Sensitive Equipment Criteria and Footfall-Induced Vibrations—Background and Problems
By Eric E. Ungar
The vibration criteria that are widely used to specify floor vibration limits in sensitive facilities are scaled from data on human perception and thus are, at most, marginally applicable to sensitive equipment. Specified limits logically should apply to vibrations resulting from all sources but often are applied only to vibrations due to footfalls. Several approaches to calculating the vibrations of a floor due to walking excitation are available, with the results depending to a considerable degree on the magnitude of the structural damping, which generally must be estimated.
In the 1980s it became apparent that the sensitive equipment used in the production of microelectronics would need to be protected from excessive vibration and that facilities housing such equipment need to be designed to enable implementation of this protection. Consequently, there arose the need for a means for specifying limits on the vibrations in these facilities, and this need was met by criteria represented by a series of curves like those of figure 1, which eventually became known as the “vibration criterion” or the “VC” curves and have found wide use.
The curve in this figure labeled “Operating Theater” corresponds to the standard threshold of tactual perception of steady vertical vibration by the most sensitive persons; the other curves were obtained by shifting the aforementioned curve up and down by successive factors of two. Thus, criteria intended to protect sensitive equipment were based somewhat illogically on the human perception threshold. Some of these curves eventually were modified, largely by replacing the sloping portions of the curves by horizontal extensions of the horizontal portions.
Even with these modifications, the VC curves rarely represent the vibration limits stated for items of sensitive equipment by their suppliers, which one would expect to be more realistic. Also, the equipment suppliers’ limits rarely are given in terms of one-third octave-band spectra of velocity, in which terms the VC curves are stated.
Nevertheless, the VC curves are still widely used for specification of the vibration environments in sensitive areas. Quite often, the requirement for a facility is stated simply as “Do not exceed X microinches (or micrometers) per second” or “Do not exceed VC-Y.” Such a simply stated limit generally is intended by designers or users of a facility to apply to the vibrations resulting from all sources, but it is often interpreted as applying only to footfall-induced vibrations. One may expect that in most practical situations the vibrations from all sources—such as the mechanical systems that serve the building, the users’ equipment, and street traffic—need to be controlled before the vibrations induced by walking personnel become of significant concern.
Approaches to predicting the vibrations of floor structures due to personnel walking on them are set forth in a number of guideline documents. Most of these focus on vibration environments from the personnel comfort standpoints using various acceptability criteria, and some address sensitive equipment rather cursorily. It appears that only one recent publication provides a relatively simple approach to calculation of footfall-induced vibrations in a form in which the calculated results can be compared directly to the VC criteria (or to other criteria stated in terms of one-third octave-band spectra of velocity).
The recent guides, in essence, distinguish between “low-frequency floors” and “high-frequency floors,” with a low-frequency floor structure defined as one whose fundamental natural frequency is lower than the frequency of the highest significantly large harmonic ( typically, the fourth) of the step (footfall impact) frequency associated with the walking speed under consideration. Thus, a series of footfalls have the potential of exciting a low-frequency floor’s fundamental mode at resonance and thus producing relatively severe vibrations. In contrast, the fundamental mode of a high-frequency floor—a floor whose fundamental frequency is greater than that of the aforementioned highest significant harmonic—cannot be excited at resonance by a significant harmonic of the step frequency. A high-frequency floor’s response to each footfall in essence consists of a “spike” (a rapid rise in displacement, followed by a somewhat-less rapid drop-off) and residual vibrations of relatively small magnitudes between successive spikes, with the interval between spikes being of much longer duration than that of a spike.
As is well known, the magnitude of a structure’s vibration at resonance is inversely proportional to the structural damping; thus, the magnitude of the footfall-induced vibrations one predicts for a low-frequency floor depends crucially on the magnitude of the damping one uses in the predictive calculations. As mentioned earlier, the footfall-induced vibrations of a high-frequency floor includes relatively extended intervals of decaying vibrations between spikes associated with individual impacts. Since the rate of decay of these vibrations depends on the structural damping, the time-averaged walking-induced vibrations one calculates for high-frequency floors also depend significantly on the structural damping. Thus, the analyst again is in the unenviable situation of needing to carry out predictive calculations, the results of which depend markedly on the value of a parameter that must be assumed on the basis of experience.
 See American National Standard ANSI S3.29-1983, “Guide to the Evaluation of Human Exposure to Vibration in Buildings,” and International Standard ISO 2631-1978, “Guide for the Evaluation of Human Exposure to Whole-Body Vibration.”
 For more details, see E. E. Ungar, “From Guess to Gospel—the Curious History of Floor Vibration Criteria,” Sound and Vibration (October 2016): 4.
 Such vibration criteria are illustrated in Eric E. Ungar, “Vibration Criteria for Healthcare Facility Floors,” Sound and Vibration 41, no. 9 (September 2007): 26–27.
 For example, RWTH—Aachen University, “Human Induced Vibrations of Steel Structures,” RFS2-CT-2007-0003; JRC European Commission, “Design of Floor Structures for Human Induced Vibrations,” EUR 24084 EN-2009; Applied Technology Council, “Minimizing Floor Vibration,” ATC Design Guide 1, i999; Steel Construction Institute, “Design of Floors for Vibration: A New Approach,” SCI Publication P354; and Concrete Society, “A Design Guide for Footfall Induced Vibration of Structures,” CP-016 (2006).
 American Institute of Steel Construction, “Vibration of Steel-Framed Structural Systems Due to Human Activity,” Steel Design Guide 11 (2016).