Furnace heaters can make a lot of noise. They are connected to ductwork that leads to nearly every room in your house, so any sounds they produce are often amplified. Vibration, however, indicates not only noise but also some type of motion that hints at a more serious problem with the system. Inspect several components to determine what may be causing the vibration and how you can fix it.
The ductwork itself may be responsible for the noise and movement you are noticing. Ductwork that has come loose from its bracketing or has not been fitted properly into vent openings in the walls or floors can create vibration. The furnace blows the air into the ducts, the duct tubing vibrates in response and the loose fittings amplify the effect, reproducing the shaking throughout the house.
Furnace mounting refers to how the furnace and its components are attached together. 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. If your furnace is located against a wall, this vibration can be carried throughout your house. If you can find the component that's shaking, you should be able to tighten the bolts and fix the problem.
If ductwork isn't creating the problem, it may be the fan itself, which can shake itself loose and start spinning with a slightly crooked angle, creating vibration. The fan motor can start to run harder as it ages, eventually creating vibration with the same effect. Because the fan system is so closely connected with the ductwork, you may notice fan problems more than other noises your furnace makes.
Clogs and Pressure Issues
For some fuel-based furnaces like oil and gas systems, the problem may be a clog or pressure-related issue in the fuel lines. Gas or oil may not be able to make it to the burners properly. The burners themselves may be faulty or clogged and start shuddering as they attempt to work properly. This cause of vibration is one of the most serious, because it's a sign of potential combustion problems and fire hazards.