Your circuit has many parts that are not needed.
Capacitor C2 passes AC but not DC so the second opamp amplifies vibrations with a gain of 23 times but does not amplify its DC input offset voltage.
The first opamp has a gain of only 2 so it is not needed and the gain of the second opamp can be doubled instead.
You are using a polarized capacitor for C2 which has AC across it that is wrong. If the values of R4 and R5 are increased then capacitor C2 can be a small film (non-polarized) capacitor.
C3 is SHORTING the output of the second opamp so it should be removed. If you want to cut high frequencies then add an RC filter at the output of the opamp, my R6 and C3 cut frequencies above 97Hz.
You do not need two rectifying opamps.
My added diode prevents the rectifier opamp from saturating as low as it can go.
Thanks AG for the circuit. Will breadboard your circuit today afternoon. I do not have a Film 1uF capcaitor. Can I take an Elko ?