Effect of Damping Notes | EduRev

Theory of Machines (TOM)

Mechanical Engineering : Effect of Damping Notes | EduRev

The document Effect of Damping Notes | EduRev is a part of the Mechanical Engineering Course Theory of Machines (TOM).
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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
Effect of Damping Notes | EduRev

Damping force ox = (x = velocity)
= c·x
Where, c = coefficient of damping
Effect of Damping Notes | EduRev

The equilibrium equation of a damped spring-mass system is given as
Effect of Damping Notes | EduRev
It is a 2nd order differential equation.
Effect of Damping Notes | EduRev

Types of Damping Systems

  1. Overdamped System(ζ>1)
    No vibrations will be present in an over-damped system.
    Effect of Damping Notes | EduRevCritically Damped Systems(ζ = 1):
    ∴ No Vibrations
    Effect of Damping Notes | EduRevNote: 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, ωd = ωn(1 - ξ2)1/2
    Time period Td = 2π/wd (Second)
    Linear frequency, fn = 1/Td (Hz)
    Hence, Amplitude of under-Damped Vibrations is not constant and it decreases exponentially w.r.t. time.
    Effect of Damping Notes | EduRev
  3. Logarithmic Decrement (δ)
    δ = In (Decrement ratio)
    Effect of Damping Notes | EduRev
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