A g-meter is much too coarse a device to get anything meaningful about vibration problems. I'd also be surprised if the accelerometers in an iphone give a good enough rate - although it would be interesting to have a go.
I'd suggest high rate electronic accelerometers, mounted appropriately, run into some form of data logger.
Running the data through an FFT analyser should then give you useful data about magnitudes and frequencies - and if you've mounted the sensors appropriately - the vibration mode also.
Almost certainly it is related to an engine speed, so you ideally also want to be logging engine speed although I have got away with doing that manually against the clock in a light aeroplane test programme where I was looking at pretty much what you're describing.
G