What is the unit for power spectrum of acceleration signals in log scale
The typical practice with decibels is to append the unit.  Unfortunately, it's informal, so you'll see things like "dBm" in RF circuits which refers to "dB with a reference of 1mW", not "dB with a reference of 1 meter".

you could:


Put a note in your graph that $0\mathrm{dB} = \mathrm{1 m/s^2}$
Use "dBg" (and use 1g as your reference)
Just keep the y-axis as the log of acceleration squared (and yes, $\mathrm{m^2/s^4}$ is awkward, but it's the correct unit).