As indicated in the: "wave propagation in structures: an FFT-based spectral analysis methodology", by James F. Doyle:
The spectral solution of 1D- elastic wave equation is as follow:
where is the wavenumber. C and D are the undetermined amplitudes at each frequency. Let the end of the bar at x = 0 be subjected to a force history F(t), that is, . E and A are the Elastic moduli and cross-sectional area respectively. The final solution is the inverse Fourier transform of the following expression: is the Fourier transform of the applied force F(t).
The numerical example for the above problem is provided as follow:
I wrote the following code in MatLab:
time_fcn = (0:n-1)/fs;
frequency = (0:n-1)*(fs/n);
nn=find(time_fcn>=0.0011 & time_fcn<=0.0013);
The result must be as follow:
However, I cannot get the same result as indicated in the abovementioned book. Can anybody tell me where is my mistake?
Thank you all,