# Vibration Control Definitions of Characteristics

Absolute: A term applied to calibration (e.g. of an accelerometer) based upon the primary standards of mass, length and time. (See also comparison calibration.)

Absorber: A device capable of soaking up vibration.

Acceleration: Acceleration is rate of change of velocity with time (denoted as dv/dt or d2x/dt2), along a specified axis, usually expressed in g or gravitational units. It may refer to angular motion.

Accelerometer: A sensor or transducer or pickup for converting acceleration to an electrical signal.

Accuracy: The capability of an instrument to indicate the true value. Do not confuse with inaccuracy (sum of hysteresis + non-linearity + temperature effect, etc.) nor with repeatability.

Aliasing: A spectrum analysis problem resulting from sampling data at too low a rate. It causes high-frequency signals to appear in a spectrum at low frequencies.

Amplitude: The magnitude of variation (in a changing quantity) from its zero value. Always modify it with an adjective such as peak, RMS, average, etc. May refer to displacement, velocity, acceleration, voltage, current force of pressure.

Angular Frequency: (Also known as circular frequency.) ω is the torsional vibration frequency in radians per second. Or divide by 2π and express in hertz (Hz) or (obsolete) cycles per second (cps).

Average: Refer to a textbook on electrical engineering. In the exclusive case of a pure sine wave, the average value is 0.636 x peak value.

Averaging: Summing and suitably dividing several like measurements to improve accuracy or to lessen any asynchronous components.

Balancing: (Mechanical) Adjusting the distribution of mass in a rotating element, to reduce vibratory forces generated by rotation.

Broadband: Vibrations (or other signals) which are unfiltered. Signals at all frequencies contribute to the measured value.

Calibration: (As applied to vibration sensors) An orderly procedure for determining sensitivity as a function of frequency, temperature, altitude, etc.

Charge Amplifier: An amplifier which converts a charge input signal (as from an accelerometer) into an output voltage; charge-to-voltage converter.

Coherence: A measure of the similarity of vibration at two locations, giving insight into possible cause and effect relations.

Comparison: A term applied to calibration (e.g. of an accelerometer) in which sensitivity is tested against a standard.

Compliance: The reciprocal of stiffness, i.e., displacement divided by force.

Critical Frequency: The particular resonant frequency (see resonance) at which damage or degradation in performance is likely.

Crossover Frequency: In sinusoidal vibration testing, the unique foreign frequency at which the required displacement yields the desired acceleration and vice versa.

Cycle: The complete sequence of instantaneous values of a periodic event, during one period.

Damping: Dissipation of oscillatory or vibratory energy, with motion or with time. Critical damping CC is that value of damping that provides most rapid response to a step function without overshoot. Damping ratio is a fraction of CC.

Decade: The interval between two frequencies which differ by exactly 10:1.

deciBel: Ratios of identical quantities are expressed in decibel or deciBel or dB units. The number of dB is ratioed against some standard or reference value in terms of base 10 logarithm of the ratio. In measuring acoustic or vibration power, as in PSD or ASD or random vibration, the number of dB = 10 log10P/P0. P0, the reference level, equals 0 dB. In measuring the more common voltage-like quantities such as acceleration, the number of dB = 20 log10E/E0. E0, the reference level, equals 0 dB.

Degrees of Freedom: In mechanics, the total number of directions of motion, of all the points being considered, on a structure being modeled or otherwise evaluated. In statistics, the number of independent variables used in constructing a mathematical model representing some collection of random variables.

Deterministic Vibration: A vibration whose instantaneous value at any future time can be predicted by an exact mathematical expression. Sinusoidal vibration is the classic example. Complex vibration is less simple (two or more sinusoids).

Displacement: Specified change of position, or distance, usually measured from mean position or position of rest. Usually applies to uniaxial, less often to angular motion.

Distortion: In electronic measurements, distortion is any unwanted signal; e.g. amplifiers may generate unwanted signals. This refers to any unwanted motion. If sinusoidal motion was desired at a fundamental frequency, distortion is any motion at harmonics or subharmonics of the frequency, or any mechanical “hash” (perhaps due to parts colliding).

Duration: of a shock pulse is how long it lasts. For “classical” pulses, time is usually measured between instants when the amplitude is greater than 10% of the peak value.

Filter: An electronic device to pass certain frequencies (pass band) but block other frequencies (stop band). Classified as low-pass (high-stop), high-pass (low-stop), band-pass or band-stop.

Forced Vibration: The vibratory motion of a system caused by some mechanical excitation. If the excitation is periodic and continuous, the response motion eventually becomes steady-state.

Forcing Frequency: In sinusoidal vibration testing or resonance searching, the frequency at which a shaker vibrates.

Fragility: The maximum load equipment can stand before failure (malfunction, irreversible loss of performance or structural damage) occurs.

Fragility Test: Expensive but highly useful dynamic tests of several samples (to account for variations in tolerances material properties and manufacturing processes) at potentially destructive frequencies, to determine fragility.

Free Vibration: Free vibration occurs without forcing, similar after a reed is plucked.

Frequency: The reciprocal of the period T in seconds (or a periodic function; 1/T0). Usually given in Hertz (Hz), meaning cycles per second (cps).

Frequency Response: The portion of the frequency spectrum over which a device can be used, within specified limits of amplitude error.

Frequency Spectrum: A description of the resolution of any electrical signal into its frequency components, giving the amplitude (sometimes also phase) of each component.

Fundamental Mode of Vibration: That mode having the lowest natural frequency.

g: The acceleration produced by Earth’s gravity. By international agreement, the value for 1 gravitational unit is 9.80665 m/s2= 386.087 in/sec2= 32.1739 ft/sec2.

Harmonic: A sinusoidal quantity having a frequency that is an integral multiple (x2, x3, etc.) of a fundamental (x1) frequency.

Hash: Distortion (usually non-harmonic) on a signal. May be viewed on an oscilloscope trace. (slang).

Impact: A collision between masses.

Impulse: The integral of force over a time interval.

Induced Environments: Conditions generated by operating some equipment, as opposed to natural environments.

Inertance (or Accelerance). The ratio of acceleration to force.

Input: The mechanical motion, force or energy applied to a mechanical system, e.g., the vibratory input from shaker to test item. Or an electrical signal, e.g. from an oscillator to the power amplifier driving a shaker.

Input Control Signal: Originates in a control sensor; sometimes selected between or averaged between several sensors. Used to regulate shaker intensity. (May originate in a force sensor for force-controlled testing.)

Intensity: The severity of a vibration or shock. Nearly the same meaning as Amplitude, defined earlier, but less precise, lacking units.

Isolation: A reduction in motion severity, usually by resilient support. A shock mount or isolator attenuates shock. A vibration mount or isolator attenuates steady-state vibration.

Jerk: The rate of change of acceleration with time.

Linear System: A system is linear if its magnitude of response is directly proportional to its magnitude of excitation, for every part of the system.

Linearity: The closeness of a calibration curve to a specified straight line, preferably passing through zero. Commonly specified as a % of full scale.

Mass: A physical property, dynamically computed as acceleration divided by force. Statically computed as W (which can be measured on a butcher scale) divided by the acceleration due to gravity. Ordinary structures are not pure masses as they contain reactive elements, i.e. springs and damping.

Mean: A value intermediate between quantities under consideration. A shaker’s mean acceleration must be zero; no steady-state acceleration. But a vehicle can have steady-state motion.

Mechanical Impedance: The ratio of force to velocity, where the velocity is a result of that force only. Its reciprocal, mobility, is today more favored.

Mode: A characteristic pattern in a vibrating system. All points reach their maximum displacements at the same instant.

Natural Environments: Conditions occurring in nature, not caused by any equipment; effects are observed whether an equipment is at rest or in operation.

Natural Frequency: The frequency of an undamped system’s free vibration; also, the frequency of any of the normal modes of vibration. Natural frequency drops when damping is present.

Noise: The total of all interferences in measurement system, independent of the presence of signal.

Notch: Minimum spectral value, at a natural frequency. Also, the deliberate reducing of a portion of a test spectrum (random vibration testing).

Octave: The interval between two frequencies differing by exactly 2:1.

Oscillation: Variation with time of a quantity such as force, stress, pressure, displacement, velocity, acceleration or jerk. Usually implies some regularity (as in sinusoidal or complex vibration).

Peak: Extreme value of a varying quantity, measured from the zero or mean value. Also, a maximum spectral value.

Peak-to-Peak Value: The algebraic difference between extreme values (as D = 2X).

Period: The interval of time over which a cyclic vibration repeats itself.

Periodic Vibration: (See also Deterministic Vibration.) An oscillation whose waveform regularly repeats. Compare with probabilistic vibration.

Phase: (Of a periodic quantity), the fractional part of a period between a reference time (such as when displacement = zero) and a particular time of interest; or between two motions or electrical signals having the same fundamental frequency.

Pickup: See Transducer.

Platform: Per MIL-STD-810, any vehicle, surface or medium that carries an equipment. For example, an aircraft is the carrying platform for internally-mounted avionics equipment and externally-mounted stores. The land is the platform for a ground radar set, and a man for a hand-carried radio.

Power Spectral Density or PSD: Describes the power of random vibration intensity, in mean-square acceleration per frequency unit, as g2/Hz or m2/s3. Acceleration spectral density or ASD is preferred abroad.

Precision: The smallest distinguishable increment (almost the same meaning as resolution); deals with a measurement system’s possible or design performance.

Probabilistic Vibration: As compared to Deterministic Vibration, one whose magnitude at any future time can only be predicted on a statistical basis.

Quadrature Motion: (Or side or lateral motion or crosstalk), any motion perpendicular to the reference axis. Shakers are supposed to have zero quadrature motion.

Quadrature Sensitivity: (Or side or lateral motion or crosstalk sensitivity) of a vibration sensor is its sensitivity to motion perpendicular to the sensor’s principal axis. Commonly expressed in % of principal axis sensitivity.

Random Vibration: (See Probabilistic Vibration.) One whose instantaneous magnitudes cannot be predicted. Adjustive ”Gaussian” applies if they follow the Gaussian distribution. May be broadband, covering a wide, continuous frequency range, or narrow band, covering a relatively narrow frequency range. No periodic or deterministic components.

Range: A statement of the upper and lower limits over which an instrument works satisfactorily.

Repeatability: (1) The maximum deviation from the mean of corresponding data points taken under identical conditions. (2) The maximum difference in output for identically-repeated stimuli (no change in other test conditions). Do not confuse with accuracy.

Resolution: The smallest change in input that will produce a detectable change in an instrument’s output. Differs from precision in that human capabilities are involved.

Resonance: Forced vibration of a true single degree of freedom system causes resonance when the forcing frequency equals the natural frequency, when any forcing frequency change decreases system response.

Response: The vibratory motion or force that results from some mechanical input.

Response Signal: The signal from a “response sensor” measuring the mechanical response of a mechanical system to an input vibration or shock.

Ringing: Continued oscillation after an external force or excitation is removed, as after a guitar string is plucked.

Rise Time: The time required for the output of a transducer to rise from 10% to 90% of its final value, as it responds to a step change in the measurand.

RMS or Root-Mean-Square Value: The square root of the time-averaged squares of a series of measurements. Refer to a textbook on electrical engineering. In the exclusive case of sine wave, σ, the RMS value, is 0.707 x the peak value.

Self-Induced Vibration: Also called self-excited vibration, results from conversion of non-oscillatory energy into vibration, as wind exciting telephone wires into mechanical vibration.

Sensitivity: Of a mechanical-to-electrical sensor or pickup, the ratio between electrical signal (output) and mechanical quantity (input).

Sensor: (See Transducer.)

Shock Machine: Or shock test machine, a device for subjecting a system to controlled and reproducible mechanical shock pulses.

Shock Pulse: A transmission of kinetic energy into a system in a relatively short interval compared with the system’s natural period. A natural decay of oscillatory motion follows. Usually displayed as time history, as on an oscilloscope.

Shock Response Spectrum (or SRS): A plot of maximum response of SDoF systems vs. their natural frequencies, as they responded to an applied shock.

Signal Conditioner: An amplifier following a sensor, which prepares the signal for succeeding amplifiers, transmitters, readout instruments, etc. May also supply sensor power.

Simple Harmonic Motion: Periodic vibration that is a sinusoidal function of time.

Slew Rate: The maximum rate at which an instrument’s output can change by some stated amount.

Source Follower: A device for converting a high impedance electrical signal to low impedance. Also referred to as an “impedance converter”. Generally has a voltage gain of unity.

Spectrum: See Frequency Spectrum.

Standard Deviation: A statistical term: σ, the square root of the variance σ2, i.e., the square root of the mean of the squares of the measured deviations from the mean value.

Stationarity: A property of probabilistic vibration if the PSD (or ASD) and the probability distribution remain constant.

Steady-State Vibration: Periodic vibration for which the statistical measurement properties (such as the peak, average, RMS and mean values) are constant.

Stiffness: The ratio of force (or torque) to deflection of a spring-like element.

Strain-Gage Transducer: A changing-resistance sensor whose signal depends upon sensitive element deformation. In an unbonded wire strain-gage accelerometer, inertia affects a mass supported by nichrome wires; the wires change resistance in proportion to acceleration. The term may include piezoresistive accelerometers.

Stress Screening: A modern electronics production tool for precipitating latent defects such as poorly soldered connections. Utilizes random vibration + rapid temperature ramping.

Subharmonic: A sinusoidal quantity having a frequency that is an integral submultiple (x1/2, x1/3, etc.) of a fundamental (x1) frequency.

Time Constant: The interval needed for an instrument’s output to move 63% of its ultimate shift as a result of a change in its input.

Tracking Filter: A narrow bandpass filter whose center frequency follows an external synchronizing signal.

Transducer: (or Pickup or Sensor). A device which converts some mechanical quantity into an electrical signal. Less commonly, the reverse conversion.

Transient Vibration: Short-term vibration of a mechanical system.

Transmissibility: In steady-state vibration, T is the non-dimensional ratio of response motion/input motion: two displacements, two velocities or two accelerations. The maximum T value is the mechanical “Q” of a system. At resonance, T is maximum.

Velocity: Rate of change of displacement with time, usually along a specified axis; it may refer to angular motion as well as to uniaxial motion.

Vibration: Mechanical oscillation or motion about a reference point of equilibrium.

Vibration Machine (or Exciter or Shaker). A device which produces controlled and reproducible mechanical vibration testing of mechanical systems, components and structures.

Vibration Meter: An apparatus (usually an electronic amplifier, detector and readout meter) for measuring electrical signals from vibration sensors. May display displacement, velocity and/or acceleration.

Weight: That property of an object that can be weighted, as on a scale; the gravitational force on an object.

White Random Vibration: That broadband random vibration in which the PSD (ASD) is constant over a broad frequency range.