Types of Vibration

• Free Vibrations: Elastic vibrations in which there are no friction and external forces after the initial release of the body.
• Forced Vibrations: When a repeated force continuously acts on a system, the vibrations are said to be forced vibration. The frequency of the vibrations is that of the applied force and is independent of their own natural frequency of vibrations.
• Damped Vibrations: When the energy of a vibrating system is gradually dissipated by friction and other resistances.
• Un-damped Vibrations (Hypothetical): When there is no friction or resistance present in system to contract vibration.
• Longitudinal Vibrations: If the shaft is elongated and shortened so that the same moves up and down resulting in tensile and compressive stresses in the shaft.
• Harmonic vibration: Vibration in which the motion is a sinsuoidal function of time.
• Fundamental vibration: Harmonic component of a vibration with the lowest frequency.
• Steady state vibration: When the particles of the body move in steady state condition or continuing period vibration.
• Transient vibration: Vibratory motion of a system other than the steady state.
• Transverse Vibrations: When the shaft is bent alternately and tensile and compressive stresses due to bending result.
• Torsional Vibrations : When the shaft is twisted and untwisted alternately and torsional shear stresses are induced.

Free Longitudinal Vibrations

Damped Longitudinal Vibration

Dunkerley’s Method

Let W1, W2, W3, … be the concentrated loads on the shaft due to masses m₁, m₂, m₃, … and δ₁, δ₂, δ₃ … the static deflections of this shaft under each load when that load acts alone on the shaft. Let the shaft carry a uniformly distributed mass of m per unit length over its whole span and the static deflection at mid-span due to the load of this mass be δ_s. Also, let

fn = Frequency of transverse vibration of the whole system

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