Malcolm J. Crocker - Engineering Acoustics

9 Chapter 9Figure 9.1 Source‐path‐receiver model for noise and vibration problems.Figure 9.2 Sources and paths of airborne and structure‐borne noise and vibra...Figure 9.3 Source–path–receiver system showing airborne and structure‐borne ...Figure 9.4 Rigid machine of mass m attached to a rigid massive floor.Figure 9.5 Rigid machine of mass m separated from rigid massive floor by vib...Figure 9.6 Relationship between natural frequency f nof machine‐isolator‐flo...Figure 9.7 Relationship (for a linear isolator) between forcing frequency f ,...Figure 9.8 Machine vibration severity chart showing peak‐to‐peak‐ vibration ...Figure 9.9 Typical ranges of material damping loss factors at small strains ...Figure 9.10 Different ways of using vibration damping materials: (a) free (u...Figure 9.11 Paths of direct and reflected sound emitted by a machine in a bu...Figure 9.12 The two main mechanisms believed to exist in sound‐absorbing mat...Figure 9.13 Typical absorption coefficient vs. octave band frequency charact...Figure 9.14 Sound absorption coefficient α and noise reduction coeffici...Figure 9.15 Effect on the sound absorption coefficient α of placing a 2...Figure 9.16 A Helmholtz resonator consists of a neck of radius r , length L a...Figure 9.17 Sound absorption coefficient vs. frequency for a slotted 20‐cm c...Figure 9.18 Slotted concrete blocks faced with fiberglass and covered with a...Figure 9.19 Geometry for a typical perforated panel absorber.Figure 9.20 Variable airspace perforated panels give broader absorption char...Figure 9.21 Porous absorbing material protected by a thin Mylar (polyester) ...Figure 9.22 Slat type of resonator absorber (normally the mineral wool is pl...Figure 9.23 Sound‐absorbing material placed on the walls and under the roof ...Figure 9.24 Sound absorption coefficient α of a 13‐mm thick acoustical ...Figure 9.25 Acoustical enclosure placed in free field.Figure 9.26 Personnel enclosure placed in a reverberant sound field.Figure 9.27 Machine enclosure placed in a reverberant environment.Figure 9.28 Close‐fitting enclosure attenuation in sound pressure level for ...Figure 9.29 Simplified one‐dimensional model for a close‐fitting enclosure [...Figure 9.30 Theoretical close‐fitting enclosure insertion loss performance [...Figure 9.31 Partial enclosure.Figure 9.32 Decrease of enclosure insertion loss, Δ IL , as a function of the ...Figure 9.33 Enclosures with penetrations (for cooling) lined with absorbing ...Figure 9.34 Basic elements of an acoustical enclosure used for machinery noi...Figure 9.35 Major components and cooling airflow of an air compressor [114]....Figure 9.36 Enclosure for a bandsaw.Figure 9.37 Ready‐made modular materials used to make enclosures and barrier...Figure 9.38 Sound waves reflected and diffracted by barrier and acoustical s...Figure 9.39 Attenuation of a barrier as a function of Fresnel number N for p...Figure 9.40 Freestanding barrier used indoors and the three diffraction path...Figure 9.41 Image method for reflections on the ground.Figure 9.42 Effect of multiple reflections on the acoustical performance of ...Figure 9.43 Elements of an active noise control system in a duct: (a) simple...Figure 9.44 Active headset in which the sound inside the headset is detected...Figure 9.45 Active noise control for fan noise reduction [146].Figure 9.46 Hybrid passive/active absorber cell [60].

10 Chapter 10Figure 10.1 Definitions of muffler performance.Figure 10.2 Typical straight‐through reactive mufflers: (a) single expansion...Figure 10.3 Cross‐section of typical U.S. automobile muffler with flow‐rever...Figure 10.4 Examples of common commercial automobile mufflers [13].Figure 10.5 Radiated sound pressure level error due to neglect of mean flow,...Figure 10.6 Influence of mean gas flow on effectiveness of silencer. ○, meas...Figure 10.7 Power reflection and phase angle for open end tube. Solid line: ...Figure 10.8 Measured values of transmission loss for prototype automotive mu...Figure 10.9 Muffler element.Figure 10.10 Expansion chamber with inlet pipe 1 and outlet pipe 3, both of ...Figure 10.11 Transmission loss TL of an expansion chamber of length l and S 2Figure 10.12 Acoustical conditions at the side‐branch of input acoustical im...Figure 10.13 Electrical analogy of the side‐branch system shown in Figure 10...Figure 10.14 Helmholtz resonator with equivalent simple mechanical system.Figure 10.15 Calculated transmission loss of Helmholtz resonator in Example ...Figure 10.16 Quarter‐wave resonator as a side‐branch.Figure 10.17 Transmission loss for side‐branch quarter‐wave resonator in Exa...Figure 10.18 (a) Comparison of theoretical and experiment attenuation charac...Figure 10.19 Multiple‐expansion‐chamber mufflers. (a) Effect of connecting‐t...Figure 10.20 (a) Mufflers with internal connecting tubes equal in length to ...Figure 10.21 Effect of varying the conductivity c 0and the tube length of co...Figure 10.22 (a) Effect of conductivity c 0using connecting tubes. (b) Effec...Figure 10.23 Combination mufflers [21, 64].Figure 10.24 Four‐pole representation of muffler element.Figure 10.25 Series connection of transmission matrices.Figure 10.26 (a) Real engine‐muffler exhaust system; (b) Volume velocity ana...Figure 10.27 Reflection of sound. (a) exhaust tail pipe, P r= R × P ...Figure 10.28 (a) Volume velocity source; (b) Pressure source.Figure 10.29 (a) simple expansion chamber (b) simple expansion chamber, show...Figure 10.30 Transmission loss of simple expansion chamber [44–46]. ×, Plane...Figure 10.31 Flow‐reversing chamber with pass tube and end plate. c : distanc...Figure 10.32 Experimental system for measuring the transmission loss. A : fre...Figure 10.33 Transmission loss for SI‐SO flow‐reversing chamber ( L = 2.0 in....Figure 10.34 Transmission loss for SI‐CO flow‐reversing chamber ( L = 2.0 in....Figure 10.35 Transmission loss characteristics for SI‐SO muffler chambers: −...Figure 10.36 Transmission loss characteristics for SI‐SO muffler chambers: −...Figure 10.37 Predicted transmission losses for combination of SI‐CO flow‐rev...Figure 10.38 Transmission loss characteristics for combination of SI‐CO and ...Figure 10.39 Transmission loss characteristics for combination of SI‐CO and ...Figure 10.40 Transmission loss characteristics for combination of CI‐CO and ...Figure 10.41 Transmission loss for single expansion chamber with the Traditi ...Figure 10.42 Transmission loss of muffler as a function of frequency: − − − ...Figure 10.43 Boundary element mesh for a simple expansion chamber muffler [8...Figure 10.44 TL for simple expansion chamber muffler in Figure 10.43: ——, BE...Figure 10.45 Sound pressure level (SPL) contour plot for the expansion chamb...Figure 10.46 Muffler model using the multidomain BEM [83].Figure 10.47 The SPL contour plot for multidomain muffler at 700 Hz [83].Figure 10.48 The transmission loss of the simple expansion chamber with leng...Figure 10.49 The transmission loss of the double expansion chamber with l e=...Figure 10.50 Transmission loss for a short concentric tube resonator; ——, nu...Figure 10.51 Transmission loss for a long concentric tube resonator; ——, num...Figure 10.52 Transmission loss for a long concentric tube resonator with a f...Figure 10.53 Concentric tube muffler with a flow plug ( L 1= 0.0317 m, L 2= 0...Figure 10.54 Comparison between the experimental data (−−−−) and the BEM pre...Figure 10.55 Comparison between the experimental data (−−−−) and the BEM pre...Figure 10.56 Muffler with two parallel perforated tubes ( L 1= 0.0245 m, L 2=...Figure 10.57 (a) Comparison between the experimental data (−−−−) and the BEM...Figure 10.58 Transmission loss of a perforate muffler with flow plug [79]. ‐...Figure 10.59 Instrumentation for impedance measurements [53].Figure 10.60 (a) Specific resistance and (b) specific reactance of single or...Figure 10.61 Transmission loss for a short resonator: −−−−, predicted (solid...Figure 10.62 Transmission loss for a long resonator: −−−−, predicted (solid ...Figure 10.63 Effect of porosity on transmission loss for a short resonator, ...Figure 10.64 Resonator configuration [54].Figure 10.65 (a) The basic two‐duct element; (b) Branch point model of perfo...Figure 10.66 Transmission loss of resonator operating in (i) linear regime: ...Figure 10.67 Cross‐flow chamber configuration [54].Figure 10.68 (a) The basic three‐duct element; (b) control volume of j thbra...Figure 10.69 Transmission loss of cross‐flow chamber operating with (i) M ∞...Figure 10.70 Theoretical insertion losses and transmission loss for an autom...Figure 10.71 Theoretical insertion losses and transmission loss for an autom...Figure 10.72 Insertion loss of an expansion chamber of the engine operating ...Figure 10.73 Radiated sound pressure level with the expansion chamber of the...Figure 10.74 (a) A sketch of a lined duct, showing the nomenclature used in ...Figure 10.75 Graph used to predict attenuation values.Figure 10.76 Normalized attenuation‐versus‐frequency curves for parallel‐baf...Figure 10.77 Normalized attenuation‐versus‐frequency curves for parallel‐baf...Figure 10.78 Attenuation of the fundamental mode in a rectangular duct with ...Figure 10.79 Attenuation of the fundamental mode in a rectangular duct with ...Figure 10.80 Predicted octave band attenuations for a rectangular duct lined...Figure 10.81 Predicted octave band attenuations for a rectangular duct lined...Figure 10.82 (a) Effect of varying the normalized flow resistance r 0 d / Z 0on...Figure 10.83 Comparison of theoretical values with experiment for given baff...Figure 10.84 Attenuation rate for full unit silencer, (■) N 1= 5, (□) N 1= 2...Figure 10.85 Attenuation rate for full unit silencer, (■) R = 20, (□) R = 5,...Figure 10.86 Comparison between experimental and simulated data for silencer...Figure 10.87 Tested silencer: (a) sketch; (b) picture [143].