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 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 ...
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.
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