Can the vibrational energy of a engine be used to increase efficiency? In whole mechanics, we never talk about wasted vibrational energy!
As we see in our daily life, a lot of energy is wasted as vibrational energy in every engine, for example as we fire our car's engine, it starts vibrating.
Use of this energy would increase the efficiency of engine. As we see that a big part of mechanical energy is wasted in Vibrational energy.
And the most efficient engine yet, is only approx. 10% efficient which is quite less.
Can Vibrational energy be used to get useful work so as to increase engine's efficiency??? If yes then how??
 A: The amount of energy lost to vibration in a car engine is typically very small. You can see this easily because the vibration (and the energy associated with it) is dissipated in the engine mounts, and if any significant amount of energy were being dissipated the engine mounts would get hot, which they don't. Most of the inefficiency is because the thermodynamic cycle used by a car engine isn't very efficient.
There are cases where vibration is used to do work. A pneumatic drill is an obvious example.
A: Physics allows four ways to transfer energy from any system (such as an engine). These are work,heat,matter,and radiation. 
Energy is lost in any of these forms. Normally when we talk of work from an engine we talk of piston work---the captured part.  Wasted work (boundary work done by the vibrating engine on the air, engine mounts, etc.) is the energy lost as work.  This is on the same footing as energy lost as heat via the cooling system, energy lost as thermal radiation (photons from the hot engine), and energy lost with matter in the exhaust. 
The fraction of this energy that can be actually converted to work (if we put piezoelectric vibration devices for example) is called its exergy. In most cases either the energy is small and/or its exergy (the redeemable fraction of that energy) is even smaller.  In the case of vibration the energy is very small as others have mentioned above. 
Biggest inefficiency in combustion engines is due to the irreversible destruction of exergy of the fuel (energy in matter) when it is converted to combustion products. After this, the energy in the exhaust (again energy in matter) has biggest exergy which is usually not captured in automotive engines but utilized in power generation gas turbine engines using a steam cycle.  Then comes the exergy in lost heat transfer (cooling in cylinder walls etc).  Some attempts are being made to capture this exergy using thermoelectrics. But that is a topic for another discussion.  Vibration and radiation emitted from engines are typically very small.
A: I can't answer your question specifically.  But I suspect between the continuous combustion of 4 to 8 cylinders and all the moving parts of the typical internal combustion engine, if one could expediently redirect that vibrating energy away from the motor, one could greatly improve the engine's trueness of operation.  Which should provide far greater benefits than attempting to harness and use the energy generated by the vibrations.
Improved vibration management can lead to greatly improved efficiencies.  Thereby lowering friction, heat, wasted energy, etc. In so doing, I suspect one could achieve excellent improved efficiency of operation that translates into reduced fuel consumption, reduced heat, longer Mean-Time-Between-Failure rates, and overall improved longevity of the engine and all its parts.
