Modeling of Mechanical (Lumped Parameter) Elements

Viscous damping elementsViscous (Linear) Damper: is the mechanical dissipative element which relatesforce to velocity. Dampers or DASHPOTS are commonly assumed asMASSLESS, so that a force F at one end must be balanced by a force F D(reaction) acting on its other end. Due to the force applied at one end, the damperfollows a motion equal to the difference between its two end velocities (V=V 2 -V 1 ).For small values of V, a linear relationship appears so that the damping constant isdefined as:D = F/V [N-sec/m, lb-sec/in]A linear damper denotes a viscous shearmechanism for its action. A damperdissipates energy lost tothe surroundings (outside of system)or transferred to other systemsusually in the form of heat. Theenergy dissipated is given as:t2x2d= ∫xD= ∫ D1tE F dX F V dt1t2 t22Ed∫ Pvdt D∫V dttt= = > 0if D > 01 1In general, for small amplitudemotions about an equilibrium point,a local or linearized dampingcoefficient can be defined as:D = -∂F/∂V⏐ owhere the sub index o denotes a pointof equilibrium.MEEN 617 Notes: Handout 1 / © Luis San Andrés 2008 1.14