I need help solving this Fourier series using Matlab.

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Wyatt Steiner 2022-10-1

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回答： Walter Roberson 2022-10-1

So I am in a composites class, and for the final project we are to desing a composite plate and graph the deformations as a result of the internal stresses and an applied force. I am stuck on getting the Fourier coeffieicnts as part of finding the displacements. I have an expression for teh Fourier coefficient of the w (z axis) displacment fourier series, but I cannot figure out how to input the x and y components of it. Also, is the Fourier series coefficient supposed to change with position? I am not very well versed in the Fourier stuff.

Below is the code for my project, this is the part I am stuck on, if you need more of the code please don't hesitate to reach out.

I have the stresses and strains further up in the code already caclulated.

As a side question, how wold you plot the deformation, I have only ever done a 2-d plot.

Also I have the 2021a verison on my home computer but I am away at my parents and my laptop has the 2016a version, I am not sure if that makes a difference.

Width = 0.1; %m
Length = 0.275; %m
syms x y
sym Amn(x,y)
for m = 1:3
    for n = 1:3
        w = sin(m*pi*x/Length)*sin(n*pi*y/Width);
Amn = 4/(Width*Length)*int(w*sin(m*pi*x/Length),x,0,Length)*int(w*sin(n*pi*y/Width),y,0,Width)
    end 
end

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Wyatt Steiner 2022-10-1

I can provide pictures of the equation in the textbok if necessary.

Torsten 2022-10-1

Yes, it would help since your description is too weird to understand the problem.

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Answer 1

Walter Roberson 2022-10-1

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Any one series of fourier coefficients would be valid for a section to be approximated as being a consistent function of time.

When you are working with a composite plate, the change in composition implies that the signal propagation function itself changes in space, and so should have different coefficients.

Imagine for example that you have a sound source at the center and up to distance D from the center sound travels at S1 m/s, and that then there is a different material and sound travels at S2 m/s out to distance 2D. You might initially think that the situation should be modeled as a single function of t with a change at D/S1 seconds (time for sound to travel to new material.) And maybe that would work for an impulse, a single entity emitted once and being studied over time. But with a repeated sound source, a sound emitted after (say) 10 seconds is still going to travel at S1 from the center to D: the properties of the system as a whole do not change with time. You have to model it by space as well, with a different function at different locations.