Recap;
This occurs when no water is being used.
The only thing that seems to make it stop closing the valve on the water heater inlet.
The heater is approximately two years old and this did not occur prior to renovations.
Turning off power to heated has no effect.
There is no recirculation pumps or "instant hot water devices" installed.

Are all of the pipes CPVC or or part copper and part CPVC?

There is no recirculation pump, is there a recirculation line? May sound like a strange question but that's the set up I have, where gravity and syphoning cause the recirculation.

At this point I would suggest that the vibration is in the water it self, not the pipes because closing the cold water valve on the heater is the only thing that will cause a change.

Suggest turning off main house valve to eliminate outside world. If vibration or pulsation is there with main valve closed the source has to be in the house.

After thought, do you have fridge with ice maker, or water dipenser, could something there be causing vibration.

The renovation is CPVC and original house is copper. I isolated most of the new plumbing, CPVC, but the vibration continued.

I'll have to check on the gravity and syphoning. Need to check what was installed and see if anything could cause that problem. This may be the answer

Closed the main house valve, pulsating still exists.

Closed the frig ice maker valve. Pulsating still there.

I turned off the cold water inlet valve to the water heater to revarify the pulsating stops. It stopped.

Would an expansion tank installed on the cold water inlet side of the water heater help?

Cold water input of heater is connected by a flex pipe to CPVC. Stop valve on the CPVC right? CPVC added to existing copper from main line into house right? I'm guessing water heater was relocated.

If it is indeed the vibration in the water, or water movement within the pipe, and not the pipes themselves, as suggest by it ceasing upon closing the heater input valve, we have eliminated the outside world and source must be in the house.

Please close valves at each fixtures, one at a time, and see if you can cause a change.

Your assumptions are correct except the water heater was not moved. The water heater is on a wall ajoining the new construction so the CPVC came to the water heater.

I'll start turning off valves and post the results when I finish.
Thanks

The first toilet I isolated seemed to solve the problem. I may have others but this seems to be the fix.

Thanks to all that helped.

Tell us more. You mean to say that a loose washer in a toilet cause all this?

My plan was to close each water valve a one at a time and see if it made a difference. When I closed the first toilet shut off valve the pulsating stopped. I kept the valve closed all night and then replaced the toilet fill valve and opened the shutoff valve this morning. So far I haven't heard or seen any pulsating. Last night was the first night in about 3 weeks I haven't heard the noise.

Flushing the hot water may have helped some.

I still may have similar issues but following the suggestions above I hope I'll be able trace them down.

Kudos and congratulations on a great job of analyzing and tracking down a difficult problem. Give yourself a pat on the back and two weeks vacation.
I love it when a asker. Especially a female, can go in and do a job just as good as a licensed plumber. GOOD JOB! Tom