Analytic Matrix Method for Frequency Response Techniques Applied to Nonlinear Dynamical Systems II: Large Amplitude Oscillations

This work is the second in a series of articles that deal with analytical solutions of nonlinear dynamical systems under oscillatory input that may exhibit harmonic frequencies. Frequency response techniques of nonlinear dynamical systems are usually analyzed with numerical methods, because in most cases analytical solutions such as the harmonic balance series solution turn out to be difficult, if not impossible, as they are based on an infinite series of trigonometric functions with harmonic frequencies. The key contribution of the analytic matrix methods reported in the present series of articles is to work with the invariant submanifold of the problem and to propose the solution as infinite power series of the oscillatory input; this procedure is a direct one that speeds up the computations compared to traditional series solution methods. The method reported in the first contribution of this series allows for the computation of the analytical solution only for small and medium amplitudes of the oscillatory input, because these series may diverge when large amplitudes are applied. Therefore, the analytic matrix method reported here, which is a reconfiguration of the method proposed in the first contribution in this series, allows the solving of problems in the regime of large-amplitude oscillations where the contributions of the high order harmonics affect the amplitudes of the low order harmonics, leading to amplitude- and frequency-dependent coefficients for the infinite series of trigonometric function expansion.

Process Intensification in Photocatalytic Decomposition of Formic Acid over a TiO2 Catalyst by Forced Periodic Modulation of Concentration, Temperature, Flowrate and Light Intensity

The effect of forced periodic modulation of several input parameters on the rate of photocatalytic decomposition of formic acid over a TiO2 thin film catalyst has been investigated in a continuously stirred tank reactor. The kinetic model was adopted based on the literature and it includes acid adsorption, desorption steps, the formation of photocatalytic active sites and decomposition of the adsorbed species over the active titania sites. A reactor model was developed that describes mass balances of reactive species. The analysis of the reactor was performed with a computer-aided nonlinear frequency response method. Initially, the effect of amplitude and frequency of four input parameters (flowrate, acid concentration, temperature and light intensity) were studied. All single inputs provided only a minor improvement, which did not exceed 4%. However, a modulation of two input parameters, inlet flowrate and the acid molar fraction, considerably improved the acid conversion from 80 to 96%. This is equivalent to a factor of two increase in residence time at steady-state operation at the same temperature and acid concentration.