# Frequency Response of a Damped Car-Suspension System

• Engineer47
In summary, the conversation discusses a half-car representation with equations of motion and constants for each component. The individual is unsure of how to find the frequency response in regards to a pothole affecting the system. The use of ODE45 in MATLAB and solving for undamped modes is suggested.
Engineer47
Homework Statement
How can I solve for the frequency response of a damped system when I have the full matrices for M, C, and K when a car suspension hits a pot-hole of a certain height?
Relevant Equations
The equation I have now to work with it M(U(double dot)) which is a 4x4 matrix, times a 4x1 matrix, -[K]*[U] -[C][U(dot)] where M is the mass matrix, k is the spring matrix, and c is the damper matrix, all of the same dimensions as the M and U(double dot) matrix above. I am trying to solve using eigenvalues or vectors I believe with modal superposition on Matlab!
The quarter car system is represented by the above picture and I currently have all of the equations of motion and constants for each spring, mass, damper, distance, and moment of inertia. How can I find the frequency response with this information and knowing both tires hit a pothole of height h at the same time? Thanks!

Helllo engineer, !

Looks more like a half-car representation to me
Even so, your wheels (front and back) won't hit the pothole simultaneously -- or is that outside the scope of your exercise ? And you draw an ##a## and a ##b## -- but do you have the moment of inertia around a wheel as a given ?

Anyway: what happens at a pothole is not described with a frequency response, but with a step response (or a pulse ersponse, but both: in the time domain, not the frequency domain.

Did you learn about Laplace transforms already ? If not, you have to solve the differential equation as is.

BvU said:
Helllo engineer, !

Looks more like a half-car representation to me
Even so, your wheels (front and back) won't hit the pothole simultaneously -- or is that outside the scope of your exercise ? And you draw an ##a## and a ##b## -- but do you have the moment of inertia around a wheel as a given ?

Anyway: what happens at a pothole is not described with a frequency response, but with a step response (or a pulse ersponse, but both: in the time domain, not the frequency domain.

Did you learn about Laplace transforms already ? If not, you have to solve the differential equation as is.
Hi! It technically is a half-car representation, and is to be treated as a rigid body. Furthermore, the moment of inertia of the wheels aren't given and can be neglected. I already have the equations of motion of each mass as well, I am just unsure on how to take those and see how a pothole affects them. And although it makes sense that the front and back wheels wouldn't hit the hole at the same time, I am to assume it is. And although I have learned about Laplace Transforms already, I think the problem requires some use of ODE45 in MATLAB and solve for undamped modes, finding the modal weights, and then summing to find the frequency response to all of the modes!

## 1. What is a damped car-suspension system?

A damped car-suspension system refers to the mechanism in a car that controls the movement and vibrations of the vehicle's wheels. It is responsible for providing a smooth and comfortable ride by absorbing the impact of bumps and uneven surfaces on the road.

## 2. What is frequency response in a car-suspension system?

Frequency response refers to the ability of a car-suspension system to handle different frequencies or vibrations. It measures the system's performance in responding to different levels of vibrations and how it affects the overall ride quality.

## 3. How is the frequency response of a damped car-suspension system measured?

The frequency response of a damped car-suspension system is typically measured using a frequency response function, which plots the system's response to different frequencies. This can be done through various methods such as road tests, laboratory experiments, or computer simulations.

## 4. What factors affect the frequency response of a damped car-suspension system?

The frequency response of a damped car-suspension system can be affected by various factors, including the design and components of the suspension system, the type of damping used, the weight and distribution of the vehicle, and the condition of the road surface.

## 5. How can the frequency response of a damped car-suspension system be improved?

The frequency response of a damped car-suspension system can be improved by adjusting the suspension design and components, using different types of damping, and optimizing the weight and distribution of the vehicle. Regular maintenance and ensuring the road surface is in good condition can also help improve the frequency response of the system.

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