Prediction of impact noise from gym sources on resilient matting Nikhilesh Patil 1 Hoare Lea 601 Royal Exchange, Manchester, M2 7FL Martin McNulty 2 Hoare Lea 601 Royal Exchange, Manchester, M2 7FL

ABSTRACT Controlling impact noise from heavy weight drops continues to be a challenging design issue in new and existing gyms. Within the design and prediction phases, in-situ measurements on bare slab and flooring test samples are often required to reduce uncertainty. However, these can be intrusive, and there is no consistent test methodology within the industry as of yet. This is further complicated by the nature of problem – a large number of source mass and height combinations and potential floor- ing test samples to be tested with such source combinations. Emerging guidance within the UK is likely to fill gaps on predictions for typical gym floors with reliance on engineering grade assump- tions and empirical limits. However, this does not necessarily subside the need for robust in-situ test data to complement such predictive approaches. As such, there is a need for a methodology which bridges the gap between prediction and in-situ test elements which is reliable, time efficient and can be used for predictions on wider source cases and in varied locations or structures. The paper dis- cusses potential ways of simplifying prediction and testing strategies with a view to estimating the noise and vibration levels from gym floors with resilient layer. It is shown that if certain quantities can be independently characterized in a laboratory, then this would avoid the need of weight drop testing in-situ.

1. INTRODUCTION

Controlling impact noise from gyms continues to be a design challenge to acoustic consultants world- wide and the adverse health effects are becoming well documented [1]. Whilst gyms have been iden- tified as a wish-list item in choosing a residential apartment, this driver has not done enough to push designers towards a robust approach in predicting its impact. To date, there is no consistent or ac- ceptable standard to predict gym impact noise that can be readily applied in early stages of design. The onus is rather put on control stage in a rather heavy-handed approach of high-performance heavy mass floating floors. This still requires a level of iterative testing on smaller samples and offers little room for optimization. For example, the architectural, cost allowance may not allow for the best floating floor and end user expectations may deviate from what a mitigation system (e.g., floating floor) has been designed in for.

1 nikhileshpatil@hoarelea.com

2 martinmcnulty@hoarelea.com

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There is an emerging consensus that such acoustic design issues could be potentially solved with a robust prediction method. When this prediction method (either wholly measurement-base, wholly simulation-based or a combination of the two) can be applied early on in the design process this can highlight expected mitigation or control system to be used on a case-by-case basis.

2. IMPACT NOISE FROM GYMS

In typical gym setting, the problem of impact noise has to be dealt with a mitigation solution. This can take form of a floating floor or resilient matting or a combination of the two. Resilient mats can exhibit non-linearity (stiffening) with increased impact loads and can offer added complexity in the predictions. In this paper, we have targeted the problem in the linear range, where the loads do not significantly lead to local stiffening from excessive compression at the impact location.

During a testing stage on site to determine the in-situ performance, often a number of matting combinations are tested. This can become cumbersome when a number of mass-height combinations of the weight drops are to be tested manually. The number of unlimited permutations can make it practically impossible to simulate every scenario within a typical test period. A judgement has to be made on part of the consultant and the end user feedback on types or weights and user patterns (if known) to simulate the most likely impact event(s). However, that still does not get rid of the require- ment to test multiple combinations of weights.

One potential way of addressing this is a hybrid approach – whereby in-situ data of the re- ceiver (sub floor) and dynamic characteristics of the resilient matting can be combined in a prediction model to enable simulation and prediction for a range of impacts and mats in a time effective manner. This would limit the need of testing multiple weights on site. Furthermore, if a library of laboratory test data of the right dynamic characteristics of the mats is available, the modelling may allow for optimized selection of mats based on predictions. The question now arises as to whether such an approach is feasible and if so, what characteristics can be adequately coupled for the receiver (sub floor) and the isolating material (the resilient matting). To this end, a discussion and methodology is presented in the next section. 3. METHODOLOGY

Let us represent the physical system as a source receiver system. For the sub floor, assuming the construction is test ready, the response of the floor to a known force can be established. This can be obtained in terms of an Accelerance (Acceleration/force, A ) or Mobility (Velocity/force, Y ) Fre- quency Response Function (FRF) which characterizes the vibration response of the floor slab to a unit force excitation at an impact location. Note that similarly a vibracoustic FRF (sound pres- sure/force) could also be measured but this is generally sensitive to background noise. If the mat is also considered a part of the receiver, then these FRFs can be measured with the mat included (i.e., with the excitation on top of the mat). Therefore, depending on whether the resilient matting is in- cluded as part of the source we can characterize two forces, namely,

 Forces above the mat into the mat-floor receiver (R1)  Forces below the mat into the floor receiver (R2)

The representation of the two receiver systems R1 and R2 is shown in Figure 1 below.

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Figure 1: Representation of resilient mat on sub floor into two possible receiver systems. R1 includes only the sub floor as receiver and R2 includes the resilient mat as part of the receiver.

We can now write the injected forces into the mat as,

−1 𝑣 𝑐1𝑐1

′ (1)

𝑓 𝑐1 = 𝑌 𝑐1𝑐1,𝑅1

𝑌 denotes the mobility FRF, and 𝑣 ’ denotes the operational velocities measured under impact source excitation. Usually, it would be difficult to measure acceleration directly at the impact or con- tact location, so we can formulate the forces remotely in terms of remote responses at ‘n’ location and transfer FRF’s as,

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′ (2)

−1 𝑣 𝑐𝑛

𝑓 𝑐1 = 𝑌 𝑐𝑛𝑐1,𝑅1

Where, 𝑐 𝑛 are the remote locations where one can easily measure responses. We can similarly write an equation for the forces into the floor as,

′ (3)

−1 𝑣 𝑐𝑛

𝑓 𝑐2 = 𝑌 𝑐𝑛𝑐2,𝑅2

Note that in both cases, only the measurement of transfer FRFs are different (with and without the resilient mat). The operational responses in both cases are still measured with the weight impact- ing on the resilient layer. Thus, we can see there are two options with which one may choose to characterise the source i.e., with or without the mat included as a source. The operational response at an unknown receiver location ‘m’ can then be predicted as,

′ = 𝑌 𝑐𝑚𝑐1,𝑅1 𝑓 𝑐1 = 𝑌 𝑐𝑚𝑐2,𝑅2 𝑓 𝑐2 (4)

𝑣 𝑐𝑚

This qualifies as the prediction methodology whereby if the forces into the mat or the floor are known and the in-situ transfer FRF’s can be measured on site, then the response at remote receiver location(s) can be predicted. This would rely on the pre-characterization of the forces in a laboratory setting by the supplier. However, for this method to be advantageous, where the process of dropping weights in-situ is not required, the forces would need to be transferable from a laboratory to in-situ setting. In literature, so far blocked forces have been proven to be a transferable quantity irrespective

of receiver [2]. A similar approach has been used within [3,4], however the study utilizes forces on top of the mat with the transfer functions of bare floor which is not mathematically consistent.

If one considers the blocked forces below the mat (i.e., mat is included in the source), this will require the transfer FRF’s to be measured from the coupling point to the receiver locations of interest – a task which would be practically challenging because of inaccessibility to the coupling point un- derneath the mat. That would leave measurement of forces at the top of the mat to be the favourable option.

The forces on top of the mat can be characterized as injected force or blocked forces. The latter has been proven to be independent in case of steady state sources. However, this may not be the case for transient or impact sources as the receiver structures’ contact stiffness can affect the source mechanism (contact times) i.e., change the source characteristic. As such, the concept of blocked forces may not be strictly applicable in such cases and has been measured before in the context of impact sources [5]. But the injected force can nevertheless be measured. Now let us exam- ine if the injected forces into the mat can be considered transferable. We present an equivalent repre- sentation of the mat and floor system as below in terms of the dynamic stiffnesses.

Figure 2: Representation of the mat-floor receiver system under impact excitation (left) and a simpli- fied version (right) when the floor stiffness is sufficiently higher than the mat ( 𝑘 𝑚𝑎𝑡 ≪𝑘 𝑓𝑙𝑜𝑜𝑟 )

For the case of ground bearing slabs (considered within this paper), the contact stiffness of the floor can be considered to be significantly higher to that of the mat’s stiffness. In such case, the system can be approximated as a mat on rigid base. The injected force then can be characterized in the laboratory on a rigid base and in principle, transferred to an in-situ setting as long as the stiffness assumptions are maintained. This may break down on a very compliant floor where the stiffness assumptions break down (thin suspended slabs). However, for the context of this paper, ground bear- ing slabs are of interest, where the stiffness assumption is generally valid. 4. TESTS AND RESULTS

To test the methodology described above, we tested a typical mat system on a ground bearing slab. As laboratory characterization of the forces was not available, two distinct locations were chosen on the floor to characterise the forces injected into the mat. If the stiffness assumptions are valid, then the injected forces into the mat should be similar. For this purpose, two locations within the L-shaped ground bearing slab were chosen. The schematic of the test setup is shown below.

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Figure 3: Force characterization at two locations on the ground bearing slab (Location A &B). In black, is the resilient mat, and in orange are the sensors.

The objective of the test was therefore twofold,  To test the similarity/transferability between characterized forces into the mat at both loca-

tions, and  To predict the response at location B using the characterized forces at a parent location A.

As per Equation (2), a series of transfer FRFs at each location were first measured from top of the mat (as the excitation location). Later, in the operational phase, a 10kg kettlebell was dropped from knee height onto the mat and operational responses measured at the same response locations. The knee height is commonly used drop height in traditional testing of gym floors. As per Equation (2), the forces measured at both locations above the mat were calculated and are presented below.

Force N 10° 10° 10! 10" Hz — Force - location A — Fore - location 8 10"

Figure 4 Injected forces into the mat at both locations A & B

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As per Figure 4, we can see that the forces measured on top of the mat are very similar to both locations A and B. This highlights that the stiffness assumption ( 𝑘 𝑚𝑎𝑡 << 𝑘 𝑓𝑙𝑜𝑜𝑟 ) is valid here. The force spectrum is a characteristic of a sine-pulse excitation with finite contact time. Above 100Hz the magnitude falls sharply and beyond 400 Hz, the spectrum is mostly an artefact of noise. Therefore, the appropriate frequency range for this setup was assessed to be up to 400 Hz. This is also a charac- teristic of low frequency source of weight drop on a resilient soft mat. Using these forces, the accel- eration response at two remote locations at B were predicted as per Equation (3). This is shown below in narrow band and one-third octave band below.

Acceleration m s~* Response at remote location B (Frocquency Hr

Figure 5: Narrow band response at remote locations B using measured forces at location A and B against directly measured response

‘Acceleration dB Response at remote location B eesesas ne

Figure 6 One-third octave band response at remote locations B using measured forces at location A and B against directly measured response

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The results in Figure 5 and Figure 6 show that the predictions at a remote receiver location can be predicted using the forces characterized at a different location (in this case A). This further shows the validity of the presented approach and the stiffness assumptions for this case.

The prediction error is also plotted below for averaged responses of the two remote locations considered. The error is plotted as (predicted – measured) responses, so that negative values highlight underprediction and vice versa. As seen below, some underprediction in the 125 Hz band using forces (A) are evident however this is a case of SNR affecting the force characterization (see Figure 4). If the forces can be characterized at a controlled condition on a laboratory setup, the results are likely to improve beyond currently obtained results.

Figure 7 Prediction error as (Predicted – Measured) results averaged over two remote locations.

6. CONCLUSIONS

Prediction of impact noise from gym floors remains a challenge. Without extensive in-situ testing of mat, mass and height combinations, which remains the current strategy, the impact cannot be assessed in a simple and time effective manner. To avoid this tedious test strategy, an option is presented whereby the source forces onto the mat can be characterized beforehand and provided by the supplier and combined with in-situ transfer functions. Thus, the site testing is limited to only measuring Fre- quency Response Functions (FRFs). This would then follow with the desktop prediction of impact noise and vibration for a range of conditions. A test case of weight drop on a ground bearing slab with mat (resilient layer) is presented. The results show that vibration on the receiver floor in presence of the mat can be predicted with reasonable accuracy when forces are characterized at a different location and transferred to the location of interest to allow prediction. Further work is needed to validate this approach on suspended slabs. The current approach would also require testing the FRFs in presence of a mat. Further development is needed to avoid the need of mat and implement only a bare floor FRF testing to be used within the predictions.

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6. REFERENCES

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Activities: Do They in Turn Unnecessarily, Indirectly Affect Our Health?. Applied Sci- ences , 11 (24), 11812. 2. Moorhouse, A. T., Elliott, A. S., & Evans, T. A. (2009). In situ measurement of the blocked force

of structure-borne sound sources. Journal of sound and vibration , 325 (4-5), 679-685. 3. Golden, M., & Musafere, F. (2019, October). Continuing Prediction of Heavy/Hard Impacts on

Resilient Sports Floors in Existing Buildings. In INTER-NOISE and NOISE-CON Congress and Conference Proceedings (Vol. 260, No. 1, pp. 261-268). Institute of Noise Control Engineering. 4. Golden, M., LoVerde, J., Dong, W., Rawlings, S., & Silva, R. (2021, August). Prediction of one-

third-octave band sound and vibration levels from heavy-hard impacts. In INTER-NOISE and NOISE-CON Congress and Conference Proceedings (Vol. 263, No. 2, pp. 4692-4700). Institute of Noise Control Engineering. 5. McNulty, M., & Patil, N. (2019, September). In-situ characterisation and prediction of heavy

impact-generating events in buildings. In INTER-NOISE and NOISE-CON Congress and Confer- ence Proceedings (Vol. 259, No. 3, pp. 6987-6996). Institute of Noise Control Engineering.

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