Bolton, J Stuart

Song, Bryan H.

English

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Purdue UniversityPurdue e-PubsPublications of the Ray W. Herrick Laboratories School of Mechanical Engineering7-1-2002Investigation of the Vibrational Modes of Edge-Constrained Fibrous Samples Placed in a StandingWave TubeBryan H. SongNASA-Kennedy Space CenterJ Stuart BoltonPurdue University, bolton@purdue.eduFollow this and additional works at: http://docs.lib.purdue.edu/herrickThis document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu foradditional information.Song, Bryan H. and Bolton, J Stuart, "Investigation of the Vibrational Modes of Edge-Constrained Fibrous Samples Placed in aStanding Wave Tube" (2002). Publications of the Ray W. Herrick Laboratories. Paper 78.http://docs.lib.purdue.edu/herrick/78INVESTIGATION OF THE VIBRATIONAL MODES OF EDGE-CONSTRAINED FIBROUS SAMPLES PLACED IN A STANDING WAVE TUBEBryan H. SongNASA-Kennedy Space CenterJ. Stuart Bolton Ray W. Herrick LaboratoriesPurdue UniversityPurdue University Herrick LaboratoriesBackground• Measurement of the surface normal velocity of vibrating panels or plates [Kruger and Mann (1999) and Muller and Moslehy (1996)]• Estimation of the mechanical properties (Young’s modulus and Poisson’s ratio) of foam materials by the laser vibration measurement [Mariez et al. (1996) and Dubbelday (1992)]• Electromagnetic approach for measuring the vibrational velocity of the frame of flexible porous materials (Khirnykh and Cummings, 1999) Introduction• Investigation of edge constraint effect on samples placed in a modified standing wave tube (J. S. Bolton et al., SAE 1997; B. H. Song et al., JASA 1999).• Internal constraints may be used to selectively enhance the transmission loss of lining materials at low frequencies (B. H. Song et al., JASA 2001).• Implications for design of low frequency noise control barriers following from constraint of porous lining materials        around their edges.Glass Fiber Material inside of Sample HolderFour Microphone MeasurementTransfer Matrix Approach I1 2 3 4AB DCPTTP  1211xx=0 x=ddxx VTTV  222102211 TT  symmetry4 Equations121122211  TTTT reciprocity• Solve for transfer matrix elementsTransfer Matrix Approach II 1 eTTTR jkdaa 0022211211001ceTTTcR jkdaa2221001211 TcTcTT  21 aR• Anechoic Reflection Coefficient2221001211 TcTcTTR aA h i T i i C ffi i taanRRcz1102221012112TcTTTeTjkda)/1log(10 2aTTL • nec o c ransm ss on oe c en0 cExperimental Setup for Low Frequency TubeAnechoic Transmission Loss (3” Sample A in a Large Tube)40Experiment                                          3035Prediction using FEM (with edge constraint)   Prediction using FEM (without edge constraint)2025(dB)1015TL Increase in TL5due to edge constraint3 dB102 1030Frequency (Hz) Surface Normal Impedance (3” Sample A in a Large Tube)45Experiment                             Prediction using FEM (Edge constrained)      23Re(zn)    Prediction using FEM (Unconstrained)   102 1030112n)-2-10Im(zn102 103Frequency (Hz)Poroelastic Material Properties used in Calculations  Material Bulk density(Kg/m3)Porosity Tortuosity Flow resistivity(MKS Rayls/m)Shear modulus(Pa)Loss factorSample A 6.73 0.99 1.1 21000 1200 0.35Investigation of Vibrational Modes of Glass Fiber Materials (1” Sample A)      Laser Measurement Setup (Large Tube 1” Sample A) ,   xComputerB & K Type 3560Pulse System(Four Channel)dABSignal AmplifierSignalPolytec FiberOFV 3000C t llx2x1GeneratorSampleon ro erPolytec FiberOFV 511Fiber interferometer123Two-MicrophoneImpedance Measurement TubeB & K Type 4206PlexiglassThree-Dimensional Finite Element Model0.350.0970.050.025SI Unit [m]Schematic of Edge- and Plane-Constrained Sample with Reflecting Tapes   Plexiglass0.83 cm0.625 cm10 cm10 cmPlane-constrained SampleEdge-constrained SampleGlass Fiber Materials with Reflecting TapeEffect of Reflecting Tape on TL (1” Sample A) 10Without reflection tapes789 With reflection tapes   FE prediction           56L (dB)34TL12102 1030Frequency (Hz)Coherence Between Reference Microphone and the Laser Velocity Signal (1” Sample A)1        0 70.80.90.50.6.erence0.30.4Coh0.10.2102 1030Frequency (Hz)FEM-Predicted Normalized Frame Velocity in Large Tube Anechoic Termination Case (1”) ,    1” SamplePlane-constrained SampleEdge-constrained SampleThe 1st and 2nd Mode Shapes of the Edge-constrained Sample (1”)  FEM Experiment0 51(a)f/p|max0 51(b)f/p|max1st Modeat 100 Hz00.0500.050.|vf/p|/|vf00.0500.050.|vf/p|/|vf  1(c)1(d)-0.05-0.05 xy -0.05-0.05 xy2nd Mode0.0500.5|vf/p|/|vf/p|max0.0500.5|vf/p|/|vf/p|maxat 350 Hz-0.0500.05-0.050xy -0.0500.05-0.050xyThe 1st and 2nd Mode Shapes of the Plane-constrained Sample (1”)  FEM Experiment0.60.81|vf/H1|max(a)0.60.81|vf/H1|max(b)1st Modet 200 H-0.05 0 0.0500.20.4|vf/H1|/|-0.05 0 0.0500.20.4|vf/H1|/|a   z0.81ax(c) 0.81ax(d)2nd Mode0.20.40.6|vf/H1|/|vf/H1|ma0.20.40.6|vf/H1|/|vf/H1|maat 500 Hz-0.05 0 0.050radius (m)-0.05 0 0.050radius (m)Normalized Frame Velocity of Sample in Large Tube Hard Termination Case (1”) ,    FEM ExperimentEdge-t i dcons ra nePlane-constrainedC l ionc us ons Direct measurements show the vibrational velocity of the solid skeleton of fibrous sample placed in a standing wave tube. The vibrational characteristics are well predicted by using        poroelastic FE model (COMET/SAFE).  Vibrational modes of edge- and plane-constrained fibrous layers have been verified using a laser vibrometer measurement.       

Investigation of the Vibrational Modes of Edge-Constrained Fibrous Samples Placed in a Standing Wave Tube

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Investigation of the Vibrational Modes of Edge-Constrained Fibrous Samples Placed in a Standing Wave Tube

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