# vibration

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## vibration,

in physics, commonly an oscillatory motion—a movement first in one direction and then back again in the opposite direction. It is exhibited, for example, by a swinging pendulum, by the prongs of a tuning fork that has been struck, or by the string of a musical instrument that has been plucked. Random vibrations are exhibited by the molecules in matter (see Brownian movementBrownian movement or motion,
zigzag, irregular motion exhibited by minute particles of matter when suspended in a fluid.
). Any simple vibration is described by three factors: its amplitude, or size; its frequency, or rate of oscillation; and the phase, or timing of the oscillations relative to some fixed time (see harmonic motionharmonic motion,
regular vibration in which the acceleration of the vibrating object is directly proportional to the displacement of the object from its equilibrium position but oppositely directed.
). Sound is produced by the vibrations of a body and is transmitted through material media in pressure waves (see wavewave,
in physics, the transfer of energy by the regular vibration, or oscillatory motion, either of some material medium or by the variation in magnitude of the field vectors of an electromagnetic field (see electromagnetic radiation).
) made up of alternate condensations (forcing of the molecules of the medium together) and rarefactions (pulling of the molecules of the medium away from one another). In sound the vibration is longitudinal, for the movement is to and fro along the direction in which the sound is traveling. When a sound wave of one frequency strikes a body that will vibrate naturally at the same frequency, the vibration of the body is called sympathetic vibration. A reinforcement of sound resulting from sympathetic vibration is called resonance. When the vibrations of a sound-producing body cause another body to vibrate in the same frequency, not normally its own, the vibration is known as forced vibration. Heat is commonly defined as the energy of molecules, part of which consists of the energy of their vibrational motion.

## Vibration

The term used to describe a continuing periodic change in the magnitude of a displacement with respect to a specified central reference. The periodic motion may range from the simple to-and-fro oscillations of a pendulum, through the more complicated vibrations of a steel plate when struck with a hammer, to the extremely complicated vibrations of large structures such as an automobile on a rough road. Vibrations are also experienced by atoms, molecules, and nuclei. See Pendulum

A mechanical system must possess the properties of mass and stiffness or their equivalents in order to be capable of self-supported free vibration. Stiffness implies that an alteration in the normal configuration of the system will result in a restoring force tending to return it to this configuration. Mass or inertia implies that the velocity imparted to the system in being restored to its normal configuration will cause it to overshoot this configuration. It is in consequence of the interplay of mass and stiffness that periodic vibrations in mechanical systems are possible.

Mechanical vibration is the term used to describe the continuing periodic motion of a solid body at any frequency. When the rate of vibration of the solid body ranges between 20 and 20,000 hertz (Hz), it may also be referred to as an acoustic vibration, for if these vibrations are transmitted to a human ear they will produce the sensation of sound. The vibration of such a solid body in contact with a fluid medium such as air or water induces the molecules of the medium to vibrate in a similar fashion and thereby transmit energy in the form of an acoustic wave. Finally, when such an acoustic wave impinges on a material body, it forces the latter into a similar acoustic vibration. In the case of the human ear it produces the sensation of sound. See Sound

Systems with one degree of freedom are those for which one space coordinate alone is sufficient to specify the system's displacement from its normal configuration. An idealized example known as a simple oscillator consists of a point mass m fastened to one end of a massless spring and constrained to move back and forth in a line about its undisturbed position (Fig. 1). Although no actual acoustic vibrator is identical with this idealized example, the actual behavior of many vibrating systems when vibrating at low frequencies is similar and may be specified by giving values of a single space coordinate.

Simple oscillator

When the restoring force of the spring of a simple oscillator on its mass is directly proportional to the displacement of the latter from its normal position, the system vibrates in a sinusoidal manner called simple harmonic motion. This motion is identical with the projection of uniform circular motion on a diameter of a circle. See Harmonic motion

When two simple vibrating systems are interconnected by a flexible connection, the combined system has two degrees of freedom (Fig. 2). Such a system has two normal modes of vibration of two frequencies. Both of these frequencies differ from the respective natural frequencies of the individual uncoupled oscillators.

Simple oscillator with two degrees of freedom

A vibrating system is said to have several degrees of freedom if many space coordinates are required to describe its motion. One example is n masses m1, m2, …, mn constrained to move in a line and interconnected by (n - 1) coupling springs with additional terminal springs leading from m1 and mn to rigid supports. This system has n normal modes of vibration, each of a distinct frequency. See Damping

## Vibration

mechanical oscillations. In engineering (machines, mechanisms, installations, structures, and so on), both useful and harmful vibration exist.

Useful vibration is caused intentionally by vibrators and is used in construction, road-building, and other machines and for performing various technical operations.

A distinction is made among various types of excitation of vibration. In dynamic, or force, excitation, external oscillating forces or force moments that are independent of the state of the system being vibrated are applied to one or more inertial elements of the system. In kinematic excitation, oscillations that are independent of the state of the system are transmitted from without to one or more points of the system. In parametric excitation, the vibration of the system is excited by changes in the value of one or more of its parameters—for example, the stiffness factor, the moment of inertia, or the resistance coefficient—that are independent of the state of the system. In self-excitation of oscillations, or natural vibrations, vibration is maintained because of the absorption of a portion of the energy from a constant source. In the majority of vibration devices, the first two principles of vibration excitation are used. Harmful vibration may be stimulated by each of the above means. Mixed excitation of vibration—for example, a combination of kinematically induced oscillations and natural vibrations—also occurs.

Harmful vibration, which arises during the movement of means of transportation and in the operation of motors, turbines, and other machines, sometimes leads to disruption of work schedules and even to destruction of apparatus. Various shielding methods are used to suppress harmful vibration and to minimize its effect.

The effect of vibration on the organism varies depending on whether the whole body is involved (general vibration) or part of it (local vibration). It arises during the operation of trains or airplanes, during work with pneumatic drills and other mechanisms, and during the launch and reentry of spacecraft. Depending on the frequency, intensity, and duration of vibration, its effect may be limited to a sensation of shaking (pallesthesia), or it may lead to changes in the nervous, cardiovascular, and support and motor systems. The biological effect of vibration depends on its frequency: frequencies up to 15 hertz (Hz) cause disturbance of the body and organs and reaction of the vestibular apparatus; frequencies up to 25 Hz are still perceived as separate jolts and cause osteoarticular changes; frequencies from 50 to 250 Hz affect the nervous system and cause vascular reactions (spasms) and vibration sickness; at higher ultrasonic frequencies, mechanical energy is transformed into thermal energy, and bactericidal and cavitation effects of vibration are observed.

### REFERENCE

Andreeva-Galanina, E. Ts., E. A. Drogichina, and V. G. Artamonova. Vibratsionnaia bolezn’. Leningrad, 1961.

## vibration

[vī′brā·shən]
(mechanics)
A continuing periodic change in a displacement with respect to a fixed reference.
(physical chemistry)
Oscillation of atoms about their equilibrium positions within a molecular system.

## Vibration

The term used to describe a continuing periodic change in the magnitude of a displacement with respect to a specified central reference. The periodic motion may range from the simple to-and-fro oscillations of a pendulum, through the more complicated vibrations of a steel plate when struck with a hammer, to the extremely complicated vibrations of large structures such as an automobile on a rough road. Vibrations are also experienced by atoms, molecules, and nuclei.

A mechanical system must possess the properties of mass and stiffness or their equivalents in order to be capable of self-supported free vibration. Stiffness implies that an alteration in the normal configuration of the system will result in a restoring force tending to return it to this configuration. Mass or inertia implies that the velocity imparted to the system in being restored to its normal configuration will cause it to overshoot this configuration. It is in consequence of the interplay of mass and stiffness that periodic vibrations in mechanical systems are possible.

Mechanical vibration is the term used to describe the continuing periodic motion of a solid body at any frequency. When the rate of vibration of the solid body ranges between 20 and 20,000 hertz (Hz), it may also be referred to as an acoustic vibration, for if these vibrations are transmitted to a human ear they will produce the sensation of sound. The vibration of such a solid body in contact with a fluid medium such as air or water induces the molecules of the medium to vibrate in a similar fashion and thereby transmit energy in the form of an acoustic wave. Finally, when such an acoustic wave impinges on a material body, it forces the latter into a similar acoustic vibration. In the case of the human ear it produces the sensation of sound. See Mechanical vibration

Systems with one degree of freedom are those for which one space coordinate alone is sufficient to specify the system's displacement from its normal configuration. An idealized example known as a simple oscillator consists of a point mass m fastened to one end of a massless spring and constrained to move back and forth in a line about its undisturbed position (Fig. 1). Although no actual acoustic vibrator is identical with this idealized example, the actual behavior of many vibrating systems when vibrating at low frequencies is similar and may be specified by giving values of a single space coordinate.

When the restoring force of the spring of a simple oscillator on its mass is directly proportional to the displacement of the latter from its normal position, the system vibrates in a sinusoidal manner called simple harmonic motion. This motion is identical with the projection of uniform circular motion on a diameter of a circle.

When two simple vibrating systems are interconnected by a flexible connection, the combined system has two degrees of freedom (Fig. 2). Such a system has two normal modes of vibration of two frequencies. Both of these frequencies differ from the respective natural frequencies of the individual uncoupled oscillators.

A vibrating system is said to have several degrees of freedom if many space coordinates are required to describe its motion. One example is n masses m1, m2, …, mn constrained to move in a line and interconnected by (n - 1) coupling springs with additional terminal springs leading from m1 and mn to rigid supports. This system has n normal modes of vibration, each of a distinct frequency.

## vibration

As applied to concrete, see concrete vibration.

## vibration

Physics
a. a periodic motion about an equilibrium position, such as the regular displacement of air in the propagation of sound
b. a single cycle of such a motion
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