How can we use a Heaviside function for differential equation having moving load ?

I have a differential equation mentioned in function file where i have to apply moving load. I want to verify the approach that i have tried to get a moving load using heaviside function. so please help me implimenting correctly the moving load.

clc
clear all

%%

% time span
 
tspan=[0:0.1:10];

 y0=[0;0];
%% moving load

F0=9.8;      % magnitude of moving load
L=4;     % length
V=0.1;    % velocity
m=28.152;
C=500;
   [t,y]=ode45(@(t,y) Lin(t,y,C,w,F0,m,L,V),tspan,y0);

function [f]=Linear12(t,y,C,F0,m,L,V)
%% moving load

 p1= F0*sqrt(2/m*L)*sin((pi*V*t)/L).*heaviside(L/V-t);
%%
f= zeros(2,1);

%%  for beam with linear absorber

f(1)=y(2);
f(2)= -50^2*y(1)-C*y(2)+p1;


end

Answer 1

[Vaibhav]

Hi Rajni

I understand that you would like to implement the moving load using the Heaviside function in your differential equation.

Ensure the function name inside the ode45 call matches the actual function definition. In your original code, you called Lin inside ode45, but your function was defined as Linear12. I have corrected this to use Linear12 in both places. Your usage of the Heaviside function to model the moving load in in the correct direction. The expression heaviside(L/V - t) effectively turns on the force as the load starts affecting the system, based on the velocity of the load and the length of the system it's moving over.

Here it the code for your reference:

clc;
clear all;

% Time span
tspan = [0:0.1:10];
y0 = [0; 0];

% Parameters
F0 = 9.8;  % Magnitude of moving load
L = 4;     % Length
V = 0.1;   % Velocity
m = 28.152;
C = 500;

% Solve the ODE
[t,y] = ode45(@(t,y) Linear12(t,y,C,F0,m,L,V), tspan, y0);

% Plot the solution
plot(t, y(:,1));
xlabel('Time');
ylabel('Displacement');
title('Displacement over Time');

function [f] = Linear12(t,y,C,F0,m,L,V)
    % Moving load
    p1 = F0 * sqrt(2/(m*L)) * sin((pi*V*t)/L) .* heaviside(L/V - t);

    % Initialize the derivative vector
    f = zeros(2,1);

    % Differential equations for the system
    f(1) = y(2);
    f(2) = -50^2 * y(1) - C * y(2) + p1;
end

Hope it helps!