Generalized Frequency Response Functions for Systems with Time-Varying Coefficients

An extension of the concept of frequency response is introduced which can be applied to systems described by differential equations whose coefficients vary periodically or almost periodically with time. Such systems are not accessible to traditional frequency response function methods because while the governing equations may be linear in the time domain they are non-linear in frequency. The basic theory of the technique is introduced and results are obtained for a wide range of systems. Time domain solutions are also deduced to complement the spectral development. Numerical results are calculated for an illustrative case that deals with a photochemical problem driven by a solar daylight cycle.