Effect of Damping | Theory of Machines (TOM) - Mechanical Engineering PDF Download

Damped Systems

• Damping is an effect which causes a Reduction in the amplitude of an oscillation as a Result of energy being drained from the system to overcame frictional/other Resistive forces.
• These are the systems in which kinetic friction is zero. Technical Name of Kinetic friction in any Vibrations system is known as, Damping.

Damping in Any System

Damping force ox = (x = velocity)
= c·x
Where, c = coefficient of damping

The equilibrium equation of a damped spring-mass system is given as

It is a 2^nd order differential equation.

Types of Damping Systems

1. Overdamped System(ζ>1)
   No vibrations will be present in an over-damped system.
   Critically Damped Systems(ζ = 1):
   ∴ No Vibrations
   Note: Critical damping response is much faster than overdamping response i.e. in critically-damped systems, the body once displaced comes into its Equilibrium Position much faster than that in overdamped systems.
2. Under Damped Systems (ζ < 1)
   ∴ Damped frequency, ω_d = ω_n(1 - ξ²)^1/2
   Time period T_d = 2π/w_d (Second)
   Linear frequency, f_n = 1/T_d (Hz)
   Hence, Amplitude of under-Damped Vibrations is not constant and it decreases exponentially w.r.t. time.
   
3. Logarithmic Decrement (δ)
   δ = In (Decrement ratio)