## FLOOR VIBRATION CONTROL

Wide column spans along with the use of high strength material (less of which would provide the needed structural integrity) tend to make modern composite floors flexible and oscillatory. Human activities (walking, running, dancing, etc.) and operating machines can induce high levels of vibration in such floors. Adding damping to the floor system, using tuned mass dampers, is a very effective way of floor vibration control.

Adding architectural features, mass and/or stiffness are normally viewed as possible solutions to floor vibration problem. Variations of these solutions include, but are not limited to, installing full-height partitions, adding framing members, and thickening the floor slab. Such solutions are costly to install in a new building and difficult to implement in, and cause inconvenience and disruption to the occupants of, existing buildings. In addition, a solution such as adding full height partitions contradicts the notion of open-plan office space popular in tenant fit-outs.

Reactive damping, provided by attaching tuned mass dampers (TMDs) to the floor, is commonly used for treating vibrating floors. Negligible weight penalty, low cost, and ease of installation make TMDs the most practical, cost-effective, and least disruptive floor vibration control solution for both new and existing floor systems.

## Background

A floor is a sophisticated, dynamic system. As a continuous structure, it has an infinite number of modes of vibration (degrees of freedom) but only the first few modes contain almost all the vibration energy of the floor. The first mode (fundamental mode) has the lowest natural frequency, the largest movement, and possesses the lion share (up to 80% in some applications) of the vibration energy. Frequently, quieting this mode alone lowers the overall floor vibration to an acceptable level.

Human activities excite floors at the first few natural frequencies. Such activities usually have to force frequencies in the range of 1.0 to 3.0 Hz. For instance, walking with a pace of about 2 Hz perturbs a flexible floor at that frequency and its higher order harmonics. When a harmonic of occupants’ activities are very close to or matches one of the natural frequencies of the floor, it makes the floor resonate at that frequency causing excessive vibration. As an example, in an office building with reported walking-induced vibration, the average walking pace of the occupants was measured around 2.35 Hz. The first resonant frequency of the floor was measured at about 4.7 Hz. Having the 2nd harmonic of walking exciting the first resonant frequency of the floor caused excessive vibration.

People are known to be very sensitive to floor vibration, e.g. vibration with an amplitude as small as 0.004 inch (0.1 mm) can cause aggravation. Floors that are most disturbing to the occupants often have low resonant frequencies; residential and office building floors having their fundamental frequency usually in the range of 3.5 to 8 Hz, fall in this category. This might be because the natural frequencies of the internal human organs are also in the same frequency range, i.e., 4 to 8 Hz. That is, floor resonance can cause the internal organs of the occupants to resonate resulting in an uneasy and irritating feeling.

Floor vibration affects not only the comfort of the occupants but also sensitive equipment that might be on the floor, especially in industrial and laboratory settings. Excessive floor vibration can even cause some equipment to malfunction.

## Typical Floors in Modern Buildings

Modern floor systems, which are frequently reported to have annoying vibration, are thin, lightweight concrete slabs supported by open-web steel joists. This economical floor system is commonly used in office buildings, schools, retail spaces, restaurants, etc.

It should be noted that on occasions a sturdy floor with thick, normal weight concrete slabs, the kind that does not fit the modern floor description, exhibits unacceptable vibration. The occurrence of vibration in such floors is most probably due to the lack of enough non-structural, architectural features on the floor, hanging from the underside of the floor, and even on the floor below. Also, having less office related live load such as filing cabinets in a paperless office can contribute to the floor vibration problem.

## Steady State and Transient Floor Vibration

Floor vibration can be classified as either transient or steady-state, depending upon the type of excitation and its duration. Floors subject to operating machines have a steady-state response because machines usually run continuously for a long period of time. Conversely, floor vibration due to occupants activities cannot easily be categorized as being either transient or steady-state. For the residential and office type environments, the excitation is the intermittent movement/walking of a small number of occupants; therefore, the floor vibration is mostly transient. But many steady-state, walking-induced floor vibration cases have also been reported in office buildings.

In a commercial environment, the floor vibration is mostly steady-state because the excitation is for the most part rhythmic walking with an approximately constant frequency. And in gymnasiums or dance studios, the forcing function is that of exercise activities or dancing resulting in mostly steady state floor vibration. As stated earlier, such activities can excite a floor at its forcing (fundamental) frequency and one (or more) of their higher order harmonics which might fall close to or exactly match one (or more) of the floor resonant frequencies causing the floor to resonate. Figure 1(a) shows a typical rhythmic activity, such as dancing, occurring at a frequency of 2.4 Hz, i.e., 2.4 steps/second. Figure 1(b) depicts such perturbation over 0.1-10 Hz frequency range. Of course, as expected, most of the power is at the fundamental frequency of 2.4 Hz but there also exist some power at 2nd, 3rd, … harmonics of that frequency.

## Human Perception of Floor Vibration

## Modeling of Floor Dynamics

The mathematical model of a vibrating floor is invaluable for investigating the dynamic behavior of a floor system and exploring the most suitable vibration mitigation solution for it. Floor models are normally constructed by identifying the modal parameters (natural frequencies, mode shapes, and damping ratios) of the floor via. experimental and/or finite element modal analysis. Considering that most of the vibration energy is in the first mode (or first few modes), it is common to include only the first mode (or the first few modes) in the floor model.

In addition to contributing to the construction of the floor model, mode shapes describing how the vibrating floor deforms at each natural frequency identify the nodal lines and the antinodes (points of maximum deflection). This information is invaluable for gaining insight into the vibration problem and optimal placing the vibration mitigation treatment on the floor.

Figure 2 shows the shapes of the first two modes of a composite floor system. The corresponding natural frequencies are 6 and 6.9 Hz, respectively. In most applications, quieting Mode 1 addresses the vibration issue in a floor system. This mode, also known as the ‘trampoline’ mode, is most active (has its anti-node) at the center of the floor.

## Floor Vibration Control

To have a floor which is lightweight provides open-space and yet is not prone to vibration (meeting the current serviceability guidelines), damping should be incorporated into its make up. If adequate damping is not provided by the construction material, architectural elements, other live loads, etc, then a damping solution should be added to the floor. Arguably the most cost effective and least disruptive techniques to damp annoying floor vibration is adding tuned mass dampers (TMDs) to the floor.

Tuned mass dampers are normally installed underneath the floor in the ceiling cavity below or above the floor in the floor cavity. In case such installation causes disruption (in an existing floor), tuned mass dampers can be installed on the floor enclosed in decorative cabinets, as well. Figure 3(a) and 3(b) depicts two tuned mass dampers appended underneath a non-composite steel joists-concrete and a composite steel beams-concrete floor system, respectively.

Figure 4(a) shows the magnitudes of frequency response functions (FRFs) of accelerance of mode 1 of a large mezzanine having the natural frequency of 4.2 Hz, without and with a 3000 lb TMD are presented in. The modal mass of the mezzanine is 103.5 lbs sec2/in (corresponding to the modal weight of 40,000 lbs), and modal damping ratio is 1.75%.

Figures 4(b) and 4(c) show the acceleration of the mezzanine in response to a heel drop perturbation as well as a tonal (harmonic) perturbation corresponding to the footfall impact of one person walking with the pace of 2.1 steps/sec, without and with the TMD. Evident from Figure 4-b, the impact-induced vibration of the structure with no TMD lingers for many seconds but with the TMD in place, the vibration subsides quickly. Moreover, the red trace in Figure 4(c) shows that the vibration of the treated mezzanine is well within 0.5% g, recommended in Design Guide 11.

Comparison of the red traces corresponding to the structure treated by tuned damping with the blue traces corresponding to the structure with no treatment, in Figure 4, clearly points to the effectiveness of the 2×1500 lb TMDs in lowering the resonant vibration of its target mode, i.e., mode 1 of the mezzanine.

In addition to designing and building the more traditional tuned mass dampers (TMDs) with viscously damped coil springs as their suspension, DEICON offers highly effective air suspended tuned mass damper engineered mainly for floor vibration control applications.