The numerical solution cod for dynamics of Vibro-Impact system with impact condition

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HUST Student 2017-9-26

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https://ww2.mathworks.cn/matlabcentral/answers/358452-the-numerical-solution-cod-for-dynamics-of-vibro-impact-system-with-impact-condition

I am trying to solve the system of differential equations that describes the dynamics of Vibro-Impact system (with impact condition). Namely, dy/dt = x; dx/dt = (A cos(2*pi*F*t))/M; dz/dt = v; dv/dt = 0. Impact occurs at y-z>d+2*w-2*r and impact law, described by the velocities before v(+) and after v(-) an impact, is: v(+) = -m*v(-) +(m+1)*x.

Where y - absolute displacement of the outer structure; x - absolute velocity of the outer structure; z - absolute displacement of the ball; v - absolute velocity of the ball.

A, F, M, d, w, r, m are parameters.

Following Euler's scheme I tried to writ matlab cod, please help me frame the impact condition:

    %Code to solve Dynamics of Impact Pair
clear; clc
    %Parameters
A=0.01; %N
F=2; %Hz
M=124.5; %g
d=42;%mm
w=6;%mm
r=5;%mm
m=1;
    %Inputs
h=0.001;
t_final=55;
N=t_final/h;
    %Initial condition
t(1)=50;
y(1)=-A/(M*(2*pi*F)^2); %abs. displacement of the outer structure M
x(1)=0; %abs. velocity of the outer structure M
z(1)=0; %abs. displacement of the ball m 
v(1)=0; %abs. velocity of the ball m
    %update loop
for i=1:N
    t(i+1)=t(i)+h;
    y(i+1)=y(i)+h*(x(i));
    x(i+1)=x(i)+h*(A*cos(2*pi*F*t(i))/M);
    z(i+1)=z(i)+h*(v(i));
    v(i+1)=v(i);
    if abs(y(i+1)-z(i+1))>(d+2*w-2*r)/2, 
        v(i+1)=-m*v(i)+(m+1)*x(i+1);
        switch k (i)= t(i+1)
            k(i+1)=k(i)+h
    end
end
figure(1); clf(1)
plot(t,z)
xlabel ('Time (s)')
ylabel ('abs. displacement M')