Results from many of today’s laboratory tools can be compromised without an adequate answer to the problem of vibration. In the case of lab flooring, this can now be accomplished with finite element analysis (FEA).
This article lists typical vibration criteria and demonstrates how FEA can be used in floor vibration prediction. It also provides options for mitigating vibration from various sources including pedestrian corridors, rotating mechanical systems, railways, roads, helicopter landing pads, and parking garages.
Vibration criteria can vary, but commonly-encountered vibration criteria can be found in the following publications.
- American Institute of Steel Construction’s (AISC) Steel Design Guide Series 11.
- Department of Defense’s Unified Facilities Criteria (UFC), Section 2-3-c.
- National Institute of Health’s (NIH) General Design Guidelines, Section 4.E.3.7.1.
- American Society of Hearing, Refrigerating and Air-Conditioning Engineers (ASHRAE) Handbook, Chapter 47.
Tool manufacturers can also have their own vibration criteria. Results can vary, too. The ISO standard for residential buildings gives 142 µm per second for night-time, but 500 µm per second is often experienced in common office buildings.
Fifty micrometers per second is a typical vibration criterion for general labs with microscopes, precision balances, etc. and 5 µm per second is common for labs using electron microscopes such as SEM, TEM, STEM, AFM, etc. with a linewidth of 1/2 µm. One micrometer per second is typical for super-sensitive equipment with linewidth smaller than 0.1 µm.
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Figure 2a. Vibration on a rectangular floor with the highest vibration at the center of each of the 25 structural bays. Girders and beams are indicated by green lines. At the corner of each bay is a column, and each contains three beams. This figure shows a lower vibration mode with the highest vibration at the center of each bay. Image: Mei Wu Acoustics
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The vibration criteria quoted above are in terms of 1/3 octave-band root-mean-square (RMS) velocity. Tool manufacturer-provided criteria can be in acceleration or displacement units, in time or frequency domain, in any bandwidth, and in any term (RMS or peak, impulse or average, etc.). These can be interchangeable if certain assumptions are made.
Predicting vibration in flooring
Floor vibration can be calculated using structural dynamics analysis—which is based on structural elements such as floor thickness, beam and girder sizes, or column spans—or FEA, which uses differential and integral equations that show all the details of the vibration.
FEA can be used to model a wide variety of situations, including the effects of large objects moving within a parking garage (Figure 1), the distribution of vibration levels in a multi-story structure, and the locations of the most intense vibrations among structural cells on a single floor. FEA can help lab designers visualize complex vibrational behavior. The chessboard pattern of Figures 2a and 2b, for example, represents the positive and negative displacement of the floor as it vibrates.
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Figure 2b. In this case, each bay of the same floor in Figure 2a contains two maximum displacements in opposite directions from each other. Image: Mei Wu Acoustics
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Figure 4 differs from Figures 2a and 2b in that it shows the vibration of the same floor caused by a vibration source at the center of the central structural bay. As expected, the central bay has higher vibration than the other structural bays. If a corridor is located along the center row of bays, vibration will be high in these bays, and significantly lower in the bays in the other rows. Sensitive research tools may have vibration problems when located in the same structural bay with a major corridor and are less likely to have a vibration problems in the bays away from the corridor, even when all structural bays have the same floor design.
Figure 5 further refines the FEA approach by showing the details of vibration distribution at the first resonant frequency over a single structural bay. At the first resonant frequency, floor vibration is highest at the center of the bay, and lowest at the corners. If the floor is designed for a general lab, vibration criteria for sensitive tools such as an SEM can be met if the tools are placed at the corners even when the vibration is 51 µm per second at mid-bay.
As can be seen, vibration control options are very dependent on the type of vibration source. To control floor vibration from pedestrian traffic in a building, for example, the floor design should be reviewed using FEA or structural dynamics calculations to predict floor vibration. If necessary, designs can be modified to control vibration magnitude. It is more feasible and effective to mitigate vibration in the design phase; it may be impossible to change the structure after construction.
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Figure 4. Floor vibration with source at the center or the central bay. Image: Mei Wu Acoustics
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Structural dynamics calculations are typically conducted to predict the maximum floor vibration at the center of a structural bay generated by an excitation force at the center. If the predicted maximum vibration exceeds the criterion, detailed calculations can predict the vibration at the sensitive equipment footprint caused by force at the actual excitation locations. The detailed calculations give more accurate (lower) floor vibration than the maximum calculations.
Floor planning can play a crucial role in controlling vibration. If excess vibration can be avoided by placing vibration sources and receivers in certain locations, the cost of vibration isolation measures can be reduced or eliminated. See Figures 4 and 5.
For new buildings, source and receiver locations should be designed in consideration of vibration from rotating machines such as generators, pumps, or fans.
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Figure 5. Vibration contour of a rectangular bay with the source at the edge of the bay. Columns are located at the four corners of the bay and girders are on the left- and right-hand sides. Beams are represented by the horizontal lines in the image, which divide the bay into three equal, parallel sections. An 80-kg individual is walking along the center of the corridor on the right at 1-m from the edge (dotted line). Image: Mei Wu Acoustics
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For existing buildings, finding the vibration source is the key step to mitigating vibration and solutions can take the form of steel springs, vibration isolation tables (with springs), or even building-in-building construction.
Steel springs are very effective, and can reduce vibration to tenth or even a thirtieth of original levels. Vibration isolation tables are a convenient low-cost solution, but only reduce vibration above 4 Hz, such as mechanical system vibration. They do not work for pedestrian-caused vibration if the building floor has low resonant frequencies.
Building-in-building construction can be used to reduce vibrations from aircraft. Also, sensitive labs can be located deep underground to reduce ground vibration since most man-made vibration is a Rayleigh wave (a surface wave).
Site vibration tests and soil attenuation calculations can be used to predict the vibration in sensitive labs located near railroads, heavily travelled roads, or construction sites. Such testing, especially in the case of buildings with parking garages or helicopter landing pads, should be done during the design stage because little can be done to mitigate vibration afterward.
Published in R & D magazine: Vol. 51, No. 6, October, 2009, p.18-19.
