Vibration

A vibrating structure has four basic properties: mass, stiffness, damping, and displacement. Mechanical vibration is the oscillation of the mass around a position of equilibrium. The nature of oscillation is determined not only by the mass but also by the stiffness and damping forces inherent to the structure.

		m = mass
	k = stiffness
	c = damping
	x = displacement

In theory, the mass can be an infinitesimally small particle, such as a lumped mass, and damping can be absent. In reality, the mass of a mechanical or physical structure has weight and spatial dimension, and damping is always a factor.

Mechanical vibrations results when the structure is perturbed from its equilibrium point by applying either an impulse or periodic excitation.

An impulse excitation produces a free vibration of the structure, which vibrates at one or more of the natural (resonance) frequencies of the structure and generates a response of a given magnitude.

A periodic excitation produces a forced vibration of the structure, which vibrates at the frequency of the periodic excitation.

When damping is present in either the free or forced vibration, the motion of the structure eventually declines to zero due to the dissipation of energy.

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