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COMMON DEFINITIONS
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APPLICABLE TO |
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SHOCK AND
VIBRATION |
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Solutions for Shock,
Vibration & Noise Control |
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Acceleration:
Acceleration is a vector quantity that specifies the time rate
of change of velocity. |
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Amplitude:
Amplitude is the maximum value of a repetitively oscillating
quantity. |
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Angular Frequency (Circular Frequency):
The angular frequency of a periodic quantity is the frequency
multiplied by 2π. The units are in radians per unit time. Or;
the angular frequency ω of a periodic vibration, in radians per unit
time, is the cyclic frequency multiplied by 2π; that is, ω = 2πf. |
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Attenuation:
Attenuation is the
opposite of
amplification and
is normally measured in
decibels. Attenuation is also defined as
a
decrease in energy per unit area of a wave occurring as the distance
from the source increases as a result of absorption. This is a more
precise description than is isolation of how a shock mount manages
the energy during the ‘roll-off’ of a shock event. |
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Applied Shock:
An applied shock is any excitation that, if applied to a mechanical
system, would produce mechanical shock. The excitation may be either
a force applied to the system or a displacement, velocity, or
acceleration shock pulse Imposed upon a particular point in the
system. |
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Band-Limited White Noise:
Band-limited white noise is a type of random vibration for which the
spectral density has a constant value over a specified frequency
range. |
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Circular
Frequency:
(See Angular Frequency) |
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Combined Spectrum:
A combined spectrum is a spectrum representing a superposition of a
discrete and a continuous spectrum. |
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Continuous Spectrum:
A continuous spectrum is a spectrum whose components are
continuously distributed over a frequency region. |
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Cycle:
A cycle is the complete sequence of magnitudes of a periodic
vibration that occur during a complete period. |
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Cumulative Probability:
The cumulative probability P(F) represents the probability
that the magnitude F has a value between prescribed limits, as
follows: |
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where P(F) is
the probability that the magnitude F has a value between F1
and F2 and p(F) is the probability density
function. |
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Damped
Natural Frequency:
Damped natural frequency is the frequency of free vibration of a
system incorporating damping. |
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Damping:
Damping is the dissipation of energy in a system undergoing
displacements. The three (3) types of damping generally encountered
are: |
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Viscous |
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Coulomb (aka Friction) |
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Hysteresis. |
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Energy dissipated by damping is converted to heat and is
mechanically observed in the suspended system as motion control
particularly at resonance where peak responses are lowered in wave
form when compared to an un-damped system. |
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Dampening:
The act of getting something wet. There is no such term as
‘dampening’ used in shock, vibration or acoustical definitions. |
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Decouple:
Isolation of one mass or surface from another. |
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Deterministic Process:
A deterministic process is a mathematical model of a vibration
phenomenon for which the instantaneous magnitude of vibration can be
specified uniquely at any given instant of time. Its characteristics
may be described in terms of explicit mathematical functions that
define the vibration magnitude at any given instant of time, Complex
periodic vibration may be represented mathematically as a
deterministic process. |
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Discrete Spectrum:
A discrete spectrum is a spectrum whose components occur at a number
of discrete frequencies. It represents the degree of vibration
energy concentrated at the discrete harmonic frequency components of
periodic vibration. |
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Duration of Shock Pulse (Shock Half Period):
The duration of a shock pulse is he time required for the
acceleration of the pulse to rise from a stated value to a maximum
and return to the stated value. |
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Dynamic Excitation:
Dynamic excitation is an external vibratory force (or other type
input, such as acceleration, velocity, and displacement) applied to
a system that causes the system to respond. |
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Ensemble of Vibration Time-Histories:
An ensemble of vibration time-histories represents a set of
vibration time-history samples that indicate the nature of the
vibration during repetitions of a defined vibration process. |
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Ergodic Vibration:
Ergodic vibration is that type of stationary vibration for which
statistical averages, such as the mean and rms magnitudes, can be
obtained from one sample of an ensemble of time-histories
representative of a vibration process. A time-average magnitude
determined across an ergodic ensemble of vibration time-histories at
an arbitrary instant of time during the defined vibration process is
equal to the value determined from a single sample of the vibration
time-history ensemble. |
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Excitation:
Excitation is an external force, acceleration, displacement or other
input applied to a system that causes the system to respond in some
way.
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Excursion:
The excursion of a harmonic vibration is the double amplitude or
peak-to-peak magnitude of displacement. |
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Foundation (Support Structure):
A foundation is a structure to which 'he mechanical system is
attached. It may be fixed in space, or it may undergo a motion that
provides excitation for the supported system. |
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Fraction of Critical Damping (Damping Ratio):
The fraction of critical damping for a system with viscous damping
is the ratio of the actual damping coefficient, C, to the critical
damping coefficient. Co. The ratio [C/Co]; is usually expressed by
the symbol, z. |
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Free Vibration:
Free vibration of a system is vibration that occurs in the absence
of forced vibration. |
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Frequency:
For a function that is periodic in time. The frequency is the number
of repetitions that occur in a reference time period. The frequency
is the reciprocal of the period. The unit is the cycle per unit time
(CPT). The unit cycle per second is called 'Hertz' (Hz). |
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Frequency Spectrum:
The frequency spectrum of a vibratory quantity is a description of
its resolution into components, each of different frequency and
usually of different amplitude and phase. |
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Half Period:
(See Duration of Shock Pulse) |
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Harmonic:
A harmonic is a sinusoidal vibration having a frequency that is an
integral multiple of the frequency of a harmonic vibration to which
it is related. |
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Impact:
An impact is a-single collision of one body upon another that may be
either in motion or at rest |
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Impulse:
Impulse is the integral of a force over the time interval during
which the force is applied, |
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where the force F(t)
is time dependent and equal to zero before time t1
and after time t2. |
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Instantaneous
Magnitude:
The instantaneous magnitude of vibration or shock is the value
(positive or negative) of the time-history representing the
vibration or shock phenomenon at a given instant of time.
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Isolation:
Isolation is a reduction in the capacity of a system to respond to
an excitation. Isolation is attained by the use of resilient
support elements between the foundation and the mechanical system or
suspended/supported mass. |
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Jerk:
Jerk is a vector that specifies the time rate of change of the
acceleration with respect to a frame of reference. |
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Linear System:
A system is linear if for every element in the system the response
is proportional to the excitation. The concept of superposition is
applicable in a linear system. |
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Magnitude Probability
Density: A
magnitude probability density function is a mathematical
representation of the probability of occurrence per unit magnitude,
as follows: |
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where p(F) is
the probability density and P(F) is the probability of
occurrence. |
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Mean Magnitude:
The mean magnitude F of a vibratory quantity F(t) is the time
average of the quantity, as follows: |
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where T is the time duration over which the averaging has taken
place. |
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Multiple
Degree-of Freedom System (MDoF):
,A multiple degree-of freedom system is one for which two or more,
coordinates are required to define the position of the system at any
given instant. |
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Natural Frequency:
Natural frequency is the frequency of free vibration of a system
that does not contain damping. |
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Normal Probability
Distribution:
The standardized form of the normal (or Gaussian) probability
density, assuming a zero mean magnitude, is given by: |
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where σ is
the standard deviation or rms magnitude of the variable F and
–
∞
< F <
∞.
The normal probability distribution has been found to describe
suitably the statistical distribution of the instantaneous magnitude
of random vibration. |
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Octave:
An octave is a frequency interval such that the frequencies at the
beginning and end are in the ratio of 1:2. One octave up is a
doubling of the starting frequency. One octave down is a halving of
the initial frequency. |
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Oscillation:
Oscillation is the variation with time of the magnitude of a
quantity with respect to a specified reference, when the magnitude
is alternately greater and smaller than the reference.
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Peak-to-peak value:
The peak-to-peak value of a vibrating quantity is the algebraic
difference between the extremes of the
quantity. |
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Period:
The period of a periodic quantity is the smallest, increment of, the
independent variable for which the function repeats itself. The
period is the time to complete one cycle
of vibration. |
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Periodic Vibration:
A periodic vibration is an oscillation having a waveform that is
repeated at certain equal increments of the independent time
variable. |
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Phase
of a Periodic Vibration:
The phase of a periodic vibration is the fractional part of a period
through which the periodic vibration has advanced, measured from an
arbitrary reference. The phase angle Ф = ωtL,
where tL is the time lag or lead that exists
between the periodic vibration and the reference. |
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Power Spectral Density (PSD):
Power spectral density is the limiting mean-square value of a
variable per unit bandwidth. !t is the limit of the mean-square
value in a given rectangular bandwidth divided by the bandwidth, as
the bandwidth approaches zero. |
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Power Density:
The power density W(f) of random vibration is the mean-square
magnitude per unit bandwidth of the output of an ideal filter with
unity gain responding to the vibration, as follows: |
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where by convention
the bandwidth Δf is usually chosen to be 1 Hz. |
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Power
Density Spectrum:
Power Density Spectrum: A power density spectrum is a graphical
presentation of values of power density W(f) displayed as a
function of frequency. It represents the distribution of vibration
energy with frequency. |
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Probabilistic Process:
A probabilistic process is a mathematical model of a vibration
phenomenon for which the instantaneous magnitude of vibration cannot
be specified uniquely at any given instant of time. Its
characteristics must be described on a statistical basis in terms of
the probability that the vibration magnitude will exceed a specified
value at any given instant of time. Random vibration may be
represented mathematically as a probabilistic process. |
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Random Vibration:
Random Vibration: Random vibration is an oscillation having
instantaneous magnitudes that vary in an unpredictable manner and,
therefore, are not specified at any given instant of time. The
characteristics of random vibration are described in statistical
terms; specifically, random vibration is described by its spectral
density and the probability distribution of
its magnitude.
Wide-band random vibration is comprised of a continuous spectrum of
frequencies, whereas narrow-band random vibration has essentially a
single frequency component and is often referred to as random
sinusoidal vibration. |
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Rayleigh Probability
Distribution:
The standardized form of the Rayleigh probability density, assuming
a zero mean magnitude, is given by: |
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where σ is the standard deviation or rms "magnitude of the
variable F and 0 < F <
∞.
The Rayleigh probability distribution describes the statistical
distribution of the peak magnitude of narrow-band random vibration
for which the instantaneous magnitudes are distributed according to
the normal probability distribution. |
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Resonance:
Resonance of a system in forced vibration exists when any change in
the excitation frequency causes a decrease in the response of the
system. The response may be acceleration, velocity, displacement or
other system variable. |
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Resonant Frequency:
The resonant frequency is a frequency at which resonance exists for
a given variable. The resonant frequencies for acceleration,
velocity and displacement are not identical for systems containing
damping. |
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RMS Magnitude:
The rms magnitude Frms of a vibratory quantity F(t) having a zero
mean magnitude F, is given by |
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Self-Induced
(Self-Excited) Vibration:
The vibration of a mechanical system is self-induced if it results
from conversion, within the system, of non-vibratory excitation to
vibratory excitation. |
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Shock Absorber:
A shock absorber is a device which dissipates energy to modify the
response of a mechanical system to applied shock. (See Attenuation)
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Shock Attenuator:
A shock attenuator is a resilient support that is designed to
mitigate inputs to a system from a given shock pulse, motion or
event. (See Attenuation; Shock Isolator). |
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Shock Half Period:
(See Duration of Shock Pulse). |
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Shock Pulse Duration;
The duration to of a shock pulse Is the time required for the
excitation quantity represented by the shock pulse to rise from and
decay to specified fractions of the maximum magnitude of the shock
pulse. |
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Shock Pulse Rise Time:
The shock pulse rise time tr is the interval of time required for
the leading edge of the pulse to rise from some specified small
fraction to some specified larger fraction of the maximum magnitude
of the shock pulse. |
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Simple Harmonic Vibration (Simple Harmonic Motion):
Simple harmonic vibration is a periodic vibration that is a
sinusoidal function of time. |
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Single Amplitude (SA):
The displacement measured from the nominal position of a vibrating
item to its maximum displacement from the nominal position. |
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Single
Degree-of-Freedom System (SDoF):
A single degree-of
freedom system is one for which only one coordinate is
required to define completely the configuration of the system at any
instant. |
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Sinusoidal Motion:
A sinusoidal motion is a motion such that the displacement is a
sinusoidal function of time. |
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Stationary Vibration:
Stationary vibration is that type of vibration for which properties,
such as the mean magnitude, the rms magnitude, the spectral density,
and the probability distribution of the random vibration magnitude,
are independent of time. The condition of stationary for random
vibration is analogous to the steady-state condition for periodic
vibration. |
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Steady-state Vibration:
Steady-state vibration exists in a system if the velocity of each
element is a continuing periodic quantity. Also that
type of periodic vibration for which properties, such as the mean
and rms magnitudes, are independent of time. |
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Stiffness:
Stiffness is the ratio of force (or torque) to the corresponding
change in translational (or rotational) deflection of an elastic
element. |
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Sub-harmonic:
A sub-harmonic is a sinusoidal vibration having a frequency that is
an integral sub-multiple of the fundamental frequency of a harmonic
vibration to which it is related. |
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Support Structure:
(See Foundation). |
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Sustained Acceleration:
Sustained acceleration is a constant level of acceleration, usually
measured as a multiple of gravitational acceleration, that is
maintained for an extended length of time. |
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Transient Vibration:
Transient vibration is temporarily sustained vibration of a
mechanical system. It may consist of forced or free vibration or
both. |
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Transmissibility (‘T’ or ‘Q’(antq.)):
Transmissibility is the non-dimensional ratio of the response
amplitude of a system in steady-state forced vibration to the
excitation amplitude or simply stated as output divided by input.
The ratio may be one of forces, displacements, velocities, or
accelerations. Transmissibility at resonance is usually the maximum
‘T’ value in any suspension system. |
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Velocity:
Velocity is a vector quantity that specifies the time rate of change
of displacement with respect to a reference frame. |
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Velocity Shock:
Velocity shock is a shock motion characterized by an instantaneous
velocity change of the support structure. |
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Vibration Isolator:
A vibration isolator is a resilient support that tends to isolate a
system from steady-state excitations. |
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Viscous Damping:
Viscous damping is the dissipation of energy that occurs when a
vibrating system is resisted by a force that has a magnitude
proportional to the magnitude of the velocity of the system and acts
in a direction opposite to the velocity direction. |
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Vibration Response:
The vibration response of a mechanical system is the motion (or
other type output, such as acceleration and velocity) resulting from
dynamic excitation under specified conditions. |
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White Noise:
White noise is a type of random vibration for which the spectral
density has a constant value for all frequencies from zero to
infinity. |
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