9 





9.1 
ALIASING Phenomenon, caused by a loss of high frequency content of an analogue signal, which can occur whenever this signal is sampled (at a rate) less than twice the maximum component frequency. 

9.2 
AMPLITUDE (OF HARMONIC VIBRATION) , COMPLEX Complex parameter, modulus of which equals the amplitude and the argument equals phase of harmonic vibration. 

9.3 
ANTIRESONANCE Minimum amplitude response to a simple harmonic excitation between two consecutive natural frequencies of a system. 

9.4 
ATTRACTOR Set of points or a subspace in phase space toward which a time history of motion, for different initial conditions, approaches after transients die out. 

9.5 
ATTRACTOR, CHAOTIC [STRANGE] Attractor characterized by the most complex form of bounded posttransient recurrent behaviour with random characteristics observed in a deterministic dissipative dynamical system. 

9.6 
ATTRACTOR, PERIODIC Closed orbit in the phase space, of an asymptotically stable time continuous dynamical system, satisfying recurrence by returning precisely to its starting point after its period. 

9.7 
ATTRACTOR, POINT Stable equilibrium point in the phase space of a dynamical system. 

9.8 
BANDWIDTH [NOISE], EFFECTIVE Bandwidth of an ideal bandpass filter that would pass the same amount of power from a white noise source, as the described filter. 

9.9 
BANDWIDTH, NOMINAL Spacing between frequencies at which a bandpass filter attenuates the signal by 3 dB. 

9.10 
BASIN [DOMAIN] OF ATTRACTION Set of initial conditions in phase space which leads to a particular longtime motion or attractor. 

9.11 
BIFURCATION Qualitative change in the topology of the attractorbasin phase portrait (multiple points generated in Poincaré mapping), realisable under the quasistatic variation of a control parameter across its critical value. 

9.12 
BIFURCATION, GLOBAL Bifurcation whose effects are not restricted to the neighbourhood of a point or cycle in phase space. 

9.13 
BIFURCATION, HOPF Emergence of a limit cycle oscillation from an equilibrium state as some system parameter is varied, characterized by complex conjugate pair of linear eigenvalues whose real part passes through zero. 

9.14 
BIFURCATION, LOCAL Bifurcation whose effects are restricted to the neighbourhood of a point or cycle in phase space. 

9.15 
BIFURCATION, SADDLENODE Bifurcation occuring if a saddle and a node coalesce, characterized by a real linear eigenvalue passing through zero whereby a system is forced to jump dynamically to a distant attractor. 

9.16 
BOUNDARY, BASIN Trajectories (in phase space) initialized on a basin boundary flow towards a saddle solution which attracts within the boundary but repels across it. 

9.17 
CEPSTRUM Inverse Fourier transform of a logarithmic spectrum. 

9.18 
CHAOS Loose generic term for a complex, seemingly irregular behaviour of deterministic dynamical systems characterised by a sensitive dependence on initial conditions and a broadband noise power spectrum. 

9.19 
CHARACTERISTIC, AMPLITUDEFREQUENCY Dependence of the amplitude of a forced vibration upon the (angular) frequency of a harmonic excitation. 

9.20 
CHARACTERISTIC, AMPLITUDEPHASE (FREQUENCY) [ARGAND’S] Dependence of the complex amplitude of a harmonic forced vibration upon the angular frequency of a harmonic excitation. 

9.21 
CHARACTERISTIC, PHASEFREQUENCY Dependence of the difference between phases of a harmonic forced vibration and a harmonic excitation upon its angular frequency. 

9.22 
COEFFICIENT [FACTOR], LOSS Measure of damping capacity of a system during forced harmonic vibration, expressed by dimensionless ratio of damping energy dissipated per cycle to 2π times strain energy at the maximum displacement. 

9.23 
CURVE, BACKBONE [SKELETON] Dependence between amplitude and frequency of free vibration of an undamped nonlinear system. 

9.24 
CURVE, RESONANCE Plot of a characteristic parameter of the response of an excited system in a certain vicinity of its resonance versus a chosen parameter of the system or excitation. Note: special kind of a resonance curve is e.g. an amplitudefrequency characteristic. 

9.25 
CYCLE, LIMIT Closed phase trajectory of a nonlinear, nonconservative autonomous system (see also nonlinear system). Note: In the dynamical systems literature it also includes forced periodic motions (see also Hopf bifurcation, periodic attractor). 

9.26 
DAMPING, COULOMB Dissipation of energy at Coulomb friction. 

9.27 
DAMPING, HYSTERETIC [RATEINDEPENDENT LINEAR] Damping due to hysteretic damping force during forced harmonic vibration of a system, causing loss of energy per cycle independent of excitation frequency. 

9.28 
DAMPING, NEGATIVE Damping dependent on velocity, when input of energy into a vibration system takes place. 

9.29 
DAMPING, PROPORTIONAL Damping of a multidegree of freedom linear system when the damping matrix is a linear combination of the inertia and stiffness matrices. 

9.30 
DAMPING, STRUCTURAL Damping due to external friction (mostly dry friction) in constraints of a system. 

9.31 
DENSITY, POWER SPECTRAL Meansquare value of a time variable quantity per unit bandwidth. 

9.32 
DIVERGENCE Instability, typified by exponentially increasing displacement from the original state of a system. 

9.33 
DOUBLING, PERIOD Sequence of periodic vibrations, in which the period doubles as some control parameter of the problem is varied. These frequencyhalving bifurcations occur at smaller and smaller intervals of the control parameter (cascade of bifurcations). 

9.34 
EIGENVALUES, LINEAR Eigenvalues of the linearized or linear system used also to examine stability of the system in the neighbourhood of an equilibrium point. 

9.35 
ENVELOPE, LIMIT Envelope to a set of amplitudefrequency characteristics for different values of a system parameter to which the envelope is invariant. 

9.36 
EQUATION, DUFFING’S Archetype equation of a driven oscillator with a cubic {polynomial} nonlinear restoring force. 

9.37 
EQUATION, HILL Linear differential equation of the second order having periodic coefficients. 

9.38 
EQUATION, MATHIEU Special case of Hill equation having harmonic coefficients. 

9.39 
EQUATION, VAN DER POL Secondorder differential equation with linear restoring force and nonlinear damping, which exhibits a limit cycle behaviour (selfexcited oscillations). 

9.40 
ERROR, BIAS [SYSTEMATIC] Systematic deviation of a determined value from the true value due to imperfections of the measuring device, method, environment, operator. 

9.41 
EXCITATION, EXTRAPARAMETRIC In a rotating system with variable moment of inertia, special kind and combination of external and parametric excitation, dependent nonlinearly upon unknown both position angle and angular velocity of the system. 

9.42 
EXCITATION, FORCE {MOMENT} Excitation of a mechanical system by an excitation force {excitation moment}. 

9.43 
EXCITATION, KINEMATIC Excitation of a mechanical system due to a prescribed motion of arbitrary points of the system. 

9.44 
EXCITATION, PARAMETRIC Excitation of a mechanical system due to change of system parameters periodically in time, independently of its motion. 

9.45 
FILTER [WAVE FILTER] Device or algorithm to transform signal. 

9.46 
FILTER, BANDPASS Filter with a single transmission band extending from nonzero lower cutoff [corner] frequencies to finite upper cutoff [corner] frequencies. 

9.47 
FILTER, CONSTANT BANDWIDTH Bandpass filter whose bandwidth (in Hertz) is constant and independent of the arithmetic center frequency. 

9.48 
FILTER, DIGITAL Filter which operates on digital data. 

9.49 
FILTER, HIGHPASS Filter with a transmission band starting at a nonzero lower cutoff [corner] frequency and extending to (theoretically) infinite frequency. 

9.50 
FILTER, LOWPASS Filter with a transmission band starting at a finite cutoff [corner] frequency and extending (down) to zero frequency. 

9.51 
FILTER, PROPORTIONAL [CONSTANT PERCENTAGE] BANDWIDTH Bandpass filter whose bandwidth is proportional to the geometric center frequency. 

9.52 
FLUTTER Selfexcited aeroelastic oscillations generated as a consequence of Hopf bifurcation instability. 

9.53 
FORCE {MOMENT}, EXCITATION Time variable force {moment} acting upon a mechanical system independently of its state. 

9.54 
FORCE, HYSTERETIC DAMPING Internal force within an elastodissipative material with magnitude proportional to displacement but with the same direction as velocity of a material element. 

9.55 
FRACTAL Geometric property of a set of points in a multidimensional space having the quality of selfsimilarity at different length scales. 

9.56 
FREQUENCY, AMPLITUDE RESONANT Frequency of a forced vibration at which the maximum amplitude of a system response occurs. 

9.57 
FREQUENCY, ANGULAR [CIRCULAR] Product of the frequency of a simple harmonic quantity and the factor 2π . 

9.58 
FREQUENCY, CENTER Arithmetic {geometric} bandwidth center of a bandpass filter (i.e. the mid point on the respectively linear {logarithmic} scale). 

9.59 
FREQUENCY, DAMPED NATURAL Frequency of the free vibration of a damped linear system. 

9.60 
FREQUENCY, PHASE RESONANT Frequency of a forced vibration at which phase is 90 degrees. 

9.61 
INSENSIBILITY Phenomenon {behaviour} described by a nonlinear static characteristic with a dead band. 

9.62 
INTEGRATOR Electrical circuit used for converting a (vibratory) acceleration signal to one which is proportional to velocity or displacement. 

9.63 
INTERMITTENCY Type of chaotic motion in which long unpredictable time intervals of almost regular, periodic or steady motion are followed by bursts of random like motion. 

9.64 
ISOLATION, VIBRATION Reduction in response of a mechanical system to an excitation, achieved by use of a resilient interface. 

9.65 
ISOLATOR, VIBRATION Resilient interface designed to attenuate the transmission of vibration in a frequency range. 

9.66 
LINEARIZATION Efficient method for solution of nonlinear systems in the first approximation, based on replacing the nonlinear mathematical equations by the linear ones. 

9.67 
MAP, SPECTRAL [WATERFALL PLOT], [CASCADE PLOT] Threedimensional plot of frequency spectra versus another variable (usually time or machine speed). 

9.68 
METER, VIBRATION [VIBROMETER] Instrument for measuring and indicating the magnitude of vibration in terms of displacement, velocity and acceleration. 

9.69 
MODULUS, DYNAMIC Ratio of stress to strain during harmonic forced vibration of a linear material. 

9.70 
MOTION, CHAOTIC Type of motion that is very sensitive to changes in initial conditions, unpredictable in the range of a chaotic attractor. 

9.71 
MOTION, GLOBAL Motion between and among equilibrium points that is not confined to a small region of phase space. 

9.72 
MOTION, LOCAL Motion that does not wander far from an equilibrium point. 

9.73 
NOISE, WHITE Broadband noise whose energy per unit bandwidth is constant. 

9.74 
NUMBER, IMPACT Number of impacts of the system motion during one period of excitation force. 

9.75 
OCTAVE Frequency interval between two frequencies with a ratio of two. 

9.76 
PARAMETER, CONTROL Parameter which governs a dynamical system and remains constant (or slowly variable) during the motions of the system. 

9.77 
PHENOMENON, SYNCHRONIZATION Phenomenon, at which frequency of a selfexcited vibration changes, due to the action of external or parametric excitation, near resonance towards the external excitation frequency. 

9.78 
PLOT [DIAGRAM], BODE Plot of (logarithmic) gain and phase versus frequency for a transfer function. 

9.79 
PLOT [DIAGRAM], CAMPBELL [CASCADE PLOT*], [WATERFALL PLOT*] Plot of resonance frequencies versus excitation frequency for a system at polyharmonic excitation (used to check for coincidence of vibration sources). 

9.80 
POINT, EQUILIBRIUM [FIXED] 1. For timecontinuous dynamical systems, point in phase space towards which a solution may approach as transients decay. 2. For timediscrete dynamical systems, a finite set of points where the system visits each point in a sequential manner as a difference equation is iterated. 

9.81 
POINT, HYPERBOLIC Equilibrium point of a dynamical system characterized by a phase portrait which is structurally stable against perturbations, having its linear eigenvalues in the stable domains. 

9.82 
POINT, SADDLE Unstable equilibrium point not directly observable in a physical system, as it repels trajectories in some phase directions but attracts in others, having real eigenvalues with at least one positive and one negative eigenvalue. 

9.83 
PORTRAIT, PHASE [STATE] Set of phase trajectories corresponding to various initial conditions of a dynamical system. 

9.84 
RANGE, DYNAMIC Ratio of the largest to the smallest signals that can be measured on a certain device. 

9.85 
REPELLOR Unstable steadystate solution {equilibrium, cycle, etc.} that repels all adjacent motions. 

9.86 
RESONANCE, COMBINATION Resonance at which excitation frequency is close to a linear combination of natural frequencies of the linearized system. 

9.87 
RESONANCE, EXTRAPARAMETRIC Resonance sustained by an extraparametric excitation, manifesting in its pronounced form by two mutually intersecting branches of a resonance curve. 

9.88 
RESONANCE, INTERNAL Resonance occurring when some natural frequencies of the linearized system are mutually in a ratio of small integer numbers. 

9.89 
RESONANCE, PARAMETRIC Amplitude response exponentially increasing in time occurring in a dynamical system due to the time periodic change of any system parameters. Regions of instability for small periodic changes of the system parameters are related to the natural frequencies of the corresponding conservative system with zero intensity of parametric excitation (single, summation or difference parametric resonances). 

9.90 
SAMPLING, STROBOSCOPIC Reading of values of physical quantities of an oscillating system in regular time intervals, at the period of the driving excitation. 

9.91 
SECTION [MAP], POINCARÉ Sequence of points in phase space generated by penetration of a continuous evolution trajectory through a generalized surface or plane in the space. 

9.92 
SELFEXCITATION Excitation due to inflow of energy from an internal nonoscillating source generated by the motion of the system. 

9.93 
SEPARATRIX Invariant boundary of dimension n(1 that separates regions in an ndimensional phase space. 

9.94 
SEVERITY, VIBRATION Criterion for predicting possible danger relative to specific values and/or parameters which characterize a vibration. 

9.95 
SEVERITY (OF A MACHINE), VIBRATION Set of maximum rms values of vibration velocity, measured at significant points of a machine (such as bearings, mountings). 

9.96 
SHIFT [DIFFERENCE] (OF HARMONIC VIBRATIONS), PHASE Phase difference of two harmonic vibrations with equal frequencies. 

9.97 
SIGNATURE (OF A MACHINE) Signal frequency spectrum which is specific to a particular machine or component, system or subsystem, at specific instant under specific operating conditions. 

9.98 
SPACE {PLANE}, PHASE [STATE] Abstract mathematical space {plane} the coordinates of which are the state variables. 

9.99 
SPECTRUM, AUTO (POWER) Spectrum the magnitude of which represents power and phase is zero, defined as the Fourier transform of the input, times its complex conjugate. 

9.100 
SPECTRUM (OF A MACHINE), BASELINE Vibration spectrum taken when a rotating machine is new or in good working conditions, used as a reference for later analysis. 

9.101 
SPECTRUM, SHOCK (RESPONSE) Spectrum of the maximum responses of a series of specified systems (usually linear single degreeoffreedom) to an applied shock as a function of their natural frequencies. 

9.102 
STATE (OF A DYNAMICAL SYSTEM) Quantitative description of behaviour of a dynamical system at any time, determined by the values of state variables. 

9.103 
STATE, RECURRENT Particular state of a dynamical system when after sufficient time the system returns arbitrary close to this state. 

9.104 
STIFFNESS, COMPLEX DYNAMIC Ratio of the complex amplitude of a harmonic excitation force to the complex response amplitude of a simple harmonic vibration. 

9.105 
THEORY, CATASTROPHE Theory which studies dependence of the number and type of equilibrium points upon the parameters near their critical values. 

9.106 
TONES, COMBINATION In acoustics and vibration, frequencies that appear as a linear combination of two fundamental frequencies. 

9.107 
TRAJECTORY, PHASE [STATE] Path in a phase space {plane}. 

9.108 
TRANSFORM, FOURIER Reversible integral transformation of a time function into a corresponding frequency function. 

9.109 
TRANSFORM, DISCRETE FOURIER Version of the Fourier transform applicable to a finite number of discrete samples. 

9.110 
TRANSFORM, FAST FOURIER (FFT) Algorithm for computation of the discrete Fourier transform in a fast and efficient way (from sampled time data to discrete frequency components). 

9.111 
VARIABLES (OF A DYNAMICAL SYSTEM), STATE Minimum set of variables which completely describe state of a dynamical system. Note: The state variables can be uniquely determined from the mathematical model of a dynamical system provided that their initial conditions are given. 

9.112 
VECTOR, STATE Vector whose components are state variables of a dynamical system. 

9.113 
VIBRATION, ALMOSTPERIODIC [QUASIPERIODIC] Vibration close to a periodic one whose harmonic components have nearly commensurable frequencies. 

9.114 
VIBRATION, COMBINED Periodic forced vibration with harmonics whose frequencies are rational multiples of frequency of a certain harmonic excitation. 

9.115 
VIBRATION, DAMPED Vibration of a mechanical system with presence of damping. 

9.116 
VIBRATION, DECAYING Free damped vibration of a mechanical system when peaktopeak values of its response variable exponencially diminish in time. 

9.117 
VIBRATION, DIVERGENT Vibration of a mechanical system with timeincreasing peaktopeak values of the response variable or its derivative. 

9.118 
VIBRATION, NONLINEAR Vibration of a nonlinear system. 

9.119 
VIBRATION, PARAMETRIC Vibration caused and maintained by a parametric excitation. 

9.120 
VIBRATION, PERIODIC Vibration whose amplitude pattern repeats itself after its period. 

9.121 
VIBRATION, SELFEXCITED [SELFINDUCED] Vibration caused and maintained by a selfexcitation. 

9.122 
VIBRATION, SUBHARMONIC Periodic forced vibration with harmonics the frequencies of which are fractions of the frequency of a certain harmonic excitation. 

9.123 
VIBRATION, SUPERHARMONIC [ULTRAHARMONIC] Periodic forced vibration with harmonics the frequencies of which are integer multiples of frequency of a certain harmonic excitation. 

9.124 
VIBRATIONS, ANTIPHASE Synchronous vibrations having at any time phase differences of 180 degrees. 

9.125 
VIBRATIONS, IN PHASE Synchronous vibrations the phases of which are the same at any instant. 