  In this paper it is shown that the Blazhko effect may result from a
near-resonant type of multi-mode pulsation, where two (or sometimes more)
periodic oscillations with slightly different frequencies gradually slip in
phase, producing a beat frequency type of modulation. Typically one of these
oscillations is strongly non-sinusoidal. Two oscillations are sufficient for
the standard Blazhko effect; additional oscillations are needed to explain
multi-frequency modulation. Previous work on this hypothesis by Arthur N. Cox
and others is extended in this paper by developing a simple (non-hydro) model
that can accurately reproduce several important features found in Kepler data
for RR Lyr, including the pulsation waveform, the upper and lower Blazhko
envelope functions and the motion, disappearance and reappearance of the bump
feature. The non-sinusoidal oscillation is probably generated by the
fundamental mode and the other oscillations are probably generated by nonradial
modes. This model provides an explanation for the strong asymmetry observed in
the side peak spectra of most RR Lyrae stars. The motion and disappearance of
the bump feature are shown to be an illusion, just an artifact of combining the
oscillations. V445 Lyr is presented as an example with dual modulation. The
mysterious double-maxima waveform observed for this star is explained,
providing additional strong evidence that this beating-modes hypothesis is
correct. Problems with other recent explanations of the Blazhko effect are
discussed in some detail.
