Initial modelling using Statistical Energy Analysis Claire - PowerPoint PPT Presentation

Airborne sound transmission across a hybrid heavyweight-lightweight timber floor: Initial modelling using Statistical Energy Analysis Claire Churchill, EMPA, Switzerland Carl Hopkins, University of Liverpool, UK Luboš Krajči, EMPA, Switzerland

Background  In most European countries, timber floor constructions are built from lightweight components such as timber and plasterboard  In Switzerland and Canada, there are hybrid lightweight-heavyweight floors which combine lightweight components with heavyweight components – a concrete base and a screed floating floor  In Switzerland these are built in the factory and transported to site

Aims  For these hybrid floors it would be beneficial to have a prediction model to determine the direct and flanking transmission in-situ  The first stage in the research which is reported in this presentation was to compare laboratory measurements of the airborne sound insulation with a prediction model based on Statistical Energy Analysis (SEA)

Hybrid lightweight-heavyweight timber floor 70mm concrete on 12mm OSB 260mm timber beams 80mm mineral wool Suspended plasterboard ceiling using resilient hangars

Airborne sound insulation: Comparison of a basic timber joist floor with the hybrid lightweight-heavyweight timber floor 90 Hybrid lightweight-heavyweight floor 80 Sound reduction index (dB) Timber joist floor 70 60 50 40 30 20 10 100 125 160 200 250 315 400 500 630 800 1000 1250 1600 2000 2500 3150 4000 5000 One-third-octave-band centre frequency (Hz)

SEA model for airborne sound insulation (Vertical transmission suite) 70mm concrete on 12mm OSB 260mm timber beams 80mm mineral wool Suspended plasterboard ceiling using resilient hangars Non-resonant transmission Non-resonant transmission 2.Concrete/ 5.Receiving W in(1) 1.Source 4.Plasterboard 3.Cavities OSB Room Room W d(2) W d(4) W d(3) W d(5) W d(1) 6.Joists W d(6)

SEA model – Simplifying assumptions 70mm concrete on 12mm OSB 260mm timber beams 80mm mineral wool Suspended plasterboard ceiling using resilient hangars The screw and metal strip connections from the concrete/OSB into the  beams can be modelled as rigid point connections from a composite plate representing the concrete and the OSB acting as a single plate The mineral wool has negligible effect on the one-dimensional and two-  dimensional sound fields in the cavity The errors incurred in predicting the three-dimensional sound field in a  cavity with one highly absorbent surface are negligible due to the strength of the structural transmission paths

SEA model – Inclusion of measured data  Some properties of the floor components were considered too complex to model in the early stages of the work  Resilient hangars used for the suspended ceiling  52 connectors  Reverberation times in the floor cavities The approach taken was to include  measured data in the SEA model where needed and consider new theoretical models at a later stage

Measurement of the coupling loss factor between beams and plasterboard across the resilient hangars  Laboratory mock-up  Excitation: Shaker on one beam  Response: Vibration levels on beam (subsystem i ) and plasterboard (subsystem j )  Coupling loss factor estimated using

Measurement of the cavity reverberation time using a laboratory mock-up Excitation for 1D sound fields  Only axial modes exist at frequencies below 500Hz  Loudspeaker was located at one end of the cavity  Decays were measured using MLS and reverse-filter analysis with 4 microphone positions Excitation for 1D, 2D and 3D sound fields  At and above 500Hz there are axial, and tangential modes  At and above 800Hz there are axial, tangential and oblique modes  Small loudspeaker was placed inside the cavity  Two source positions and four microphone positions for each source postion

Mode count in the cavity 16 14 Number of modes 12 10 N (1D) 8 N (2D) 6 N (3D) 4 2 0 50 63 80 100 125 160 200 250 315 400 500 630 800 Third octave band centre frequency (Hz)

Measurements: Cavity reverberation time 0.7 0.6 Reverberation time (s) 0.5 Small speaker in 0.4 cavity 0.3 Large loudspeaker 0.2 at one end 0.1 0 50 500 5000 One-third octave band centre frequency (Hz)  Very short reverberation times, on the verge of not being measurable in the low-frequencies even when using reverse-filter analysis  Reverberation times were used to calculate the total loss factors for the cavity

170 240 1  3  5 1  3  5 SEA transmission paths SEA transmission paths 230 dotted lines = 1D sound field in cavity dotted lines = 1D sound field in cavity 1  3  4  5 1  3  4  5 160 80 solid lines = 2D/3D sound field in cavity solid lines = 2D/3D sound field in cavity 220 1  2  3  5 1  2  3  5 150 70 1  2  3  4  5 1  2  3  4  5 210 1  2  6  4  5 1  2  6  4  5 200 120 140 60 190 110 130 50 180 100 170 90 120 40 80 160 110 30 Sound reduction index (dB) Sound reduction index (dB) 150 70 140 60 100 20 Subsystem 1: Source room 130 50 10 90 Subsystem 2: Chipboard 120 40 Subsystem 6: Subsystem 3: Subsystem 1: Source room 80 Joist 0 110 30 Cavity Subsystem 2: Concrete/OSB Subsystem 4: Plasterboard 100 20 70 Subsystem 5: Receive room Subsystem 6: 90 10 Subsystem 3: Joist Measured Cavity 60 80 0 Subsystem 4: Plasterboard SEA matrix solution Subsystem 5: Receive room 70 (1D sound field in cavity) 50 SEA matrix solution 60 (2D/3D sound field in cavity) 40 50 40 Measured 30 SEA matrix solution 30 (1D sound field in cavity) 20 20 SEA matrix solution (2D/3D sound field in cavity) 10 10 50 80 125 200 315 500 800 1250 2000 3150 5000 50 80 125 200 315 500 800 1250 2000 3150 5000 One-third-octave-band centre frequency (Hz) One-third-octave-band centre frequency (Hz)

Conclusions Basic timber joist floor   Good agreement between measurements and SEA in the frequency range 100Hz to 5kHz  Hybrid lightweight-heavyweight timber floor  Good agreement between measurements and SEA up to 200Hz  SEA overestimates the sound transmission by approx. 10dB between 250Hz and 5kHz  Problem lies in modelling the coupling between the concrete/OSB and the beams  Future work  Take additional measurements to re-assess the modelling of the rigid connections between the concrete/OSB and the beams  Re-assess measurement of the coupling loss factor across the resilient hangars  Predict transmission via the resilient hangars using measured dynamic stiffness