plot(t,x(:,2))
grid on
xlabel('Time(s)')
ylabel('Displacement x2(m)')
title('m2 displacement response')

%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% FREQUENCY ANALYSIS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Calculate the FFT of modal co-ordinates
fft_q1=fft(Q1N(:,1),N);   %FFT with N data length
fft_q2=fft(Q2N(:,1),N);
%
%Below plot magnitude of FFT of modal co-ordinates
%
%Plot on linear scale
figure(5)
plot(freq,(abs(fft_q1)),'r')  
grid on
hold on   %to allow adding more curves to the same plot window
plot(freq,(abs(fft_q2)),'b')  
hold off  %to end adding more curves to this plot window
xlabel('Frequency(Hz)')
ylabel('Mag of FFT of Modal Disp')
title('Mag of FFT of Modal response plotted in [0,fs]')
legend('FFT for mode 1','FFT for mode 2')
xlim([0 f_Nyquist])      %plot in frequency range [0,f_Nyquist]

%
%Plot on dB scale
figure(6)
plot(freq,db(abs(fft_q1)),'r') 
grid on
hold on
plot(freq,db(abs(fft_q2)),'b')  
hold off
xlabel('Frequency(Hz)')
ylabel('Mag of FFT of Modal Disp (dB)')
title('Mag of FFT of Modal response plotted in [0,fs/2]')
legend('FFT for mode 1','FFT for mode 2')
xlim([0 f_Nyquist])      %plot in frequency range [0,f_Nyquist]

% calculates and plots the FFT of physical co-ordinates
%============================== Begin [11] ==============================
%Calculate the FFT of the displacement of each mass
fft_d1=fft(x(:,1),N);
fft_d2=fft(x(:,2),N);
%
%Below plot magnitude of FFT of the displacements of the masses
%
%Plot on linear scale
figure(7)
plot(freq,(abs(fft_d1)),'r')  
grid on
hold on
plot(freq,(abs(fft_d2)),'b')  
hold off
xlim([0 f_Nyquist])      %plot in frequency range [0,f_Nyquist]
xlabel('Frequency(Hz)')
ylabel('Mag of FFT of mass displacement')
title('Mag of FFT of mass displacement plotted in [0,fs/2]') 
legend('FFT of m1 disp','FFT of m2 disp')

%
%Plot on dB scale
figure(8)
plot(freq,db(abs(fft_d1)),'r')  
grid on
hold on
plot(freq,db(abs(fft_d2)),'b')  
hold off
xlabel('Frequency(Hz)')
ylabel('Mag of FFT of Modal Disp (dB)')
title('Mag of FFT of mass displacement (dB) plotted in [0,fs/2]') 
legend('FFT of disp 1','FFT of disp 2')
xlim([0 f_Nyquist])      %plot in frequency range [0,f_Nyquist]

%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% TRANSMISSIBILITY %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

x_dot = x_dot';    %convert the velocity vector from row vector to a column vector

c1 = 2*z1*sqrt(k1*M1); %damping coefficient
 
Fground = x(:,1).*k1 + x_dot(:,1).*c1;     %Force acting on the ground

plot(t,Fground)  % plot the force acting on the ground in the time domain
xlabel('time (sec)')
ylabel('Ground Force')

freq=0:df:((df*N)/2)-1;  %Generate a frequency array with increment df
L = length(freq);

% Fast Fourier Transform of Input force  and Ouput force
FIN = fft(Force,N);      
FOUT = fft(Fground,N);
TR = abs(FOUT)./abs(FIN); %Transmissibility

figure(9)
plot(freq,TR(1:L,1))   %plot the Transmissibility in the frequency domain
xlabel('frequency (Hz)')
ylabel('Force Transmissibility')
grid on
hold on

figure(10)

plot(freq,db(TR(1:L,1)))   %plot the Transmissibility in the frequency domain dB scale
xlabel('frequency (Hz)')
ylabel('Force Transmissibility (dB)')
grid on
hold on

[Walter Roberson]

We do not have your Example1_AnyInput to test with.

Note: please format your code. First use the editor here to delete the code you posted; then click the > button in the CODE section of the editor header here; then paste your code from your file into the code area that is created by the > button.

[Elis Till]

edited it, and put the code in

[Walter Roberson]

Unrecognized function or variable 'Example1_AnyInput'.

[Jan]

clear all;
clc;
close all;
clear all;
clc

It is a waste of time to run clear all once, but why are you doing it twice?

The code runs and shows diagrams until it stops with the message:

Unrecognized function or variable 'Example1_AnyInput'.

Where is this function?