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.
Furnace blower motor vibration.
Called starving the suction of the blower.
Pipe brackets burner parts cold air returns access panels into the burner chamber and blower chamber or even the plenum itself could be loose.
Check the fan and motor for signs of dust or debris build up or any other kind of obstruction and clear it away to see if the problem has been solved.
Your initial assumption about load on blower due to new filter is valid.
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.
The answer is a number of different bolt systems.
When one set of bolts begins to come loose it starts to vibrate as the furnace works.
In search of a solution to a vibrating furnace.
Are the fins of the blower wheel filled with dirt.
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.
Sometimes if enough dirt gets in the squirrel cage it will cause the wheel to vibrate when running.
It is not the ho.
If your furnace is located against a wall this vibration can be carried throughout your house.
Blower motor mount squirrel cage plenum filter too small or the furnace itself vibrating.
Furnace mounting refers to how the furnace and its components are attached together.
Loose access panels and framing also.
The circulation fan often is to blame especially if it is attached directly to the metal cabinet.
Unbalanced blower motor there could be something off balance within your blower causing the fan to make vibrating sounds when it spins.
If the furnace housing is vibrating i d suggest tightening the screws on the housing.