How to convert the input bump's height to force exerted by that bump?

Dear fellows, I am working on mass damper system in simulink. I have modelled the simple mass damper equation i.e. F=MXdd+CXd+KX.

In the given equation "M" is no doubt the mass of the load. Looking at the picture provided, its 100kg.

Now I want to calculate the force i.e. "F", that will be the input to the system. For that I have created a simple sinusoidal form, considering it as the bump input height. But I just cant input the sinusoidal form instead of the force, as it will be considered as force then. I want to convert this bump's height to Force that will go into the system.

So If I apply F=ma, a could be the double derivative of the height what will be the mass! Is it will be the mass of the load i.e. 100kg or it will be the mass of the damper or something else? (Considering a quater car model)

Answer 1

[MULI]

Hi Faheem,

To accurately simulate the effect of a road bump on your mass-damper system you can follow these steps:

• Modelling the Bump Height: Represent the bump height as a half sine function and you can compute the acceleration by taking the second derivative of this function.
• Force Calculation: Use the 100 kg load as the mass in your force (F=m∗a) calculation.
• Reasoning: The 100 kg load should be used in calculation since it is the part of the system directly impacted by the road bump, experiencing the acceleration from the bump's profile.

You can refer to the below link for simple quarter car ride model

https://www.mathworks.com/matlabcentral/fileexchange/72842-quarter_car

[Sam Chak]

Hi @MULI

A standard road bump shouldn't be modeled as a sinusoidal function because the profile of the bump isn't oscillating. Therefore, your proposed modeling is inaccurate.

The road bump should be modeled as a distribution-like or a squashed bell-shaped function.

x   = linspace(-2, 2, 1001);
y   = zeros(1, numel(x));
h   = exp(-1);      % desired height of the normalized road bump
H   = h/exp(-1);    % coefficient of the normalized road bump

for i = 1:numel(x)
    if abs(x(i)) < 1
        y(i) = H*exp(- 1/(1 - x(i)^2));
    else
        y(i) = 0;
    end 
end

plot(x, y, 'linewidth', 2, 'color', '#265EF5'), 
axis equal, grid on, grid minor
xlabel('Normalized distance, x')
ylabel('Bump height, y')
title('Profile of a Road Bump')

[MULI]

Will take this into consideration. Thank you!