To illustrate, I have a thermal problem with nonlinear parameters that depend on temperature, for example, dependecne of specific heat Cp(T) on temperature.
and the problem will be solved with Finite Element Method the generated solution will be in Time domain, I want to know if it is possible to generate a solution in the frequency domain by using the Fast Fourier Transform, and what are the effect of the amplitude and the phase angle,
Another point can I neglect the phase angle upon doing the Fast Fourier Transform
Dear Ahmad, in the book Reza Malek-Madani, Advanced Engineering Mathematics, vol.2, Chapter 14, there is a discussion on how applying Fourier Series on a non-linear PDE equation for string with variables time and space. You can try using temperature as time. I think FFT use is possible for your problem. Gianluca
You can apply FFT to numerically find a solution of an intital-boundary value problem of a nonlinear PDE, lots of examples along with matlab code can be found here https://people.maths.ox.ac.uk/trefethen/spectral.html .
You can do non-linear calculations and use FFT afterwards to switch important parameters into frequency domain. Theoretically it works independently of system complexity, experimental modal analysis is a good example. If You want to switch to frequency domain before non-linear calculations, it is necessary to check feasibility firstly and spend time developing an appropriate model, but it would be still only an approximation. In my mind the best way is to do the non-linear stuff in time domain and FFT for important parameters afterwards.
Neglection of phase angle would drop information about phase, so it would be no more possible to switch back to time domain correctly without it. But it is up to You, when You don't need it, You can drop it. When using FFT, You automatically obtain the phase angle as complex numbers in the output.
- Badges
- Science method