Dempning

Dempning, or damping in English, refers to processes that dissipate mechanical energy in a vibrating or moving system, reducing amplitude over time and converting energy into heat or other forms. Damping is a key property of structures, machines, and materials because it limits resonances, suppresses vibrations, and improves stability and control.

Damping arises from several mechanisms. Frictional damping converts energy through sliding or rolling friction. Viscous damping comes from a fluid or air resisting motion, often modeled as proportional to velocity. Structural or material damping results from internal friction within materials. Coulomb damping is a form of dry friction with constant force independent of velocity.

In linear second-order systems, damping is described by equation m x'' + c x' + k x = 0, where m is mass, c is damping coefficient, and k is stiffness. The natural frequency is ω_n = sqrt(k/m) and the damping ratio ζ = c / (2 sqrt(m k)). Behavior depends on ζ: underdamped (ζ<1) shows oscillations with exponential decay; critically damped (ζ=1) returns to equilibrium as quickly as possible without oscillating; overdamped (ζ>1) returns without oscillating but more slowly.

Applications include automobile suspensions and engines, where damping smooths motion; civil engineering against wind or earthquakes; vibration isolation for machinery; acoustic and electrical damping in circuits.

Damping is quantified by the damping coefficient c, damping ratio ζ, and quality factor Q = 1/(2ζ). Designers tailor damping with hydraulic or gas dampers, viscoelastic materials, tuned mass dampers, or air gaps. Excess damping reduces responsiveness; too little allows resonant amplification.