# Mechanical Engineering Extended Project: Fourier Series Ideas?

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In summary, the speaker is a 17-year-old working on an extended project on the Fourier Series and is seeking suggestions for types of waves to study that relate to Mechanical Engineering. They mention considering sound waves and waves through a material, but are concerned about complicating factors such as dampening. Another person suggests studying resonances of structures and using an accelerometer and spectrum analyzer for analysis. The speaker expresses interest in this suggestion but notes they are focusing on the theoretical side of things.
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Hey so this is my first post, I am 17 years old and I am currently doing an extended project on the Fourier Series. I wanted to know if you guys have any ideas for what types of waves I could use.

I want to study Mechanical Engineering at uni and currently my idea is to investigate it with a sound wave, however I realize this focuses more on the Electrical Engineering side. I thought about waves through a material but then you would have to consider other factors such as dampening, which would complicate things a lot more for me.
So if you guys have any suggestions on what type of waves I could anaylse relating to Mechanical Engineering, I'd appreciate it.

Thanks

How about resonances of structures? There's damping involved in that too. But you can pick materials and designs that make it negligible.

Last time I did something like this I just hooked an accelerometer to a spectrum analyzer and whacked the part with a big bolt I found lying around. But you could do Fourier analysis too!

Unrest said:
How about resonances of structures? There's damping involved in that too. But you can pick materials and designs that make it negligible.

Last time I did something like this I just hooked an accelerometer to a spectrum analyzer and whacked the part with a big bolt I found lying around. But you could do Fourier analysis too!

Yeah thanks, Ill look into it. Unfortunately for me hitting stuff with a bolt is out of the question as I am focusing more on the theoretical side of things, but thanks for the suggestion!

## 1. What is a Fourier series?

A Fourier series is a mathematical tool used to represent a periodic function as a sum of sine and cosine functions. It is named after the French mathematician Joseph Fourier, who first introduced the concept in the early 19th century.

## 2. How is a Fourier series useful in mechanical engineering?

In mechanical engineering, Fourier series are commonly used for analyzing and designing oscillating systems, such as engines, turbines, and vibrating structures. They allow engineers to break down complex motion and forces into simpler components, making it easier to understand and predict the behavior of mechanical systems.

## 3. Can you give an example of a project idea involving Fourier series in mechanical engineering?

One possible project idea could be to investigate the use of Fourier series in optimizing the design of a car suspension system. By analyzing the periodic vibrations and forces experienced by a car while driving, a Fourier series could be used to find the most efficient spring and damper settings to improve ride comfort and handling.

## 4. Are there any limitations to using Fourier series in mechanical engineering?

While Fourier series can be a powerful tool for analyzing mechanical systems, they do have some limitations. They are most effective for systems with linear behavior and can struggle with non-periodic or non-linear systems. Additionally, they may not be suitable for systems with high frequencies or sharp discontinuities.

## 5. What are some possible future developments or applications of Fourier series in mechanical engineering?

As technology advances, Fourier series may continue to find new applications in mechanical engineering. Some potential developments could include using Fourier series in machine learning algorithms to optimize designs, or using them in conjunction with other mathematical tools to analyze more complex and dynamic systems.

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