Note 1 to entry: 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 to entry: 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 to entry: Displacement can be:
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.

Note 1 to entry: In general, velocity is time-dependent.

Note 2 to entry: 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 to entry: 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 to entry: Velocity can be:
Velocities of short time duration are defined as transient velocities. Non-oscillatory velocities are defined as sustained velocities, if of long duration.

Note 1 to entry: In general, acceleration is time-dependent.

Note 2 to entry: 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 to entry: 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 to entry: 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 to entry: Acceleration can be:
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.

Note 1 to entry: 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.

Note 2 to entry: This “standard value” (g_n = 9,806 65 m/s² = 980,665 cm/s² ≈ 386,089 in/s² ≈ 32,174 0 ft/s²) should be used for reduction to standard gravity of measurements made in any location on Earth.

Note 3 to entry: Frequently, the magnitude of acceleration is expressed in units of g_n.

Note 4 to entry: 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.

Note 1 to entry: A force could also change a body’s size or shape if the body resists motion.

Note 2 to entry: 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.

Note 1 to entry: Variations with time such as shock processes or creeping motions are also considered to be oscillations in a more general sense of the word.

Note 1 to entry: The ratio may be one of forces, displacements, velocities or accelerations.

Note 2 to entry: This is sometimes known as a transmissibility function.

Note 1 to entry: 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 to entry: The difference between the maximum transient response and the value B is the value of the overshoot. This is usually expressed as a percentage.

Note 1 to entry: 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 to entry: The difference between the minimum transient response and the value B is the value of the undershoot. This is usually expressed as a percentage.

Note 1 to entry: This definition implies that the principle of superposition can be applied to the relationship between output response and input excitation.

Note 1 to entry: It can be fixed in a specified reference frame or it can undergo a motion.

Note 1 to entry: Seismic systems are usually idealized as single-degree-of-freedom systems with viscous damping.

Note 2 to entry: 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 to entry: 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.

Note 1 to entry: Many types of equivalence are common in vibration and shock technology:

Note 1 to entry: This applies to mechanical systems, not to be confused with statistical degrees of freedom.

Note 2 to entry: It is often referred to by the acronym DOF.

Note 1 to entry: 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.

Note 1 to entry: If the field is uniform, the centre of gravity coincides with the centre of mass (1.33).

Note 1 to entry: This is the point at which an object is in balance in a uniform gravitational field.

Note 1 to entry: 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 to entry: 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.

Note 1 to entry: 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.

Note 1 to entry: 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 to entry: 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).

Note 1 to entry: 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 to entry: 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.

Note 1 to entry: See the notes under complex excitation (1.42).

Note 1 to entry: It renders the system both inertially and elastically uncoupled, i.e. the modal mass and modal stiffness matrices are transformed into diagonal matrices.

Note 1 to entry: 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.

Note 1 to entry: 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 to entry: In the case of torsional mechanical impedance, the terms “force” and “velocity” should be replaced by “torque” and “angular velocity”, respectively.

Note 3 to entry: In general, the term “impedance” applies to linear systems only.

Note 4 to entry: The concept is extended to non-linear systems where the term “incremental impedance” is used to describe a similar quantity.

Note 1 to entry: See the notes under mechanical impedance (1.48).

Note 1 to entry: See the notes under mechanical impedance (1.48).

Note 1 to entry: Historically, often no distinction has been made between blocked impedance and free impedance. Caution should, therefore, be exercised in interpreting published data.

Note 2 to entry: 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.

Note 1 to entry: 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 to entry: Any changes in the number of measurement points or their location will change the blocked impedances at all measurement points.

Note 3 to entry: 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.

Note 1 to entry: 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 to entry: 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).

Note 1 to entry: 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 to entry: The term “point” designates both a location and a direction.

Note 3 to entry: The velocity response can be either translational or rotational, and the excitation force can be either a rectilinear force or a moment.

Note 4 to entry: 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 to entry: Mechanical mobility is the matrix inverse of mechanical impedance.

Note 1 to entry: 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.

Note 1 to entry: The terms “dynamic elastic constant” and “dynamic spring constant” are sometimes used.

Note 2 to entry: The dynamic stiffness may be dependent upon strain (amplitude and frequency), strain-rate, temperature or other conditions.

Note 3 to entry: The dynamic stiffness, k*, of a linear translational single-degree-of-freedom system characterized by the equation
is equal to

Note 1 to entry: The base of the logarithm, the reference quantity and the kind of level shall be specified.

Note 2 to entry: Examples of kinds of levels in common use are electric-power level, sound-pressure level, and voltage-squared level.

Note 3 to entry: The definition is expressed symbolically as:

Note 4 to entry: A difference in the levels of two like quantities q₁ and q₂ is described by the same formula because, by the rules of logarithms, the reference quantity is automatically divided out as follows:

Note 5 to entry: 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.

Note 1 to entry: 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).

Note 1 to entry: 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.

Note 2 to entry: 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.