ISO 2041:2009

INTERNATIONAL ISO
STANDARD 2041
Third edition
2009-08-01
Mechanical vibration, shock and
condition monitoring — Vocabulary
Vibrations et chocs mécaniques, et leur surveillance — Vocabulaire

Reference number
©
ISO 2009
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©  ISO 2009
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ii © ISO 2009 – All rights reserved

Contents Page
Foreword .iv
Introduction.v
Scope.1
1 General.1
2 Vibration.15
3 Mechanical shock.29
4 Transducers for shock and vibration measurement .31
5 Signal processing.34
6 Condition monitoring and diagnostics .40
Bibliography.43
Alphabetical index.44

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
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International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
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adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 2041 was prepared by Technical Committee ISO/TC 108, Mechanical vibration, shock and condition
monitoring.
This third edition cancels and replaces the second edition (ISO 2041:1990) which has been technically
revised. This revision reflects advances in technology and refinements in terms used in the previous version.
As such, it incorporates more precise definitions of some terms reflecting changes in accepted meaning. New
terms which were driven by changes in technology (primarily in the areas of signal processing, condition
monitoring and vibration and shock diagnostics and prognostics) and, in order to be a stand-alone standard,
terms from ISO 2041:1990 still in common usage are incorporated.

iv © ISO 2009 – All rights reserved

Introduction
Vocabulary is the most basic of subjects for standardization. Without an accepted standard for the definition of
terminology, the development of other technical standards in a technical area becomes a laborious and time-
consuming task that would ultimately result in the inefficient use of time and a high probability of
misinterpretation.
INTERNATIONAL STANDARD ISO 2041:2009(E)

Mechanical vibration, shock and condition monitoring —
Vocabulary
Scope
This International Standard defines terms and expressions unique to the areas of mechanical vibration, shock
and condition monitoring.
1 General
1.1
displacement
relative displacement
〈vibration and shock〉 time varying quantity that specifies the change in position of a point on a body with
respect to a reference frame
NOTE 1 The reference frame is usually a set of axes at a mean position or a position of rest. In general, a rotation
displacement vector, a translation displacement vector, or both can represent the displacement.
NOTE 2 A displacement is designated as relative displacement if it is measured with respect to a reference frame other
than the primary reference frame designated in a given case.
NOTE 3 Displacement can be:
— oscillatory, in which case simple harmonic components can be defined by the displacement amplitude (and
frequency), or
— random, in which case the root-mean-square (rms) displacement (and band-width and probability density distribution)
can be used to define the probability that the displacement will have values within any given range.
Displacements of short time duration are defined as transient displacements. Non-oscillatory displacements are defined as
sustained displacements, if of long duration, or as displacement pulses, if of short duration.
1.2
velocity
relative velocity
〈vibration and shock〉 rate of change of displacement
NOTE 1 In general, velocity is time-dependent.
NOTE 2 The reference frame is usually a set of axes at a mean position or a position of rest. In general, a rotation
velocity vector, a translation velocity vector, or both can represent the velocity.
NOTE 3 A velocity is designated as relative velocity if it is measured with respect to a reference frame other than the
primary reference frame designated in a given case. The relative velocity between two points is the vector difference
between the velocities of the two points.
NOTE 4 Velocity can be:
— oscillatory, in which case simple harmonic components can be defined by the velocity amplitude (and frequency), or
— random, in which case the root-mean-square (rms) velocity (and band-width and probability density distribution) can
be used to define the probability that the velocity will have values within any given range.
Velocities of short time duration are defined as transient velocities. Non-oscillatory velocities are defined as sustained
velocities, if of long duration.
1.3
acceleration
relative acceleration
〈vibration and shock〉 rate of change of velocity
NOTE 1 In general, acceleration is time-dependent.
NOTE 2 The reference frame is usually a set of axes at a mean position or a position of rest. In general, a rotation
acceleration vector, a translation acceleration vector, or both and the Coriolis acceleration can represent the acceleration.
NOTE 3 An acceleration is designated as relative acceleration if it is measured with respect to a reference frame other
than the inertial reference frame designated in a given case. The relative acceleration between two points is the vector
difference between the accelerations of the two points.
NOTE 4 In the case of time-dependent accelerations, various self-explanatory modifiers, such as peak, average, and
rms (root-mean-square), are often used. The time intervals over which the average or root-mean-square values are taken
should be indicated or implied.
NOTE 5 Acceleration can be:
— oscillatory, in which case simple harmonic components can be defined by the acceleration amplitude (and
frequency), or
— random, in which case the rms acceleration (and band-width and probability density distribution) can be used to
define the probability that the acceleration will have values within any given range.
Accelerations of short time duration are defined as transient accelerations. Non-oscillatory accelerations are defined as
sustained accelerations, if of long duration, or as acceleration pulses, if of short duration.
1.4
standard acceleration due to gravity
g
n
unit, 9,806 65 metres per second-squared (9,806 65 m/s )
NOTE 1 Value adopted in the International Service of Weights and Measures and confirmed in 1913 by the 5th CGPM
as the standard for acceleration due to gravity.
2 2 2 2
NOTE 2 This “standard value” (g = 9,806 65 m/s = 980,665 cm/s ≈ 386,089 in/s ≈ 32,174 0 ft/s ) should be used for
n
reduction to standard gravity of measurements made in any location on Earth.
NOTE 3 Frequently, the magnitude of acceleration is expressed in units of g .
n
NOTE 4 The actual acceleration produced by the force of gravity at or below the surface of the Earth varies with the
latitude and elevation of the point of observation. This variable is often expressed using the symbol g. Caution should be
exercised if this is done so as not to create an ambiguity with this use and the standard symbol for the unit of the gram.
1.5
force
dynamic influence that changes a body from a state of rest to one of motion or changes its rate of motion
NOTE 1 A force could also change a body’s size or shape if the body resists motion.
NOTE 2 The newton is the unit of force. One newton is the force required to give a mass of one kilogram an
acceleration of one metre per second squared.
1.6
restoring force
reaction force caused by the elastic property of a structure when it is being deformed
1.7
jerk
rate of change of acceleration
2 © ISO 2009 – All rights reserved

1.8
inertial reference system
inertial reference frame
coordinate system or frame which is fixed in space or moves at constant velocity without rotational motion and
thus, not accelerating
1.9
inertial force
reaction force exerted by a mass when it is being accelerated
1.10
oscillation
variation, usually with time, of the magnitude of a quantity with respect to a specified reference when the
magnitude is alternately greater and smaller than the specified reference
NOTE 1 See vibration (2.1).
NOTE 2 Variations with time such as shock processes or creeping motions are also considered to be oscillations in a
more general sense of the word.
1.11
environment
aggregate, at a given moment, of all external conditions and influences to which a system is subjected
NOTE See induced environment (1.12) and natural environment (1.13).
1.12
induced environment
conditions external to a system generated as a result of the operation of the system
1.13
natural environment
conditions generated by the forces of nature and the effects of which are experienced by a system when it is
at rest as well as when it is in operation
1.14
preconditioning
climatic and/or mechanical and/or electrical treatment procedure which may be specified for a particular
system so that it attains a defined state
1.15
conditioning
climatic and/or mechanical and/or electrical conditions to which a system is subjected in order to determine
the effect of such conditions upon it
1.16
excitation
stimulus
external force (or other input) applied to a system that causes the system to respond in some way
1.17
response (of a system)
output quantity of a system
1.18
transmissibility
non-dimensional complex ratio of the response of a system in forced vibration to the excitation
NOTE 1 The ratio may be one of forces, displacements, velocities or accelerations.
NOTE 2 This is sometimes known as a transmissibility function.
1.19
overshoot
when the maximum transient response exceeds the desired response
NOTE 1 If the output of a system is changed from a steady value A to a steady value B by varying the input, such that
value B is greater than A, then the response is said to overshoot when the maximum transient response exceeds value B.
NOTE 2 The difference between the maximum transient response and the value B is the value of the overshoot. This is
usually expressed as a percentage.
1.20
undershoot
when the minimum transient response falls below the desired response
NOTE 1 If the output of a system is changed from a steady value A to a steady value B by varying the input, such that
value B is less than A, then the response is said to undershoot when the minimum transient response is less than value B.
NOTE 2 The difference between the minimum transient response and the value B is the value of the undershoot. This is
usually expressed as a percentage.
1.21
system
set of interrelated elements considered in a defined context as a whole and separated from their environment
1.22
linear system
system in which the magnitude of the response is proportional to the magnitude of the excitation
NOTE This definition implies that the principle of superposition can be applied to the relationship between output
response and input excitation.
1.23
mechanical system
system comprising elements of mass, stiffness and damping
1.24
foundation
structure that supports a mechanical system
NOTE It can be fixed in a specified reference frame or it can undergo a motion.
1.25
seismic system
system consisting of a mechanical system attached to a reference base by one or more flexible elements, with
damping normally included
NOTE 1 Seismic systems are usually idealized as single-degree-of-freedom systems with viscous damping.
NOTE 2 The natural frequencies of the mass as supported by the flexible elements are relatively low for seismic
systems associated with displacement or velocity transducers, and are relatively high for acceleration transducers, as
compared with the range of frequencies to be measured.
NOTE 3 When the natural frequency of the seismic system is low relative to the frequency range of interest, the mass of
the seismic system may be considered to be at rest over this range of frequencies.
1.26
equivalent system
system that can be substituted for another system for the purpose of analysis
4 © ISO 2009 – All rights reserved

NOTE Many types of equivalence are common in vibration and shock technology:
a) a torsional system equivalent to a translational system;
b) an electrical or acoustical system equivalent to a mechanical system, etc.;
c) equivalent stiffness;
d) equivalent damping.
1.27
degrees of freedom
minimum number of generalized coordinates required to define completely the configuration of a mechanical
system
NOTE 1 This applies to mechanical systems, not to be confused with statistical degrees of freedom.
NOTE 2 It is often referred to by the acronym DOF.
1.28
discrete system
lumped parameter system
mechanical system in which the mass, stiffness, and/or damping elements are discretely located
1.29
single-degree-of-freedom system
SDOF
system requiring only one coordinate to define completely its configuration at any instant
1.30
multi-degree-of-freedom system
system for which two or more coordinates are required to define completely the configuration of the system at
any instant
1.31
continuous system
mechanical system in which the mass, stiffness, and/or damping properties are spatially distributed rather
than discretely located
NOTE The configuration of a continuous system is specified by a function of a continuous spatial variable, or variables,
in contrast to a discrete or lumped parameter system that requires only a finite number of coordinates to specify its
configuration.
1.32
centre of gravity
point through which the resultant of the weights of its component particles passes without resulting in moment
for all orientations of the body with respect to a gravitational field
NOTE If the field is uniform, the centre of gravity coincides with the centre of mass (1.33).
1.33
centre of mass
point of a body where the first moment of the overall mass with reference to a Cartesian coordinate system is
equal to the first moments of mass of all points of the body
NOTE This is the point at which an object is in balance in a uniform gravitational field.
1.34
principal axes of inertia
three mutually perpendicular axes intersecting each other at a given point about which the products of inertia
of a solid body are zero
NOTE 1 If the point is the centre of mass of the body, the axes and moments are called central principal axes and
central principal moments of inertia.
NOTE 2 In balancing, the term “principal inertia axis” is used to designate the one central principal axis (of the three
such axes) most nearly coincident with the shaft axis of the rotor and is sometimes referred to as the balance axis or the
mass axis.
1.35
moment of inertia
sum (integral) of the product of the masses of the individual particles (elements of mass) of a body and the
square of their perpendicular distances from the axis of rotation
1.36
product of inertia
sum (integral) of the product of the masses of the individual particles (elements of mass) of a body and their
distances from two mutually perpendicular planes
1.37
stiffness
ratio of change of force (or torque) to the corresponding change in translational (or rotational) deformation of
an elastic element
NOTE See also dynamic stiffness (1.58).
1.38
compliance
reciprocal of stiffness
NOTE See also dynamic compliance (1.57).
1.39
neutral surface
neutral surface of a beam in simple flexure
surface in which there is no strain
NOTE It should be stated whether or not the neutral surface is a result of the flexure alone, or whether it is a result of the
flexure and other superimposed loads.
1.40
neutral axis
neutral axis of a beam in simple flexure
line or plane in a beam where the longitudinal stress, tensile or compressive is zero
1.41
transfer function
mathematical representation of the relationship between the input and output of a linear time-invariant system
NOTE 1 A transfer function is usually a complex function defined as the ratio of the Laplace transforms of the output to
the input of a linear time-invariant system.
NOTE 2 It is usually given as a function of frequency, and is usually a complex function. See response (1.17),
transmissibility (1.18) and transfer impedance (1.50).
1.42
complex excitation
excitation expressed as a complex quantity with amplitude and phase angle
NOTE 1 The concepts of complex excitations and responses were evolved historically in order to simplify calculations.
The actual excitation and response are the real parts of the complex excitation and response. If the system is linear, the
concept is valid because superposition holds in such a situation.
NOTE 2 This term should not be confused with excitation by a complex vibration, or vibration of complex waveform. The
use of the term “complex vibration” in this sense is deprecated.
6 © ISO 2009 – All rights reserved

1.43
complex response
response of a system expressed as a complex quantity with amplitude and phase angle from a specified
excitation
NOTE See the notes under complex excitation (1.42).
1.44
modal analysis
vibration analysis method that characterizes a complex structural system by its modes of vibration, i.e. its
natural frequencies, modal damping and mode shapes, and based on the principle of superposition
1.45
modal matrix
linear transformation matrix which consists of the eigen vectors or modal vectors of a system
NOTE It renders the system both inertially and elastically uncoupled, i.e. the modal mass and modal stiffness matrices
are transformed into diagonal matrices.
1.46
modal stiffness
stiffness element associated with a specified mode of vibration
1.47
modal density
number of modes per unit bandwidth
NOTE Modal density is a measure widely used in structural dynamics as a diagnostic tool in assessing vibration power
flow in complex, structural systems. It can play a crucial role in determining changes in vibration power flow that may be a
precursor to fatigue failure in some part of the structure, or a metric used in structural condition monitoring evaluations. In
addition to these applications, it is a parameter required by the Statistical Energy Analysis method for evaluating the high-
frequency response of complex structures and in selecting appropriate vibration-control methods and devices.
1.48
mechanical impedance
complex ratio of force to velocity at a specified point and degree-of-freedom in a mechanical system
NOTE 1 The force and velocity may be taken at the same or different points and degrees-of-freedom in the system
undergoing simple harmonic motion.
NOTE 2 In the case of torsional mechanical impedance, the terms “force” and “velocity” should be replaced by “torque”
and “angular velocity”, respectively.
NOTE 3 In general, the term “impedance” applies to linear systems only.
NOTE 4 The concept is extended to non-linear systems where the term “incremental impedance” is used to describe a
similar quantity.
1.49
direct mechanical impedance
driving point mechanical impedance
complex ratio of the force to velocity taken at the same point or degree-of-freedom in a mechanical system
during simple harmonic motion
NOTE See the notes under mechanical impedance (1.48).
1.50
transfer (mechanical) impedance
complex ratio of the force applied at point i, in a specified degree-of-freedom in a mechanical system, to the
velocity at another point j in a specified direction or degree-of-freedom in the same system, during simple
harmonic motion
NOTE See the notes under mechanical impedance (1.48).
1.51
free impedance
ratio of the applied excitation complex force to the resulting complex velocity with all other connection points of
the system free, i.e. having zero restraining forces
NOTE 1 Historically, often no distinction has been made between blocked impedance and free impedance. Caution
should, therefore, be exercised in interpreting published data.
NOTE 2 Free impedance is the arithmetic reciprocal of a single element of the mobility matrix. While experimentally
determined free impedances could be assembled into a matrix, this matrix would be quite different from the blocked
impedance matrix resulting from mathematical modelling of the structure and, therefore, would not conform to the
requirements for using mechanical impedance in an overall theoretical analysis of the system.
1.52
blocked impedance
impedance at the input when all output degrees of freedom are connected to a load of infinite mechanical
impedance
NOTE 1 Blocked impedance is the frequency-response function formed by the ratio of the phasor of the blocking or
driving-point force response at point i, to the phasor of the applied excitation velocity at point j, with all other measurement
points on the structure “blocked”, i.e. constrained to have zero velocity. All forces and moments required to fully constrain
all points of interest on the structure need to be measured in order to obtain a valid blocked impedance matrix.
NOTE 2 Any changes in the number of measurement points or their location will change the blocked impedances at all
measurement points.
NOTE 3 The primary usefulness of blocked impedance is in the mathematical modelling of a structure using lumped
mass, stiffness and damping elements or finite element techniques. When combining or comparing such mathematical
models with experimental mobility data, it is necessary to convert the analytical blocked impedance matrix into a mobility
matrix or vice versa.
1.53
frequency-response function
frequency-dependent ratio of the motion-response Fourier transform to the Fourier transform of the excitation
force of a linear system
NOTE 1 Excitation can be harmonic, random or transient functions of time. The test results obtained with one type of
excitation can thus be used for predicting the response of the system to any other type of excitation.
NOTE 2 Motion may be expressed in terms of velocity, acceleration or displacement; the corresponding frequency-
response function designations are mobility, accelerance and dynamic compliance or impedance, effective (i.e. apparent)
mass and dynamic stiffness, respectively (see Table 1).
1.54
mobility
mechanical mobility
complex ratio of the velocity, taken at a point in a mechanical system, to the force, taken at the same or
another point in the system
NOTE 1 Mobility is the ratio of the complex velocity-response at point i to the complex excitation force at point j with all
other measurement points on the structure allowed to respond freely without any constraints other than those constraints
which represent the normal support of the structure in its intended application.
NOTE 2 The term “point” designates both a location and a direction.
NOTE 3 The velocity response can be either translational or rotational, and the excitation force can be either a
rectilinear force or a moment.
NOTE 4 If the velocity response measured is a translational one and if the excitation force applied is a rectilinear one,
the units of the mobility term will be m/(N⋅s) in the SI system.
NOTE 5 Mechanical mobility is the matrix inverse of mechanical impedance.
8 © ISO 2009 – All rights reserved

1.55
direct (mechanical) mobility
driving-point (mechanical) mobility
complex ratio of velocity and force taken at the same point in a mechanical system
NOTE Driving-point mobility is the frequency-response function formed by the ratio, in metres per Newton second, of the
velocity-response complex amplitude at point j to the excitation force complex amplitude applied at the same point with all
other measurement points on the structure allowed to respond freely without any constraints other than those constraints
which represent the normal support of the structure in its intended application.
1.56
transfer (mechanical) mobility
mechanical mobility where the velocity and the force are considered at different points of the system
1.57
dynamic compliance
frequency-dependent ratio of the spectrum, or spectral density, of the displacement to the spectrum, or
spectral density, of the force
1.58
dynamic stiffness
complex ratio of the force, taken at a point in a mechanical system, to the displacement, taken at the same or
another point in the system
NOTE 1 The terms “dynamic elastic constant” and “dynamic spring constant” are sometimes used.
NOTE 2 The dynamic stiffness may be dependent upon strain (amplitude and frequency), strain-rate, temperature or
other conditions.
∗
NOTE 3 The dynamic stiffness, k , of a linear translational single-degree-of-freedom system characterized by the
equation
ddxx
iωt
mc++kx=F where F = F e
dt
dt
is equal to
kF=+()mωωx− icx/x
00 00
where
c is the linear (viscous) damping coefficient;
e is the base of natural logarithms;
F is the force amplitude;
i =−1 ;
k is the elastic (spring) constant;
m is the mass;
t is the time;
x is the displacement;
x is the displacement amplitude;
ω is the angular frequency.
Table 1 — Equivalent definitions to be used for various kinds of output/input ratios
Motion expressed Motion expressed Motion expressed
as displacement as velocity as acceleration
a b c
Term Dynamic compliance Mobility Accelerance
Symbol x /F Y = v /F a /F
i j ij i j i j
2 –1
Unit m/N m/(N⋅s) m/(N⋅s ) = kg
Boundary conditions F = 0; i ≠ j F = 0; i ≠ j F = 0; i ≠ j
j j j
See Figure 3 1 2
Comment Boundary conditions are easy to achieve experimentally.
Term Dynamic stiffness Blocked impedance Blocked effective mass
Symbol F /x Z = F /v F /a
i j ij i j i j
Unit N/m N⋅s/m N⋅s /m = kg
Boundary conditions X = 0; i ≠ j v = 0; i ≠ j A = 0; i ≠ j
j j j
Comment Boundary conditions are very difficult or impossible to achieve experimentally.
Term Free dynamic stiffness Free impedance Effective (apparent) mass
(free effective mass)
Symbol F /x F /v = 1/Y F /a
j i j i ij
j i
Unit N/m N⋅s/m N⋅s /m = kg
Boundary conditions F = 0; i ≠ j F = 0; i ≠ j F = 0; i ≠ j
j j j
Comment Boundary conditions are easy to achieve, but results shall be used with great caution in
system modelling.
a
Dynamic compliance is also called receptance.
b
Mobility is sometimes called mechanical admittance.
c
Accelerance has unfortunately been called inertance in some publications. Inertance is not a standard term and is not acceptable
because it is in conflict with the common definition of acoustic inertance and is also contrary to the implication carried by the word
inertance.
10 © ISO 2009 – All rights reserved

Key
X frequency, in hertz (Hz)
Y1 phase angle, in degrees
Y2 mobility magnitude, in decibels (dB), [ref. 1 m/(N⋅s)]
a
Downwards sloping lines are used for mass.
b
Upwards sloping lines are used for stiffness.
Figure 1 — Mobility plot
Key
X frequency, in hertz (Hz)
Y accelerance, in decibels (dB), [ref. 1 m/(N⋅s )]
a
Upwards sloping lines represent stiffness.
b
Horizontal lines represent mass.
Figure 2 — Accelerance magnitude plot corresponding to the mobility graph
plotted in Figure 1
12 © ISO 2009 – All rights reserved

Key
X frequency, in hertz (Hz)
Y dynamic compliance, in decibels (dB), [ref. 1 m/N]
a
Horizontal lines represent stiffness.
b
Downwards sloping lines represent mass.
Figure 3 — Dynamic compliance magnitude plot corresponding to the mobility graph
plotted in Figure 1
1.59
dynamic mass
complex ratio of force to acceleration
1.60
accelerance
frequency-dependent ratio of the spectrum, or spectral density, of the acceleration to the spectrum, or spectral
density, of the force
1.61
spectrum
description of a quantity as a function of frequency or wavelength
1.62
level (of a quantity)
logarithm of the ratio of the quantity to a reference of the same kind
NOTE 1 The base of the logarithm, the reference quantity and the kind of level shall be specified.
NOTE 2 Examples of kinds of levels in common use are electric-power level, sound-pressure level, and voltage-
squared level.
NOTE 3 The definition is expressed symbolically as:
q
L = log
r
q
where
L is the level of the kind determined by the kind of quantity under consideration, measured in units of log ;
r
r is the base of the logarithms and the reference ratio;
q is the quantity under consideration;
q is the reference quantity of the same kind.
NOTE 4 A difference in the levels of two like quantities q and q is described by the same formula because, by the
1 2
rules of logarithms, the reference quantity is automatically divided out as follows:
qq q
12 1
log −=log log
rrr
qq q
NOTE 5 In vibration terminology, the term “level” is sometimes used to denote amplitude, average value, root-mean-
square value, or ratios of these values. These uses are deprecated.
1.63
bel
unit of level when the base of the logarithm is 10
NOTE Use of the bel is restricted to levels of quantities proportional to power. See also the notes under level (1.62) and
decibel (1.64).
1.64
decibel
dB
one tenth of a bel
NOTE 1 The magnitude of a level in decibels is ten times the logarithm to the base 10 of the ratio of power-like
quantities, i.e.
X X
L==10 lg 20 lg
X X
NOTE 2 Examples of quantities that qualify as power-like quantities are sound-pressure squared, particle-velocity squared,
sound intensity, sound-energy density and voltage squared. Thus, the bel is a unit of sound-pressure-squared level;
however, it is common practice to shorten this to sound-pressure level because ordinarily no ambiguity results from so
doing.
14 © ISO 2009 – All rights reserved

2 Vibration
2.1
vibration
mechanical oscillations about an equilibrium point. The oscillations may be periodic or random
NOTE See oscillation (1.10).
2.2
periodic vibration
vibration where the values of the vibration parameter recur for certain equal increments of the independent
time variable
NOTE 1 A periodic quantity, y, which is a function of time, t, can be expressed as:
y = f (t) = f (t ± nτ)
where
n is a whole number;
t is the independent time variable;
τ is the period.
NOTE 2 A quasi-periodic vibration is a vibration which deviates only slightly from a periodic vibration.
2.3
simple harmonic vibration
sinusoidal vibration
periodic vibration where the values of the vibration parameters can be described as sinusoidal functions of the
independent time variable
NOTE 1 Simple harmonic motion can be described as:
ˆ
yy=+sin(ωt ϕ )
where
yˆ is the amplitude;
t is the independent time variable;
y is the simple harmonic vibration;
ϕ is the initial phase angle of the vibration;
ω is the angular frequency.
NOTE 2 A periodic vibration consisting of the sum of more than one sinusoid, each having a frequency which is a
multiple of the fundamental frequency, is often referred to as a multi-sinusoidal vibration. The use of the term “complex
vibration” in this context is deprecated.
NOTE 3 A quasi-sinusoidal vibration has the appearance of a sinusoid, but varies relatively slowly in frequency and/or
in amplitude.
2.4
random vibration
stochastic vibration
vibration where the instantaneous value cannot be predicted
NOTE The probability that the magnitude of a random vibration is within a given range can be described by a probability
distribution function.
2.5
angular vibration
vibration associated with the three rotational degrees of freedom of a point on a body
2.6
torsional vibration
periodic vibration caused by an object twisting about its own axis
NOTE 1 See angular vibration (2.5).
NOTE 2 This term is commonly used when referring to the rotation of shafts in the plane of the shaft cross-section.
2.7
angular displacement
displacement of a body, characterized by one of its rotational degrees of freedom
2.8
angular velocity
velocity of a body, characterized by one of its rotational degrees of freedom
2.9
angular acceleration
acceleration of a body, characterized by one of its rotational degrees of freedom
2.10
non-stationary vibration
vibration with time-dependent statistical properties
2.11
stationary vibration
vibration that has statistical characteristics that do not change with time; therefore, the amplitude does not
increase or decrease with time
NOTE The vibration can be deterministic or random.
2.12
noise
undesired signal, generally of a random nature, the spectrum of which does not exhibit clearly defined
frequency components
NOTE By extension of the above definition, noise may consist of electrical oscillations of an undesired or random nature.
If ambiguity exists as to the nature of the noise, a term such as “acoustic noise” or “electrical noise” should be used.
2.13
random noise
stochastic noise
noise for which the instantaneous value cannot be predicted
NOTE See random vibration (2.4) and the accompanying note.
2.14
Gaussian random vibration
Gaussian stochastic vibration
random vibration whose instantaneous magnitudes have a Gaussian distribution
2.15
white random vibration
white stochastic vibration
vibration that has equal energy for any frequency band of constant width (or per unit bandwidth) over the
spectrum of interest
16 © ISO 2009 – All rights reserved

2.16
pink random vibration
pink stochastic vibration
vibration that has a constant energy within a bandwidth proportional to the centre frequency of the band
NOTE The energy spectrum of pink vibration as determined by an octave bandwidth (or any fractional part of an octave
bandwidth) filter will have a constant value.
2.17
narrow-band random vibration
narrow-band stochastic vibration
random vibration having its frequency components within a narrow band only
NOTE 1 The defining of what is meant by “narrow” is a relative matter depending upon the problem involved. It is
usually equal to or less than one-third octave.
NOTE 2 The waveform of a narrow-band random vibration has the appearance of a sine wave, the amplitude and
phase of which vary in an unpredictable manner.
NOTE 3 See random vibration (2.4).
2.18
broad-band random vibration
broad-band stochastic vibration
random vibration having its frequency components distributed over a broad frequency band
NOTE 1 The definition of what is meant by “broad” is a relative matter depending upon the problem involved. It is
usually one octave or greater.
NOTE 2 See random vibration (2.4).
2.19
dominant frequency
frequency at which a maximum value occurs in a spectrum
2.20
steady-state vibration
continuous vibration that has on average reached equilibrium
2.21
transient vibration
vibration, typically of short duration, that decays with time
NOTE This term is basically associated with mechanical shock (3.1).
2.22
forced vibration
vibration of a system due to an external time-dependent force
NOTE The vibration (for linear systems) has the same frequencies as the excitation.
2.23
free vibration
vibration of a system that occurs after the removal of excitation or restraint
NOTE A linear system vibrates as a linear combination of natural modes.
2.24
non-linear vibration
vibration of a system which has a non-linear response and can only be described by non-linear differential
equations
NOTE In a non-linear system, the relationship between cause and effect is no longer proportional and the principle of
superposition does not hold for their solution.
2.25
longitudinal vibration
vibration along longitudinal axis in an elastic body
2.26
self-induced vibration
self-excited vibration
vibration of a mechanical system resulting from conversion, within the system, of energy to oscillatory
excitation
2.27
ambient vibration
all-encompassing vibration associated with a given environment usually a composite vibration from many
surrounding sources
2.28
extraneous vibration
total vibration other than the vibration of principal interest
NOTE Ambient vibration contributes to the magnitude of extraneous vibration.
2.29
aperiodic vibration
vibration that is not periodic
2.30
jump
phenomenon where vibration response changes suddenly due to small change in frequency of an excitation
force
2.31
cycle, noun
complete range of states or values through which a periodic phenomenon or function passes before repeating
itself identically
NOTE See cycle, verb (2.111).
2.32
fundamental period
period
smallest increment of time for which a periodic function repeats itself
NOTE 1 If no ambiguity is likely, the fundamental period is called the period.
NOTE 2 See periodic vibration (2.2).
2.33
frequency
reciprocal of the period
NOTE The unit of frequency is the hertz (Hz), which corresponds to one cycle per second.
2.34
fundamental frequency
lowest natural frequency in an oscillating system
NOTE 1 The normal mode of vibration associated with the lowest natural frequency is known as the fundamental mode.
NOTE 2 See natural frequency (2.88).
18 © ISO 2009 – All rights reserved

2.35
harmonic (of a periodic quantity)
harmonic vibration, the frequency of which is an integral multiple of the fundamental frequency
NOTE The term “overtone” has frequently been used in place of harmonic, the nth harmonic being called the (n – 1)th
overtone. The term “overtone” is deprecated.
2.36
sub harmonic
harmonic vibration, the frequency of which is an integral sub-multiple of the fundamental frequency of the
quantity to which it is related
2.37
harmonic excitation
sinusoidal excitation
2.38
beats
periodic variation in the magnitude of an oscillation resulting from the combination of two oscillations of slightly
different frequencies
NOTE The beat occurs at the difference frequency.
2.39
beat frequency
absolute value of the difference in frequency of two oscillations of slightly different frequencies
2.40
angular frequency
pulsatance
product of the frequency of a sinusoidal quantity and the factor 2π
NOTE The unit of angular frequency is the radian (rad) per unit of time.
2.41
phase angle
angle of a complex response which characterizes a shift in time at a given frequency
2.42
phase difference
phase angle difference
between two harmonic vibrations of the same frequency, the difference between their respective phases or, in
the case of sinusoidal vibrations, between their phase angles measured from the same origin
2.43
amplitude
magnitude, size or value of a quantity
2.44
peak value
peak magnitude
positive peak value
negative peak value
maximum value of a vibration during a specified time interval
NOTE A peak value vibration is usual
...