Effect of Circumferential Edge Constraint on the Transmission Loss of Glass Fiber Materials

Transcription

1 Purdue University Purdue e-pubs Publications of the Ray W. Herrick Laboratories School of Mechanical Engineering Effect of Circumferential Edge Constraint on the ransmission Loss of Glass Fiber Materials J. Stuart Bolton Purdue University, Bryan Song Yeon June Kang Seoul National University Follow this and additional works at: Bolton, J. Stuart; Song, Bryan; and Kang, Yeon June, "Effect of Circumferential Edge Constraint on the ransmission Loss of Glass Fiber Materials" (1999). Publications of the Ray W. Herrick Laboratories. Paper his document has been made available through Purdue e-pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for additional information.

2 Effect of Circumferential Edge Constraint on the ransmission Loss of Glass Fiber Materials Bryan H. Song and J. Stuart Bolton Ray W. Herrick Laboratories Purdue University Yeon June Kang Seoul National University Purdue University Herrick Laboratories

3 Introduction Why: Investigation of edge constraint t effect on samples placed in a modified standing wave tube (B. H. Song et al., JASA 1999, In Press; J. S. Boltonetal., SAE 1997). How: Comparison of L and impedance measurements with FEM predicted results using an axisymmetric model COME / SAFE (Y. J. Kang et al., JASA 1999). Demonstration of how the materials mechanical and physical properties control L What: Implications for design of low frequency noise control barriers following from constraint of porous lining materials around their edges.

4 Experimental Setup High Frequency ube Dual Channel Signal Analyzer B&K ype 232 Computer CH A CH B Signal Generator Signal Amplifier Microphones Anechoic ermination New Sample Holder wo-microphone Impedance Measurement ube B & K ype cm diameter samples, 7.5 cm deep Aviation grade glass fiber, 9.61 Kg/m 3

5 ransfer Matrix Approach I A B C x x= x=d D P V x P V xd (symmetry) Four Equations 1 (reciprocity) Solve for transfer matrix elements

6 ransfer Matrix Approach II 1 R a a e R a e 21 a 22 c c jkd jkd Anechoic Reflection Coefficient R a c 21 c c c Anechoic ransmission i Coefficient i Z n 1 R a 1 1 R R a a 2 a c jkd 2 e c L 1 log(1 / a 2 )

7 Anechoic ransmission Loss 4 35 Experiment Prediction using FEM (with edge constraint) Prediction without edge constraint 3 25 (db) L 2 15 Increase in L due to edge constraint 1 5 Shearing mode

8 Anechoic Absorption Coefficient Absorptio on coefficient Experiment Prediction using FEM (with edge constraint) Prediction without edge constraint

9 Surface Normal Impedance Re(Zn) Experiment Prediction using FEM (with edge constraint) Prediction without edge constraint Im (Zn) Change from mass-like reactance to stiffness reactance

10 Estimation of Material Mechanical Properties Error surface Objective Function m m i FEM L L i i FEMi J 2 2 i m i Lm i i 2 Poiss s ons ratio Bulk Measured / Porosity ortuosity Young s Loss density Predicted Flow modulus factor Poisson ratio (kg/m 3 ) resistivity (Pa) (MKS Rayls/m) / Youngs modulus [Pa] + Minimum location

11 ransmission Loss Absorption Coefficient Shear modulus controls minimum location in L curve G = E/2(1+v) = 2845 Pa L (db) E=825 Pa v=.45 5 E=7397 Pa v=.3 E=6828 Pa v=.2 E=6259 Pa v= fficient Absorption coef E=825 Pa v=.45 E=7397 Pa v=.3.1 E=6828 Pa v=.2 E=6259 Pa v=

12 Variation of Shear Modulus As shear modulus increases, the minimum location moves to higher frequencies G=1466 Pa G=2845 Pa G=4224 Pa 25 L

13 Flow Resistivity Loss Factor L (db) Flow resistivity controls L in low and high frequency limit Flow resistivity=2 MKS Rayls/m Flow resistivity=4 MKS Rayls/m Flow resistivity=6 MKS Rayls/m L (db) Loss factor controls depth of L minimum loss factor =.1 loss factor =.3 loss factor =

14 Axial Particle Velocity at the Front of Sample Solid phase (unconstrained) Fluid phase (unconstrained) velocity (m/s) Solid v velocity (m/s) Fluid v radius (m ) radius (m ) Solid phase (constrained) Fluid phase (constrained) Solid velocity (m/s) Fluid velocity (m/s) radius (m ) radius (m )

15 Solid Phase of Constrained Sample (SDX) 2 Hz 11 Hz 5 Hz 18 Hz

16 Fluid Phase of Constrained Sample (ADX) 2 Hz 11 Hz 5 Hz 18 Hz

17 Effect of Sample Size Experimental Setup for Low Frequency ube Dual Channel Signal Analyzer B & K ype 232 Computer CH A CH B Signal Generator Signal Amplifier Microphones Anechoic ermination New Sample Holder wo-microphone Impedance Measurement ube B & K ype cm diameter samples, 7.5 cm deep Aviation grade glass fiber, 9.61 Kg/m 3

18 ransmission Loss (5 Hz - 16 Hz) 4 35 Experiment FEM (G=181 Pa) 3 25 L(dB) Frequency(Hz)

19 ransmission Loss (1 Hz - 64 Hz) Experiment (large) FEM (G=181 Pa) Unconstrained case Experiment (small) FEM (G=2845 Pa) (db) 25 L( cm samples very nearly approximates unconstrained case Frequency(Hz)

20 air foam air Conclusions Acoustical performances of fibrous layers such as transmission loss and absorption coefficient are affected by constraint on the boundary of the samples. he edge constraint effect is well predicted by using poroelastic FEM model (COME/SAFE). Light and stiff fibrous materials combined with edge constraint mechanisms may enable us to design, light, high performance low frequency noise control barriers.