The steady state deflection is given by:
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.© BrainMass Inc. brainmass.com February 4, 2021, 6:39 pm ad1c9bdddf
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
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 ...
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.