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Experiment A: Schematic of the reverberation chamber containing the suspended Aluminium plate. TSEA subsystem numbers are shown in brackets.
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This paper forms the second part of two companion papers on the use of Transient Statistical Energy Analysis
(TSEA) to predict maximum time-weighted sound pressure and vibration levels in built-up structures. It focuses
on experimental validation of the TSEA modelling procedures defined in Part 1. Two experimental designs are
used to ensure the val...
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... wo-subsystem TSEA model is formed by a4 .8 mm thick Aluminium plate (subsystem 1) that wass uspended by elastic cord in the centre of a1 22 m 3 reverberation chamber (subsystem 2).As chematic of the experimental set-up is shown in Figure 1w ith details for the twos ubsystems giveni n Table I. These twos ubsystems were chosen as theyb oth had very lowinternal loss factors which could be systematically increased by the application of damping material onto the plate and the placement of absorptive material into the room. ...
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... is nowp ossible to investigate the effect of different damping conditions on the response of the subsystems in Experiment Aa ss hown on Figure 10. Fort he three different room damping conditions there is close agreement between maximum velocity levels predicted using TSEA and the average measured values. ...
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... stage of the validation concerns TSEA prediction of the maximum sound pressure leveli nar everberant room due to ap late that is mechanically excited by at ransient force. Forexperiments Aand B, the measured and TSEA predicted maximum sound pressure levels are shown in one-third octave bands in Figure 11 and Figure 12 respectively. From Experiment A, Figure 11 shows the measured and TSEA predicted maximum sound pressure levels in the partially damped room (subsystem 2b)w ith excitation of the partially damped Aluminium plate (subsystem 1b). ...
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... stage of the validation concerns TSEA prediction of the maximum sound pressure leveli nar everberant room due to ap late that is mechanically excited by at ransient force. Forexperiments Aand B, the measured and TSEA predicted maximum sound pressure levels are shown in one-third octave bands in Figure 11 and Figure 12 respectively. From Experiment A, Figure 11 shows the measured and TSEA predicted maximum sound pressure levels in the partially damped room (subsystem 2b)w ith excitation of the partially damped Aluminium plate (subsystem 1b). ...
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... Aand B, the measured and TSEA predicted maximum sound pressure levels are shown in one-third octave bands in Figure 11 and Figure 12 respectively. From Experiment A, Figure 11 shows the measured and TSEA predicted maximum sound pressure levels in the partially damped room (subsystem 2b)w ith excitation of the partially damped Aluminium plate (subsystem 1b). The results showg ood agreement (i.e. ...
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... agreement occurred with other combinations of damping conditions. From Experiment B, Figure 12 shows similarly close agreement between TSEA and measurements for the 140 mm concrete floor.These experiments confirm that steady-state coupling loss factors that are used in SEA for sound radiation can also be used in TSEA to predict maximum sound pressure levels when the time interval is chosen as described in Part 1o ft his paper in section 2.4 [1]. Figures 11 and 12 also provide evidence that close agreement can be obtained between TSEA predictions and measurements when TSEA uses either ameasured, hybrid or synthetic transient power input. ...
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... final stage is to investigate the effect of different damping conditions in Experiment A. Figure 13 shows close agreement between measured and TSEA predicted ACTA ACUSTICA UNITED WITH ACUSTICA Vol. 100 (2014) maximum sound pressure levels due to transient excitation of the plate for different room and plate damping conditions. The TSEA predicted levels tend to lie within the 95% confidence intervals of the measurements. ...
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... underlying reasons for the differences between the undamped and damped plates in Figure 13 are likely to be due to acombination of (a) the smearing effect of the Fast time-weighting and (b) the energy balance during the time period in which the maximum sound pressure levelisdetermined. The latter aspect can be considered using TSEA. ...
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... latter aspect can be considered using TSEA. Fort he damping conditions shown in Figure 13, the time period during which the maximum sound pressure level is determined (measured or predicted)v aries between 0.2 and 1s.T og ives ome insight into the net power flowb etween the plate and the room during this time period it is instructive to use the time-varying modal energies from the TSEA model. This is because the net power flowtransferred between twocoupled subsystems is proportional to the difference in their modal energies. ...
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... is because the net power flowtransferred between twocoupled subsystems is proportional to the difference in their modal energies. Fort he damping conditions in Figure 13, the time-varying modal energy leveld i ff erence at 1kHz is shown in Figure 14 as the ratio of the plate modal energy to the room modal energy. The results are shown during the 1stime period after transient excitation. ...
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... is because the net power flowtransferred between twocoupled subsystems is proportional to the difference in their modal energies. Fort he damping conditions in Figure 13, the time-varying modal energy leveld i ff erence at 1kHz is shown in Figure 14 as the ratio of the plate modal energy to the room modal energy. The results are shown during the 1stime period after transient excitation. ...
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... stage of the validation concerns TSEA prediction of the maximum velocity leveldue to structure-borne sound transmission from as ource plate to either an adjacent or non-adjacent receiving plate using the heavyweight building from Experiment B. The maximum velocity levels are predicted with TSEA using ameasured transient power input because it wass hown in section 3t hat the accuracy is similar to that for hybrid and synthetic transient powers. The measured and TSEA predicted maximum velocity levels are shown on Figure 15a and 15b for adjacent plates and Figure 15c for non-adjacent plates. In all cases there is good agreement between measurements and TSEA, with at endencyf or TSEA to underestimate by up to 5dBi n the mid-and high-frequencyranges. ...
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... stage of the validation concerns TSEA prediction of the maximum velocity leveldue to structure-borne sound transmission from as ource plate to either an adjacent or non-adjacent receiving plate using the heavyweight building from Experiment B. The maximum velocity levels are predicted with TSEA using ameasured transient power input because it wass hown in section 3t hat the accuracy is similar to that for hybrid and synthetic transient powers. The measured and TSEA predicted maximum velocity levels are shown on Figure 15a and 15b for adjacent plates and Figure 15c for non-adjacent plates. In all cases there is good agreement between measurements and TSEA, with at endencyf or TSEA to underestimate by up to 5dBi n the mid-and high-frequencyranges. ...
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... It was found that the calculation results of the two methods were basically consistent, which verifies the effectiveness of the TSEA method. Robinson and Hopkins [16,17] studied the theoretical prediction method of the response of the structure under transient excitation based on the TSEA method and verified it by experiments. Dalton et al. [18] first proposed the VMSS method and clarified the principle and basic formula of VMSS. ...
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... To allow prediction of Lp,Fmax from any form of heavy impact source excited in heavyweight buildings, Robinson and Hopkins [5,6] showed that Transient Statistical Energy Analysis (TSEA) can be used to predict from the combination of direct and flanking paths. They subsequently showed that TSEA can be used to predict Lp,Fmax due to excitation of a concrete base floor that is directly excited by the rubber ball or human footsteps [7]. ...
To aid design decision concerning heavy impacts on heavyweight floors, it is necessary to be able to predict Fast-time weighted maximum sound pressure levels (Lp,Fmax) in the receiving room. For excitation directly on the heavyweight floor this can be carried out using Transient Statistical Energy Analysis (TSEA) in a predictive mode. However, the performance of floating floors is not always possible to accurately predict hence an inverse approach to TSEA, referred to as ITSEA, has been developed to determine the transient power. This paper compares the prediction of the Lp,Fmax using TSEA with normalized transient power input determined by ITSEA with measurements conducted in two test chambers with and without floor small floor toppings. For one-third octave bands, the maximum difference in Lp,Fmax between measurement and TSEA ranged from 5.3 to 8.3dB and 6 to 7dB when using W`in,ForcePlate and W`in,ITSEA respectively. For octave bands, the maximum difference in Lp,Fmax between measurement and TSEA ranged from 2.1 to 7.5dB and 2 to 7dB when using W`in,ForcePlate and W`in,ITSEA respectively
... For laboratory and field measurements, the rubber ball was developed to assess these types of impacts [1] with measurement procedures described in International standards [2][3][4]. For heavyweight concrete floors, it has been shown that Transient Statistical Energy Analysis (TSEA) can be used to predict the maximum Fast time-weighted sound pressure level [5][6][7] and this has been extended to include a floating floor [8]. It has also been shown to be feasible to use the Finite Element Method (FEM) with a concrete floor radiating into a room [9]. ...
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... For laboratory and field measurements, the rubber ball was developed to assess these types of impacts [1] with measurement procedures described in International standards [2][3][4]. For heavyweight concrete floors, it has been shown that Transient Statistical Energy Analysis (TSEA) can be used to predict the maximum Fast time-weighted sound pressure level [5][6][7] and this has been extended to include a floating floor [8]. It has also been shown to be feasible to use the Finite Element Method (FEM) with a concrete floor radiating into a room [9]. ...
The ISO rubber ball is used in measurement standards to assess heavy impacts on floors such as from footsteps in bare feet or children jumping. This paper investigates the prediction of impact sound insulation using the Finite Element Method (FEM) and Transient Statistical Energy Analysis (TSEA). FEM is used to model the rubber ball impact on a timber floor by simulating the rubber ball and the floor. The contact force is then applied directly into the FEM model to reduce computation time and is found to introduce negligible error. An experimentally validated FEM model of a small timber floor is compared with TSEA in terms of the spatial-average maximum time-weighted vibration level on the surface of the timber floor using a TSEA model that only considers the chipboard walking surface.
... The rubber ball is referred to in International measurement standards (2)(3)(4) to assess heavy impacts through measurement of the maximum Fast time-weighted sound pressure level, L Fmax . For heavyweight buildings it is possible to predict L Fmax using Transient Statistical Energy Analysis (TSEA) (5)(6)(7)(8) and with Finite Element Methods (FEM) (9)(10). However, for lightweight buildings there are no validated prediction models that can be used to predict the performance in both the laboratory and the field. ...
In lightweight buildings there can be problems due to heavy impacts, such as from footsteps in bare feet or children jumping. For this reason the standard rubber ball is used in measurement standards to assess heavy impacts. In this paper, experimental work on a mock-up timber floor is used to provide benchmark data to validate a model using Finite Element Methods (FEM) of the standard rubber ball exciting a timber floor. Experimental Modal Analysis was initially used to extract damping information and the Modal Assurance Criterion was used to confirm that the FEM model of the timber floor was reasonable. A FEM model was then used to predict the time-domain response of the timber floor when excited by a single impact from the standard rubber ball which was included in the FEM model. Comparison of these FEM predictions with experimental data was assessed using the Frequency Domain Assurance Criterion which indicated reasonable agreement with the experimental results.
... In heavyweight buildings it is possible to predict the impact sound insulation due to transient excitation in terms of maximum Fast time-weighted sound pressure levels using Transient Statistical Energy Analysis (TSEA) (4,5). This requires measurements of the blocked force from the transient excitation for which the approach has been validated for heavy impacts from the ISO rubber ball and the bang machine on heavyweight floors with and without floating floors (6,7). ...
At present the prediction model in EN 12354-5 for sound transmission due to structure-borne excitation from building machinery is limited to sources running under steady-state conditions. As machinery noise also needs to be assessed under time-varying conditions, building regulations on installation noise in some European countries set requirements based on the maximum Fast time-weighted sound pressure level in the receiving room. This paper proposes an approach that could predict this information at the design stage and validates it using idealised time-varying signals applied via a shaker into a concrete floor. A heavyweight reception plate is used to quantify the structure-borne sound power using equivalent continuous levels over 125ms time periods from which the highest value can be used as the power input into an SEA or SEA-based prediction model. An empirical correction (developed in previous work by the authors) is then applied to the output from this model to estimate the maximum Fast time-weighted sound pressure level. This approach is validated with measurements in a room below a concrete floor (where there is suppressed flanking transmission) from which the results show close agreement between predictions and measurements for one-third octave bands and A-weighted values.
... However, the impedance model does not account for flanking transmission and is limited to direct transmission. To allow prediction of L p,Fmax from any form of transient excitation in heavyweight buildings, Robinson and Hopkins [12,13] showed that Transient Statistical Energy Analysis (TSEA) can be used to predict this parameter from the combination of direct and flanking paths. They subsequently showed that TSEA can be used to predict L p,Fmax due to excitation of a concrete base floor that is directly excited by the rubber ball or human footsteps [14]. ...
For heavy impacts on floors in heavyweight buildings, prediction models are needed at the design stage to estimate the spatial-average Fast time-weighted maximum sound pressure level in the receiving room. This paper extends previous work using Transient Statistical Energy Analysis (TSEA) in heavyweight buildings by introducing an inverse form of TSEA (ITSEA) to determine the transient structure-borne sound power input from heavy impact sources into a heavyweight base floor with a floating floor. The difference in the power input with and without a floating floor gives a correction factor that can be used to modify the power input into the base floor. This allows the effect of the floating floor to be incorporated in a TSEA model of a heavyweight building. ITSEA is initially validated with heavy impacts from a rubber ball directly onto a concrete base floor and with small, locally reacting, mass-spring systems. Laboratory experiments are then used to quantify the transient structure-borne sound power input into a full-size concrete base floor when a heavy impact is applied to the base floor, and to the base floor with a full-size Ondol floating floor. The resulting TSEA model shows close agreement with the predicted change in the Fast time-weighted maximum sound pressure level due to the floating floor.
... These require measurement of the Fast time-weighted maximum sound pressure level, Lp,Fmax in the room underneath the excited floor. To allow prediction of Lp,Fmax from transient excitation in heavyweight buildings, Robinson and Hopkins have shown that Transient Statistical Energy Analysis (TSEA) can be used to predict the combination of direct and flanking transmission [5,6]. More recent work shows that TSEA can be used to predict Lp,Fmax in a room due to excitation of a concrete base floor by the ISO rubber ball and human footsteps [6]. ...
... In stage 1, the blocked force measured on a force plate from a rubber ball drop is compared with that from the FEM model. In stage 2, a laboratory measurement of impact sound insulation with a rubber ball from a previous study [5,6] is compared with FEM (as well as TSEA). After the validation, numerical experiments with FEM and TSEA are defined using nine different situations. ...
... In validation stage 2, a laboratory measurement in a vertical transmission suite was used from a previous study [5,6]. The rubber ball was dropped on a 140mm concrete base floor. ...
To aid design decisions concerning heavy impacts on heavyweight floors, it is necessary to be able to predict Fast-time weighted maximum sound pressure levels (L p,Fmax) in the receiving room. This paper compares predictions from Transient Statistical Energy Analysis (TSEA) with those from Finite Element Methods (FEM) to assess the results at low-frequencies. Experimental validation of the FEM model indicated that the contact force was correctly predicted and that the vibroacoustic interaction in the time domain between the excited plate and acoustic cavity was also modelled correctly. Numerical experiments were subsequently carried out for the ISO rubber ball impacting a 140mm concrete floor with different room volumes (50, 37.5 and 25 m 3) and different reverberation times (1.5s, 0.75s and 0.375s). These showed that TSEA and FEM are similar in the low-frequency range; hence in many cases it could be advantageous to use TSEA as it is quicker to create the model and run the simulation.
