Floor Vibration in Laboratory Buildings

Mei Wu¹, Slobodan Lukić², L. Zeng³

This article lists typical vibration criteria and demonstrates how Finite Element Analysis can be used in floor vibration prediction. It also gives options of mitigating vibration from various sources including pedestrian corridors, rotating mechanical systems, railways, roads, helicopter landing pads, and parking garages.

1. Vibration Criteria

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.

The following are a few generic vibration criteria for laboratory tools. There are many other generic criteria in between these, and there are always vibration criteria specified by the tool manufacturers.

50 micro-meters per second (2,000 micro-inches per second) is a typical vibration criterion for general labs with microscopes, precision balances, etc.

5 micro-meters per second (200 micro-inches per second) is common for electron microscopes such as SEM, TEM, STEM, AFM, etc. with a linewidth of 1/2 micro-meters.

1 micro-meters per second (50 micro-inches per second) for super-sensitive equipment with linewidth smaller than 0.1 micro-meters.

For comparison, ISO standard for residential buildings gives 142 micro-meters per second for night-time. Additionally, 500 micro-meters per second is often experienced in common office buildings.

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.

2. Floor Vibration Prediction

Floor vibration can be calculated using structural dynamics analysis or Finite Element Analysis (FEA) based on building structural elements, such as floor thickness, beam and girder sizes, column spans, etc. FEA is a powerful tool using differential and integral equations that shows all the details of the vibration. The following figures show how FEA is applied in some commonly encountered structural configurations.

Figure 1 shows a FEA model for in a building with three underground parking levels and five above-grade levels. The parking levels have a flat concrete floor (green) and the upper levels have concrete floors with steel beams and girders. The lower levels are connected by a common shear wall. Beams, girders, columns, and diagonal bracing members are also shown. The model is used to predict floor vibration on the upper floors caused by moving vehicles on the underground parking floors.

Figure 1. Building model used to predict floor vibration on the upper floors caused by moving vehicles on the underground parking floors.

Figure 2 shows a vibration mode (Mode 14) of a multi-story structural. The structure has concrete floors with steel girders and beams. The columns are shown as blue vertical lines. Girders and beams are shown as light blue lines. The color patterns represent the vibration levels over the floor. Red represents the highest vibration and dark blue represents the lowest floor vibration.

Figure 2. Vibration Mode 14 of a multi-story structural.

Figure 3a and 3b show the floor vibration modes of a rectangular floor with 25 structural bays. Girders and beams are indicated by green lines. Columns are located at the corner of each bay; each bay contains three beams. Two different vibration modes are shown; the one in Figure 3a is a lower mode with the highest vibration at the center of each structural bay. The structural bays alternate in a chessboard pattern for positive and negative displacement as the floor vibrates. Figure 3b shows a higher vibration mode where each bay contains two maximum displacements in opposite directions from each other.

Figure 3a. Vibration on a rectangular floor with the highest vibration at the center of each structural bay.

Figure 3b. Vibration on a rectangular floor where each bay contains two maximum displacements in opposite directions from each other.

Figure 4 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. This is important because it shows us that if there is a corridor 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 a vibration problem when located in the same structural bay with a major corridor, and are less likely to have a vibration problem in the bays away from the corridor, even when all structural bays have the same floor design.

Figure 4. Floor vibration with source at the center or the central bay.

Figure 5 shows the details of vibration distribution at the first resonant frequency over a single structural bay. Columns are located at the four corners of the bay, while 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. There is a corridor at the right edge of the bay, with an 80-kg person walking along the center of the corridor at 1 m from the edge (dotted line). The figure shows that at the first resonant frequency, floor vibration is highest at the center of the bay, and lowest at the corners. This is important because it shows if the floor is designed for a general lab, vibration criteria for sensitive tools such as SEM can be met if they are placed at the corners even when the vibration is 51 micro-meters per second at mid-bay.

Figure 5. Vibration contour of a rectangular bay with the source at the edge of the bay.

3. Vibration Control Options

Vibration control options very much depend on the type of vibration source.

For floor vibration generated by pedestrians in a building:

The first step should be to review the floor design and perform either FEA or structural dynamics calculations to predict floor vibration and modify the design if necessary to control vibration magnitude. It is more feasible and effective to mitigate vibration in the design phase since it may be practically impossible to change the structure after construction.

Usually structural dynamics calculations are 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 are conducted to predict the vibration at the sensitive equipment footprint caused by force at the actual excitation locations. Usually the detailed calculations give more accurate and therefore 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 the vibration source(s) and receivers in certain locations, this can reduce or eliminate the cost of vibration isolation measures. See examples in figures 4 and 5.

For rotating machines in a building, such as generators, pumps, or fans:

For new buildings, floor planning should include considering vibration transmission when choosing source location and receiver location.

For existing buildings, the first step to reduce vibration is to identify source and try to mitigate vibration at the source; for example steel springs reduce vibration to one tenth, air springs reduce vibration to one-thirtieth of the original vibration. Alternatively, vibration isolation tables may be used at the research tool.

Vibration isolation tables (with air springs) are low in cost and easy to apply, but they usually have a resonant frequency around 3 to 4 Hz. Therefore they only reduce vibration above 4 Hz, such as mechanical system vibration. They do not work for pedestrian-generated vibration if the building floor has low resonant frequencies.

Vibration generated by parking garage and helicopter landing pads:

For vibration generated by a parking garage in the basement or a helicopter landing pad on roof, it is best to do vibration calculations at the design stage, since there is little that can be done to mitigate the vibration after construction.

Vibration impact from sources outside the building:

For external mechanical systems, such as generators, pumps and fans, vibration control options will be the same as for indoor mechanical systems, with the addition of soil attenuation to the overall vibration calculation.

For roads with heavy vehicles and railways, site vibration tests and soil attenuation calculations can be used to predict the vibration at sensitive labs. Then a suitable lab location can be chosen. Trenches in the ground do not usually reduce vibration because significant attenuation occurs only when the trench depth is comparable with the wavelength in soil, which is impractical to achieve.

For construction vibration, such as pile driving near a lab building, site vibration tests and soil attenuation calculations can be used to predict vibration on lab floors. Low vibration construction procedures can be used to reduce the vibration if it is too high; for example, a vibratory pile driver can be used instead of a hammer.

Vibration control for super-sensitive tools:

There are vibration control options for super-sensitive tools with special needs. For example, building-in-building construction can be used to control air vibration generated by flying aircraft causing ground vibration. Also, sensitive labs can be located deep underground to reduce ground vibration since most man-made vibration is a Rayleigh wave (a surface wave).

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This is a brief overview of floor vibration control. The few examples given are typical ones to illustrate the principles of vibration control; the actual application of the principles can vary from case to case.

Sample Projects in Floor Vibration

¹Mei Wu is a principal at Mei Wu Acoustics.
²Slobodan Lukić is an acoustical consultant at Mei Wu Acoustics.
³L. Zeng is an FEA specialist affiliated with Mei Wu Acoustics.