Modern floors with steel frames and concrete slabs extend across spans almost twice as wide as what used to be practiced a few decades ago; joist and girder spans exceeding 40 ft (~12 m) and 24 ft (~7.3 m), respectively, are common in office buildings. Wide column spans along with the use of high strength material (less of which would provide the needed structural integrity), as well as large column heights (in some commercial buildings) tend to make these floors flexible and oscillatory. Human activities (walking, running, dancing, etc.) and operating machines can induce high levels of vibration in such floors. 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 floors.

DEICON offers engineering services in vibration measurement and analysis of your floor, followed by customizing DEICON’s tuned mass damper(s) to your floor to abate its vibration.

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Background Typical Floors in Modern Buildings Steady State and Transient Floor Vibration Human Perception of Floor Vibration Modeling of Floor Dynamics Floor Vibration Control DEICON Tuned Mass Dampers

Background A floor is a sophisticated, dynamic system. As a continuous structure it has 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 forcing 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 is 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 floors, 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 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 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, the forcing function is that of dancing or exercise activities resulting also in mostly steady state floor vibration. As stated earlier, such low-frequency activities can excite a floor at its forcing frequency and its higher order harmonics one of which might fall close or exactly match one of the floor resonant frequencies causing the floor to resonate.

Human Perception of Floor Vibration Since the 1930s the perception of humans to floor vibration has been studied and a number of scales relating objective evaluation of a vibrating floor (in terms of vibration movement and its frequency) to a set of subjective perceptions (such as barely perceptible or definitely perceptible) have been developed. More recently American Institute of Steel Construction (AISC) has published the guide to serviceability design: Design Guide 11: “Floor Vibration Due to Human Activity” authored by Professor Murray, a leading authority in floor dynamics. In this guide, walking induced vibration (which can be viewed as steady state vibration) measured at 0.005g or higher in a quiet space such as an office and 0.02g or higher in a commercial, e.g. retail, are considered objectionable. Lenzen (Lenzen, K. H., 1966, “Vibration of Steel Joist-Concrete Slab Floors,” Engineering Journal, AISC, 3, pp. 133-136) presented a criterion for judging the transient floor vibration severity. According to Lenzen, the occupants would sense only the initial impact, e.g. of a heel drop, if the floor response diminishes within the first four cycles of oscillation. That is, when the amplitude of vibration after the fifth cycle is less than 20% of the initial amplitude, the floor vibration is barely perceptible, or not perceptible at all.

Modeling of Floor Dynamics Mathematical model of a vibrating floor is invaluable for investigating the dynamic behavior of a floor 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 few modes, it is common to include only these 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 to the vibration problem and optimally placing the mitigation treatment on the floor.

Figure 1 shows the natural frequencies and mode shapes of the first 3 modes of a test floor at Virginia Polytechnic Institute and State University (VPI). This 15 by 25 ft, one-bay floor is composed of a steel frame of two side girders (W14X22) and seven parallel joists (16K4) supporting a concrete slab on a metal deck. The lightweight concrete slab is 3.5 in. thick and is supported by 1.0 C metal deck. The floor is supported at the corners by four steel pipe columns, each with a diameter of 8 in. It has five modes of vibration in the frequency range of 0 to 30 Hz, all having less than 1% damping.

Mode 1 at 7.16 Hz Mode 2 at 10.44 Hz Mode 3 at 15.9 Hz Figure 1 The first 3 mode Shapes

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 load, 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 TMD(s) to the floor.

The two time traces in Figure 2-b show the transient vibration responses, to a heel drop excitation (see Figure 2-a), of the first mode of the VPI floor without and with a tuned mass damper. Evident from Figure 2-b, without the TMD the floor vibration lingers for many seconds but with the damper in place only the initial impact is felt and the vibration subsides quickly.

The heel-drop impact is commonly used to evaluate the vibratory characteristics of a floor. This perturbation is the dynamic load of a 190 lb (85.5 Kg) person who stands on the toes of both feet, then strikes the floor with both heels from a distance of 2 inch (5 cm); see Figure 2-a.

Figure 2 Heel drop excitation (a) and floor vibration response (b)

DEICON Tuned Mass Damper DEICON has recently introduced highly effective air suspended tuned mass damper and Viscoelastic Tuned Mass Dampers engineered mainly for floor vibration contorl applications. Tuned mass dampers are normally installed below the floor in the ceiling cavity. In case such installation causes disruption to the occupant (in an existing floor), tuned damperd can be installed on the floor enclosed in decorative cabinets, as well.

After analyzing the vibration of a particular floor, DEICON will customize its tuned dampers to the vibrating floor. The damper(s) will then be fabricated and shipped to the site with the installation instructions. DEICON will oversee the installation and fine tune the damper(s) after its (their) installation.

Air Suspended Tuned Mass Dampers Viscoelastic Tuned Mass Dampers

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