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Solution to the steady state load-deflection equation.

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The steady state deflection is given by:

y''''+c^4*y=f(x)

calculate and plot the deflection for a load:

f = 1 for |x|<10, f=0 everywhere else.

using Fourier transform.

Plot the deflection for various values of c.

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Solution Summary

the solution utilizes Fourier transform and complex-variables integration to solve this fourth order non-homogeneous differential equation. The solution contains 9 pages of derivations and graphs.

Solution Preview

Please see the attached file.

The equation is:

The Fourier transform of the equation is:

The function is a simple "boxcar" function.

A boxcar function of the form

And:

Thus:

We need to evaluate:

The integrand has 5 simple poles.
One is obviously k=0 and the others are the roots of the equation:

The roots ...

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