Empirical Evidence for Incorrectness of Using Separation of Variables according to the Fourier Method in Oscillation Theory
The investigation concerns resonance properties. Separation of variables is the primary method of solving boundary value problems in oscillation theory. Separating variables means accepting the Fourier hypothesis that resonance at a given frequency involves all points on a given geometry oscillating at the same frequency (the resonant frequency). According to the Fourier hypothesis, the frequency response peaks of different sensors should lie on the same vertical line. Nastran and ANSYS use the Fourier hypothesis. We carried out frequency tests of items in the range of 10...100 Hz. Analysis of the test results showed (Fig. 2) that a resonance (at the same frequency) involved different points on the item geometry oscillating at different frequencies. We discovered frequency shifts measuring 1 Hz. Thus, the Fourier hypothesis does not work, and it is not correct to use separation of variables to solve the respective modal analysis problem.