A linear Sagnac interferometer works in regard to producing fringe shifts when accelerated. This can easily be understood by considering the Doppler effect and the retardation that the light does along the linear path of the light. The Doppler effects do not cancel out since there is a delay in mixing source and destination signals.
Redo the experiments with light frequency changing over time, for example as a ramp function, to get an effect on speed and not only acceleration. If there is a linear Sagnac effect even in this case the beat frequency would differ at different speeds. Do this experiment on a rotating frame as well. The common understanding is that the rotating frame would be affected by speed and the linear interferometer would not. Agree? Mail this suggestion to Wang if you have his address. David David Jonsson, Sweden, phone callto:+46703000370