Investigating the use of dynamic sub-structuring methods in predicting floating floor performance. Martin McNulty 1 Hoare Lea Vibration Royal Exchange, Manchester, M2 7FL Nikhilesh Patil 2 Hoare Lea Vibration Royal Exchange, Manchester, M2 7FL

ABSTRACT Floating floors are a common means of reducing airborne and structure-borne noise, however, pre- diction of in-situ performance remains a challenge for many consultants. The specification of such floors, usually based on single degree of freedom assumptions, does not account for the influence of floating floor dynamics, dynamics of host structures or interplay/power flow between the two via the isolating mounts. Reliance on single degree of freedom systems tend to over-predict the performance of the floating floor element, often leading to noise/vibration issues in the finished construction. A more robust approach is needed, though is challenging due to complexities in characterising large- scale constructions, where source-to-receiver Frequency Response Functions (FRFs) must account for multiple points of contact between floating and structural elements. This paper first presents a hybrid method for evaluating the source-receiver FRF of a simple floating floor via a sub-structured approach and confirms the validity of the method to that of the source-receiver FRF measured di- rectly whilst accounting for real world limitations in a building acoustics consultancy setting.

1. INTRODUCTION

The design of floating floors to control vibration has become crucial in recent times, owing in part to the increased levels of urban densification and mixed-used developments. A common example of this is the siting of gymnasium facilities within high-rise apartment dwellings. It was often assumed by suppliers and acoustic practitioners alike that the reduction in vibration (and therefore noise) offered by floated floor systems would be similar to laboratory or theoretically derived transmissibility values based on Single Degree of Freedom (SDOF) systems. It has been the case that many such installations have been inadequate in controlling noise and vibration transfer, not least since impact events from falling weights are impulsive in nature, producing a broad spectral response. To be able to accurately predict the performance of floating floors prior to procurement of them is advantageous, since the cost and spatial implications associated with such systems can be prohibitive. This paper presents efforts to predict the frequency response function of a concrete floating floor on helical springs via dynamic substructuring methods. No active source is present in this study, since

1 martinmcnulty@hoarelea.com

2 nikhileshpatil@hoarelea.com

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the floating floor element, under impact excitation for example, essentially becomes the source ele- ment itself. Methods to couple similar assemblies with active sources [1] have been shown to be effec- tive when adopting an experimental approach to characterising the individual elements. Predictions herein are based on a hybrid model comprising measurement data of the receiving element, namely a structural subfloor, and simulated components being that of the floated concrete floor and the isolators upon which it is mounted. 2. THEORY

In keeping with dynamic substructuring nomenclature, a coupled assembly comprising individual components of Source, S , Receiver, R , and Isolator, I , can be visualised as per Figure 1 below with primary components described in Table 1. Table 1: Component identification.

Element Reference Component

Source S Floating Floor

Isolator I Spring isolators

Receiver R Structural sub-floor

Figure 1: Source, Receiver and Isolator nomenclature

Further referencing is required to rationalise the fully coupled system (as per Figure 1) into its sub- structured components and thus express the Frequency Response Function (FRF) relationships be- tween them. The appropriate referencing is provided in Table 2 and Figure 2. Table 2: Assembly referencing notation

Element Reference

Fully coupled assembly C

Partial assembly X

Source-side contact points to isolator c

Receiver-side contact points with isolator d

Receiver side observation point (remote point) e

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Figure 2: Assembly and substructure referencing

Traditionally, the dynamic characteristics of each element (S, I, R) are required to enable prediction within dynamic substructuring or similar approaches. Within problems in building acoustics such as vibration from a potential gym installation, the choice of how individual elements are or can be char- acterised is limited. For example, the receiver floor slab which forms part of a complex building structure may not suit well to full scale simulation approaches due to inherent complexities of mod- elling large scale structures. An in-situ measurement can be relatively easier yet demanding approach for this receiver element. On the other hand, the source structure i.e., a floating floor slab (traditionally a rectangular plate of finite thickness) may be well suited for modelling. A direct measurement for a full scale “independent” floating floor slab is impractical prior to installation. As such, modelling option for the source element is suitable subject to careful consideration to the material properties. For the third element, namely the Isolator (I), usually only the static stiffness data is available from floating floor system manufacturers. The ISO 10846 standard deals with dynamic characterisation of isolators however the adoption of such detailed characterisation within floating floor manufacturers is limited so far. On the other hand, these methods are heavily adopted and widely used by the auto- motive industry. Nonetheless, to enable a frequency-wide prediction, dynamic stiffness data (rather than static stiffness) is more preferable. Note that in this context, the dynamic stiffness refers to fre- quency dependent stiffness for a given load, not the change in stiffness with respect to load. The latter is used to describe the non-linear behaviour in isolators, especially of elastomeric makeup. The au- thors have assumed the isolators within the scope of this current study (helical springs) to behave linearly even within the operating load range. Acknowledging the above, and assuming that individual elements S, I and R can be characterised independently, the dynamic response of the coupled floating floor system can be expressed in terms of a coupled transfer FRF. This FRF can be predicted according to Equation 1 [1]

point (6) : ae os, : SS asenty Receiverside i Mexreostenheomressnte Recener (8)

−1 𝐴 𝐼 ൣ− 𝐴 𝐼 (𝐴 𝐼 + 𝐴 𝑅,𝑑𝑑 ) −1 𝐴 𝐼 + 𝐴 𝐼 + 𝐴 𝐶,𝑐𝑐 ൧

−1 𝐴 𝐶,𝑐𝑏 (1)

𝐴 𝑋,𝑒𝑏 = 𝐴 𝑅,𝑒𝑑 ൣ𝐴 𝐼 + 𝐴 𝑅,𝑑𝑑 ൧

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For the above, a series of subscripts are necessary to describe the coupling between the various ele- ments and are provided in the table below with information as to how they have been obtained in this paper. The method of characterisation is in-line with a typical case of floating floor problem where the receiver could be measured, the characteristics of the floating floor can be simply modelled, and the characteristics of the isolators can be assumed from the very limited static stiffness data. Thus, the predictions presented later are in keeping with Equation [1] whilst accommodating the practical options of a real-world scenario. It is of interest to understand on if and how well such predictions can be made under these conditions. Table 3: Coupling reference notation and description of methods used to obtain them.

Metric Reference Measured/ Predicted

𝐴 𝑅,𝑑𝑑 Accelerance matrix of the uncoupled re-

Measured

ceiver subfloor 𝑅 . Excited at 𝑑 , observed at 𝑑

𝐴 𝑅,𝑒𝑑 Accelerance matrix of the uncoupled re-

Measured

ceiver subfloor 𝑅 . Excited at 𝑑 , observed at 𝑒

𝐴 𝐶,𝑐𝑐 Accelerance matrix of the uncoupled

Predicted (via Finite Element Modelling)

source floating floor 𝐶 . Excited at 𝑐 , observed at 𝑐

𝐴 𝐼 Accelerance matrix of the isolators.

Predicted (via static stiffness data)

𝐴 𝐶,𝑐𝑏 Accelerance matrix of the uncoupled

Predicted (via Finite Element Modelling)

source floating floor 𝐶 . Excited at 𝑏 , observed at 𝑐

𝐴 𝑋,𝑒𝑏 Accelerance matrix of the fully coupled

Predicted (Substructuring) and Measured

(for Validation)

assembly 𝑋 . Excited at 𝑏 , observed at 𝑒

3. MEASUREMENTS – COUPLED ASSEMBLY AND RECEIVER

Testing was undertaken on a floating floor sample, installed upon a ground bearing slab in the sub- basement of Hoare Lea’s Manchester Office at the Royal Exchange, Manchester. A brief description of the floor is provided below.

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Table 4: Test element description

Element Detail

Floating floor Reinforced concrete 1.6 x 1.2 x 0.1m

38 er ® oO

Isolators (jacks) 6 no. steel helical spring isolators

Structural subfloor Ground bearing concrete slab, thickness unknown

Figure 3: Test floor diagram

To obtain the measurement-based metrics stated in Table 3, it was necessary to undertake testing of both the coupled assembly (for the purpose of validation) and the uncoupled (bare) receiver floor. The uncoupled aspect was undertaken following removal of the floating floor which resulted in a degree of subfloor damage which may have influenced the quality of data for 𝐴 𝑅,𝑑𝑑 elements.

Figure 4: Floating floor (left) and subfloor (right). Image right shows signs of damage which oc-

curred during dismantling of the floating floor element.

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Sensors were arranged at each of the contact points between isolator and structural subfloor with an additional remote receiver location, to enable validation. Accelerance FRF measurements of 𝐴 𝑅,𝑒𝑑 , 𝐴 𝑅,𝑒𝑏 and 𝐴 𝑅,𝑑𝑑 were undertaken with a 16 channel DEWESOFT Sirius modular Data Acquisition System (DAQ) with excitation provided via instrumented force sledgehammer. The specified isolation frequency of the mounts for the load provided was 3.167Hz which would typically qualify as a high-performance system. Given that and consequently measuring FRFs of a system on a stiff subfloor, coherence issues were evident at the remote point location below 100Hz and above 500Hz

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Coherence

1 10 100 1000

Hz

Figure 5: Remote point coherence

In addition to the metrics stated in Table 3, tests were undertaken to review the mode shapes presented during FRF testing of the floating floor. The grid arrangement was sufficient to capture the first 5 modes of the floor and then post process the results to visually inspect the modal behaviour of the floating floor and later compare to the simulated components. 4. SIMULATED COMPONENTS – FLOATING FLOOR SLAB

Prediction of slab behaviour was undertaken using ANSYS (2021 R2) proprietary Finite Element (FE) modelling software. A series of steps were undertaken comprising modal and harmonic response forms of analysis. Input data regarding isolator stiffness was taken directly from supplier literature for the units provided. Floating floor mass estimates were assumed first by reliance on typical material properties for concrete (circa 2300kg/m 3 density). This was later refined via review of measurements which identified the first mode of the slab on springs to be in the region of 3.2Hz as per the isolator catalogue information. A constant structural damping coefficient value of 0.01 (1% of critical damp- ing) was used throughout. The geometry of the model does not include any reinforcing elements through the concrete as per the installed condition – this was intentional to reduce computational time and test the feasibility of modelling floors of this type in a relatively simple manner. The isolator elements in modal studies were modelled as a COMBIN14 idealised springs with fixed supports ap- proximating contact with the structural subfloor. Note that this does not model the inherent dynamics of the spring but merely applies an idealised spring with static stiffness.

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The results of the modal analysis were compared to mode shape measurements, obtained from a grid- array of sensors during physical FRF measurements of the floating floor. Four of the 5 modes cap- tured by the study (modes 1,3,4 and 5) are presented below. Mode 2 is omitted since the frequency is at a similar frequency to mode 1 and therefore difficult to extract from measured data.

Mode Measured Frequency

Measured mode shape

Simulated

Simulated mode shape

Fre- quency

1 3.2Hz 3.2Hz

3 4.2Hz 4.02Hz

4 34Hz 34Hz

5 44.3Hz 43.2Hz

Given confidence that the FE model was able to reasonably capture the early modes of the floating floor, the FE modal survey was extended to resolve the first 2500 modes and the results then utilised via the modal superposition method to determine the accelerance FRF with 1N point excitation in the central region, up to 1000Hz. The results of the simulations undertaken are summarised in Figure 6 and include further results from alternative modelling approaches. The additional approaches consid- ered were that of solid body mesh refinement, direct solution method, shell modelling of the floating floor and shell modelling with jack locations as holes in the slab - as per the installed condition. It can be seen that results provide a reasonable fit to the measured FRF, though some modal peaks are absent in the 200-300Hz region. This may be attributed to material property inconsistencies, the ef- fects of geometry rationalisation, static spring modelling, or effects from the substructure given the in-situ measurement was a fully coupled assembly. The simulated results used in this paper are also those based on a single set of material properties with no randomised parameterisation utilised to predict a suite of FRFs. This would likely be a more viable and lower risk approach in commercial applications since test structures may not be available for model validation purposes.

—SS

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Measured vs Predicted FRF

1.00E+00

1.00E-01

1.00E-02

Accelerance

1.00E-03

1.00E-04

1.00E-05

1.00E-06

1 10 100 1000

Hz

MEASUREMENT FE Coarse Mesh MSUP FE Fine Mesh MSUP FE Fine Mesh FULL SHELL MODESUP SHELL FULL SHELL FINE WITH HOLES

Figure 6: Source side - Measured FRF (floating floor system on subfloor) vs predicted FRF (float-

ing floor slab on idealised spring isolators on rigid base).

5. PREDICTION - FULLY COUPLED ASSEMBLY

Following model validation of the centrally excited floating floor FRF, the FE model was extended to predict the uncoupled accelerance terms 𝐴 𝐶,𝑐𝑐 and 𝐴 𝐶,𝑐𝑏 of the floating floor with separate calcu- lations undertaken to estimate the accelerance of the isolator using static stiffness data only. The results of the full-assembly prediction are provided in Figure 7. This compares the predicted FRF (from source location to remote receiver location) to the measured FRF between same points.

Figure 7: Prediction for the fully-coupled floating floor system on ground bearing slab. Shown are

transfer FRF’s from source to remote receiver location (on sub floor)

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It can be seen in Figure 7 that the general behaviour is captured within the narrow band and one-third octave band predictions. Peaks in the predicted response are observed to align closely but not exactly to those in the measured response, despite good agreement between simulated and directly measured FRFs of the floating floor. This illustrates the sensitivity of the substructuring approach whereby poor SNR (Signal-to-Noise Ratio) within subfloor data, assumptions regarding isolator stiffness and/or simulation uncertainties can have notable changes on the observed response. Despite this, the one- third octave band response provides satisfactory trend agreement, typically within +/- 3dB per band, limited only in regions where coherence adversely affects the validity of the measured FRF compo- nents. The reader is again reminded here that the objective of the paper was to predict responses using substructuring methods but also accounting for real world assumptions and difficulties of measured and modelled data in a typical floating floor problem. Should each element be characterised com- pletely in a laboratory environment, the prediction may be expected to improve. Nevertheless, the predictions show real promise of dynamic subsstructuring application within the building acoustics industry.

0 5 10 15 20

Error dB

-5

-20 -15 -10

10 12.5 16 20 25 31.5 40 50 63 80 100 125 160 200 250 315 400 500

Third octave band centre frequency (Hz)

Figure 8: Third-octave band error (as predicted-measured level).

6. CONCLUSIONS

The work presented herein is an attempt to explore the validity of hybrid methods to predict the vibration response of floating floors using dynamic substructuring techniques. Modelling approaches for the Source, idealised Isolator assumptions, and measured Receiver results were utilised within this framework. The results indicate that prediction of the fully coupled FRF can be representative of the measured response of the coupled system, however sensitivities in the measurement and predic- tion process can lead to errors or a limited frequency range of useable data. Regarding the application of the method to general acoustics consultancy, it is considered that such techniques would be difficult to execute without specialised knowledge, software or apparatus. How- ever, the work has attempted to utilise the practical options available within the limits of a typical acoustical consultant. Based on decent substructuring results from these initial attempts, it is expected that there is promise in application of substructuring techniques within building acoustics industry. Further work upon improving the performance of this method and investigating the possibility of an engineering-grade method is expected to be undertaken. Efforts to explore this will be presented at the conference.

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5. ACKNOWLEDGEMENTS

We gratefully acknowledge the support of Mason Industries and Mason UK for permission in using test floor data in this paper. 6. REFERENCES

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