The Lagrangian formalism Application

The Frahm damper, also called a tuned mass damper (TMD), is a device used to attenuate the vibrations of a mechanical system. It consists of an oscillating damped mass which forms the auxilliary system that is attached to a particular location of a structure (the main system) to minimise its mechanical vibrations . The TMD's are very useful in engineering applications as they can prevent damage or outright structural failure. They are included, for instance, in floor systems, balconies, monumental staircases and pedestrian bridges. They are also frequently used in power transmission and cars. When designing a TMD, the key factor is the tuning of some of parameters to achieve the desired performance. We aim to study the optimization of the TMDs. For that purpose, the Lagrangian approach to deriving the equations of motion is used. We define the dynamical amplification factor that will be used to study the optimization of the TMD. Some commands of Maple software are used to achieve this goal.