Installing an acoustic rubber pad under the furnace specially if it is sitting on concrete will damp the vibration you hear through the pipes although the blower fan and motor are the most obvious parts to check take a look at the complete unit.
Furnace blower motor vibration.
If the merv rating of the filter is too high this will starve the blower suction and cause any minor vibration in the blower motor wheel assembly to amplify.
Unbalanced blower motor there could be something off balance within your blower causing the fan to make vibrating sounds when it spins.
Are the fins of the blower wheel filled with dirt.
In search of a solution to a vibrating furnace.
Sometimes if enough dirt gets in the squirrel cage it will cause the wheel to vibrate when running.
If the furnace housing is vibrating i d suggest tightening the screws on the housing.
The circulation fan often is to blame especially if it is attached directly to the metal cabinet.
The answer is a number of different bolt systems.
Your initial assumption about load on blower due to new filter is valid.
Loose access panels and framing also.
Easy fix pull out the blower disconnect the motor and clean the squirrel cage with hot water in a utility sink or garden hose outside.
Loose parts are to blame for vibrating sounds from a furnace.
Called starving the suction of the blower.
Blower motor mount squirrel cage plenum filter too small or the furnace itself vibrating.
If your furnace is located against a wall this vibration can be carried throughout your house.
Furnace mounting refers to how the furnace and its components are attached together.
It is not the ho.
When one set of bolts begins to come loose it starts to vibrate as the furnace works.
Pipe brackets burner parts cold air returns access panels into the burner chamber and blower chamber or even the plenum itself could be loose.