index [link.springer.com]978-3-662-07296-7/1.pdfformulas of acoustics 1153 index index the material...

Formulas of Acoustics 1153 Index

Index

The material of the Index is arranged according to the Chapters, because it is supposed that

the reader is searching within some context. Capitalised entries (if not names) indicate

Sections.

B General Linear Fluid Acoustics

A absorption coefficient, of periodic surface 44; adiabatic exponent 5; 35; adiabatic sound velocity 35; Adjoined wave equation 24;

B balance of energy 34;

of entropy 34; basis vectors 25; bilinear concomitant 24; Bloch waves 42; Boundary condition

at a moving boundary 37; at liquids and solids 38;

boundary conditions, general I;

C

for medium with losses 4; isothermal 4; adiabatic 4;

characteristic wave numbers, for viscous wave 2; for density wave 3; for thermal wave 3;

Christoffel symbols 28; compressibility, isothermal 5; 35;

isotrope 35; conservation of impulse 1; 2;

of mass 1; 2; of wave numbers 37;

co-ordinate systems 25; covariant 26; contravariant 26; transformation between 26;

Comer conditions 39;

D density 5; Dirac delta function 10;

and Green's function 12; divergence 30; 31; 32; Doppler shifted frequencies 37;

E energy equations 34; equation

F

of continuity 33; of state I; 2; 35

field admittance 7; field variables 33;

G gas constant 5; gradient 30; 31, 32; Green's integral 8; Green's function 9;

of a set of plane waves 13; of cylindrical waves 13; in polar co-ordinates 14; in infinite space 14; in spherical harmonics 14; in cylindrical co-ordinates 15; of a point source above a plane 15;

grid on half-infinite porous layer; thin grid 49; grid of finite thickness 52; grid of finite thickness with wide slits 54;

H Hamilton's principle 23; Hartree harmonics 42; heat conductivity 2; 5; 34 Helmholtz Huygens equation 10;

Formulas of Acoustics

I Integral relations 8; integral transforms 12; intensity 7;

L Lagrange

density 24; function 23; multipliers 23;

Laplacian, of a scalar 30; 31; 32; of a vector 30;

losses, caloric 1; 2; viscous 1; 2;

M material constants of air 4; mean free molecular path length 36; modes 11;

orthogonality of 11; expansion in 11; weight function for 12;

molecular weight 5;

N Nabla operator 30; Navier-Stokes equation 33;

o Orthogonality of modes in a duct

with locally reacting walls 17; with bulk reacting walls 18;

orthonormal basis vectors 29;

p

particle velocity 9; 36; Periodic structures, admittance grid 42;

grooved wall, narrow grooves 45; grooved wall, wide grooves 47;

point source 10; potentials 2; Prandtl number 5; Principles of superposition 20;

R

first principle of superposition 20; second principle of superposition 21; third principle of superposition 22;

reciprocity principle 8; relative density 3; relative pressure 3; relative temperature 3; rotation 30; 31; 32;

S shock front equation 38; shock front, stationary 38; Sommerfeld's condition 20;

1154

sound velocity 5; adiabatic 1 ; temperature dependence 7; of gas mixture 7;

Source conditions 18; spatial harmonics 42; specific heat 5; surface wave,

at locally reacting plane 39; along a locally reacting cylinder 41;

T temperature conductivity 5; temperature wave 36; thermal expansion 5; 35; thermodynamic relations 35; total time derivative 33;

U unitary tensors 26;

V variation of density 36;

of entropy 36; of temperature 36; of pressure 36;

vector algebra 27; scalar product 27; 30; length of a vector 27; angle between vectors 27; cross product 27; 30; triple product 27; 30; derivatives of vectors 28; derivative of a tensor 29;

Vector and tensor formulation 25; viscosity, dynamical 5·

kinematic 5; viscous loss 34;

W wave equation, homogeneous 1; 9:

inhomogeneous 9; with losses 2; with monopole source 1;

Index


c Equivalent Networks:

B Boundary conditions 62;

C Chain circuit 71; characteristic impedance 66; characteristic propagation constant 66; corresponding elements

D

in the UK analogy 64; in the Uv analogy 65;

Distributed network elements 65;

E electro-acoustic analogies 59; Elements with constrictions 70; end correction 59; 70; equivalent networks,

Fundamentals 59; equivalent oscillating mass 70;

F four-pole equations 66; four-poles 65;

H hard termination 62; Helmholtz resonator 68; 70; Helmholtz theorem 62; 71;

I internal source impedance 62;

L layer of air 69; layer of porous material 69; lumped element 65;

M mesh theorem 62;

N node theorem 62;

o oscillating mass 59;

p passive electrical and mechanical circuit components

60; perforated plate 69;

R radiation impedance 68; reciprocal electrical elements 63; reciprocal network 62;

S soft termination 62; sources 62; Superposition of multiple sources 71;

T T-circuit impedances 66; T-network 65; tube section

U

with hard termination 67; with hard termination, filled with porous material 67; with open termination 67; with open termination, filled with porous material 68;

UK-analogy 62; Uv-analogy 62;

IT IT -circuit impedances 66; IT-network 65;


o Reflection of Sound

A Absorbent strip in a hard baffle wall 89; 91;

with Mathieu functions 94; absorption coefficient 75; 76; 83;

for diffuse incidence 79; absorption cross section 83' 90' 92' 98' Absorption of finite-size ab~ob~rs,' ,

as a problem of radiation 98; acoustic corner effect 97; adjoint field 91;

B boundary condition 75; 96; Brekhovskikh's rule Ill; bulk reacting 76; 110;

C characteristic propagation constant 75; circular absorber 85; condition for pole crossing 103; contour diagram of absorption 77; cross impedance 107; cross intensity 91;

D diffuse sound incidence 85; Diffuse sound reflection

at a locally reacting plane 79; at a bulk reacting porous layer 81;

directivity diagram 85;

E effectively infinite thickness 81; elliptic-hyperbolic cylinder co-ordinates 94' equivalent network for finite-size absorber 99; extinction cross section 83; extinction theorem 83;

F Fresnel's integrals 89;

G Green's function 82; 88;

H Helmholtz's theorem of superposition 91;

I input admittance of layer 76; 78;

L law of refraction 76; locally reacting 74; 76;

M Mathieu functions 94;

azimuthal 95; radial 95;

1156

mirror source 83; 107; mirror source approximation 101; mode coupling coefficients 96; mode norms 96;

Index

Monopole line source above a plane absorber 99; with principle of superposition 107;

Monopole point source above a bulk reacting plane, exact forms 109; approximations 124;

Monopole point source above a locally reacting plane, exact forms 112;

o

exact saddle point integration 114; approximations 117;

orthogonality 96;

p path of steepest descent 100; Plane wave reflection

at a locally reacting plane 74; at an infinitely thick porous layer 75; at a porous layer of finite thickness 76' at a multiple layer absorber 78; ,

polar angle 74; pole contribution 100; 117; 118; principle of superposition 107; 124;

Q quantitative corner effect 97;

R radiation impedance 99; random roughness 87; rectangular absorber 84; reflection and scattering

at finite-size local absorbers 82; reflection factor 74; 76; 78; 110; 112; reflection factor for spherical wave 123; 124; refracted angle 75; rigid backing 78;

S saddle point integration 100; 110; 111; 114; scattered far field 84; 85; 86; 87; 90; 92; Scattering

at the border of an absorbent half-plane 88; scattering cross section 83;

U Uneven absorber surface 86; uniform pass integration 104;

W wall admittance 74; wave equation 94; wave impedance 75;


E Scattering of Sound:

A absorption cross section 131; 132; 135; 138; addition theorem 143; air bubble in water 205; angular distribution 204; azimuthal characteristic equation 145;

B back scatter cross section 136; 205; boundary condition 130; 143; 154; 168; 196; 199; bulk reacting scatterer 129; 183;

C characteristic values 190; composite medium 173; 190; 191; convex comer 147; Cylindrical or plane wave scattering at a comer 145; Cylindrical wave scattering at cylinders 143;

D diffracted wave 209; 210;

E effective compressibility 142; 190; effective density 142; 190; effective propagation constant 142; 187; effective wave 173; elliptic-hyperbolic co-ordinates 153; 160; expansion of plane wave 130; 133; 137; 162; extinction cross section 131; 135; extinction theorem 132;

F flat dam 158;

H hard screen with a mushroom-like hat 157; high dam 158;

I Impulsive spherical wave scattering at a hard wedge

208;

L locally reacting scatterer 129; 189;

M massivity 142; Mathieu functions 162; mechanical impedance of shell mode 202; 204; mirror source 209; Mixed monotype scattering in random media 186; modal admittance 137; modal reflection factors 145; 154; modal surface impedances 130; monotype scattering 173; 175; 180; movable scatterer 183;

1157 Index

Multiple scattering 142; Multiple triple-type scattering in random media 191;

P Plane wave backscattering by a liquid sphere 205; Plane wave scattering at

cylinders 129; cylinders and spheres 132; hard screen 152;

cylindrical shell 202; principle of superposition 151; 167;

Q quality factor of resonance 204;

R radiation impedance of shell mode 202; radiation loss 204; REICHE's experiment 175;

S scatter directivity 139; scatter resonance 136; scattered far field 203; 207; scattered field 130; 133; 137; 143; 144; 168; 170; scatterers

elastic 199; rigid 200; porous 200; freely movable 200;

Scattering at a flat dam 167; Scattering at a screen with an elliptical cylinder atop

153; Scattering at a semi-circular dam 169; scattering cross section 131; 134; 138; scattering cross section in resonance 203; Scattering in random media 173; shell resonances 203; 204; Sound attenuation in a forest 184; source condition 146; 154; Spherical wave scattering at

hard screen 210; perfectly absorbing wedge 206;

T thin screen 147; triple type scattering 173;

U Uniform scattering at screens and dams 158;


F Radiation of Sound:

A array of finte size radiators 259;

B breathing sphere 219;

C circular membrane and plate 258; circular piston radiator 228; circular radiator with nodal lines 259; complex power 217; Cylindrical radiator 222;

D dipole 262; directivity 255; directivity coefficient 255; directivity factor 255; directivity index 255; Directivity of radiator arrays 256; directivity value 255;

E elliptic piston 229; End corrections 243; 214; 215; excitation efficiency 269;

F far field 217; far field directivity 218; 241; Fence in a hard tube 253; field excited 236;

H Hankel transforms 268; higher modes in the neck 248; Huygens-Rayleigh integral 256;

I interior end correction 249;

with higher modes 250; with thermo-viscous losses 250;

L lateral quadrupole 263; linear quadrupole 264;

M Measures of radiation directivity 255; modal impedance 219; 222; modal velocity on sphere 219; monopole 261; Monopole and multipole radiators 261;

1158 Index

o orifice in contact with porous material 251; oscillating free circular disk 229; oscillating mass 214; 215; 220; 267; oscillating sphere 220;

p Piston radiator 218;

on a sphere 224; radiating into a hard tube 253; plane 227; plane, in a baffle wall 264;

point sources, two 256;

R

placed along a line 257; densely packed on line 257; densely packed on circular array 257; with intervals on a circle 257;

radiation efficiency 215; radiation factor 216; radiation impedance

definition 214; mechanical 215; evaluation 216; examples 225; 226; 229; 232; 237; 238; 240; 253; 266;

radiation loss 214; Radiation of finite length cylinder 260; Radiation of plates 269; rectangular piston 231; 258; rectangular, free plate 258; Ring-shaped piston 254;

S sharpness of directivity 255; Spherical radiator 218; strip-shaped radiator 217; Strip-shaped radiator on cylinder 226; Strip-shaped, field excited radiator

U

narrow 236; wide 238;

Uniform end correction 236;

W Wide rectangular, field excited radiator 240;


G Porous Absorbers:

A absorber variable 275; 280; 283; 296; 302; adiabatic sound wave 277;

B BlOT's theory 309; boundary conditions 286;

C capillaries,

circular 277; flat 280;

characteristic propagation constant 272; characteristic values 276; 278; 279; 280; 283; 285;

325; characteristic wave impedance 272; closed cell model 294; compressional wave 314; coupling density 310; covered layer 316;

D distribution parameters 285;

E effective compressibility 278; 280; 283; 294; 297;

301; effective density 278; 280; 283; 294; 297; 301; 314; effective resistivity 276; Empirical relations for characteristic values 319;

F fibre orientation

parallel 275; random 275;

fibrous materials 272; flow resistance 275; flow resistivity 272; 275; 278; 281; 282; 291; Flow resistivity in parallel fibres,

G

longitudinal 281; transversal 285;

granular media 272;

I isothermal sound wave 277;

M massivity 272; material data of porous materials 273; model structures 274; multiple scattering model 298; 304;

o open cell model 296; open-cellular foam 273;

1159

p Poisson distribution 283; 292; porous layer 315; potential coupling factor 311;

Q Quasi-homogeneous material 272; 276;

R random arrangement 282; randomised fibres 284; 292; RAYLEIGH model

with round capillaries 277; with flat capillaries 280;

relaxation frequency 284;

S scattering in random media 272; shear wave 314; Sound in parallel fibres,

longitudinal 283; transversal 293;

structure factor 273; Structure parameters 272; surface porosity 273;

T

Index

Theoretical models fitted to experimental data 324; tortuosity 310;

V volume porosity 272; 310;

W weak coupling 314;


H Compound Absorbers:

A absorbed power 421; 422; Absorber of flat capillaries 330; absorption coefficient 331; 408; 417; Array of circular holes 354; auxiliary quantities 337; 341; 348; 351; 356; 359;

B back orifice impedance 349; 352; 357; 359; 370; 372;

373; 377; boundary conditions 334; 337; 379; 385; 391; 398;

C capillary mode 407; characteristic equation 385; cylindrical shell 392;

D diffuser, quadratic residue diffuser 401;

primitive root diffuser 402; directivity function 405;

E effective compressibility 385; effective density 385; effective partition impedance 425; end correction 335; 342; 343; 350; 358; 361; 372; 373;

377; equivalent network 360; 369; 381; 387;

F far field distribution 403; Foil resonator 395; foil,

tight, limp 391; porous, limp 391; tight, elastic 391; elastic with losses 392; elastic, porous 392;

front orifice impedance 349; 352; 357; 359;

G general equivalent network 329;

H Helmholtz resonator 344; Helmholtz resonators with circular necks 359; higher modes 336; 340; homogenised admittance 329;

I input impedance 331; 381;

L lowest resonance 344; 395;

M Mathieu functions 414;

modal reflection factor 364; 368; 376; mode coupling coefficients 337; 348; 356; 366; 379;

412; 416; 420;

o orifice impedance,

front side 334; 338; 342; back side 334; 338; 342;

oscillating mass 329; 370;

p partition impedance 391; 423; periodic structure 362; plate vibration 413; Plate with narrow slits 333; Plate with wide slits 336; Poro-elastic foils 390; Porous panel absorber, rigorous solution 423;

R radiation impedance 339; 350; radiation loss 345; reflection factor 331; resonance condition 344; resonance frequency 361; Resonator array with porous layer in the volume 362;

369;375; Resonator array with porous layer on front orifice 377; resonator in an array 345; Ring resonator 397;

S scattered far field 405; simply supported plate 423; slit input impedance 351; Slit resonator with viscous and therrnallosses 351; Slit resonator,

dissipationless 340; resonance frequencies 344;

Slit resonators covered with a foil 387; Slit resonators with subdivided neck plate 381; 383; Slit with viscous and thermal losses 346; spherical shell 393; surface porosity 330; surface wave 407;

T Tight panel absorber,

rigorous solution 412; approximations 420;

V viscous and therrnallosses 330;

W Wide-angle absorber 401; 407; working frequency 402;


Sound Transmission

A absorber variable 432;

B bending wave equation 455; bending wave equation 480; Berger's law 464; boundary conditions 435; 447; bulk reacting lining 446;

C Chambered joint 449; characteristic equation 505; characteristic wave speeds 455; clamped plate 481; 486; classical plate supports 481; coincidence frequency 455; critical frequency 455;

D double sheet 524; Double shell with thin air gap 468; double-shell resonance 468; duct mode 497; 484; 491; 502; duct mode mixtures 487;

E effective bending modulus 472; elastic modules 460; equivalent network 467; 470;

F Finite size double wall with an absorber core 501; Finite size plate 480; Finite size plate

with front side absorber layer 497; with back side absorber layer 500;

flanking transmission loss 506; free plate 483; 487;

H Hole transmission with equivalent network 444;

I Infinite double shell with absorber fill 466;

L locally reacting lining 445;

M Mathieu functions 495; modal partition impedance 480; 493; 495; modal reflection factor 500; modal transmission coefficient 486; 493; mode coupling coefficients 451; 492; 498; 503; 510;

513;

1161

N niche effect 489; niche modes 491; Noise barriers 431; Noise sluice 450;

o Office fences 511;

with 20d principle of superposition 513;

p partition impedance 456; 462; 505; plastic sealing 434; Plate between two different fluids 517; plate material data 458; plate modes 480; 484; 491; 502; Plate with absorber layer 469; Plenum modes 504;

R radiation impedance 436;

S Sandwich panels 471; Sandwich with elastic core 519; Sandwich with porous board,

on front side 472; on back side 475; as core 477;

silencer modes 451; simply supported 481; 486; 495; Single plate across a flat duct 484; Single plate in a wall niche 489;

Index

Sound transmission through plates 454; 462; Strip-shaped wall in infinite baffle wall 494; suspended ceiling 504;

T thick plates 465; transmission coefficient 432; 433; 436; 437; 441; 445;

447;449;452;463;467;475;477;479;496;499; 500;503;507;510;520;

transmission factor 432; 433; 469; transmission loss 432; 437; 441; 442; 448; 453; 470;

523; Transmission through a hole in a wall 439; Transmission through a slit in a wall 434; Transmission through lined slits in a wall 445; Transmission through suspended ceilings 506; triple sheet 524

W Wall of multiple sheets 522;


J Duct Acoustics

A adjoint absorber 659; 662; Admittance of annular absorbers 575; amplitude nonlinearity 676; Annular ducts 580; approximate solutions 541;

B

I Influence of flow on attenuation 665; Influence of temperature on attenuation 673; isothermal boundary 572; iteration through the modal angle 557; least attenuated mode 535; 558; 579; 618;

L boundary condition 552; 528; 530; 532; 534; 580; 586; Least attenuated mode in rectangular ducts 541; branch points 545; 565; 669; Lined duct comers and junctions 625; C Lined ducts, general 534;

Capillaries, flat, isothermal 572; flat, adiabatic 530; circular, isothermal 531;

Cascades of silencers 602; characteristic equation 528; 530; 532; 534; 538; 553;

555;559;560;562;577;582;584;607; Concentrated absorber 607; Conical duct transitions,

hard walls 634; lined walls, as stepping duct 637; lined walls, by stepping admittance 637;

continued fraction 537; 543; 549; 555; 559; 562; 585; converging cone 639; coupling coefficients 613; 621; 624; 627; 631; CREMER's admittance 653;

with parallel resonators 658; CREMER's principle extended 655; cross-joints 629;

D density wave 572; design point 655; diverging cone 640; Duct section with feedback 603; Duct with cross-layered lining 583;

E effective compressibility 533; effective density 532;

F feedback 602; fictitious volume source 607; field matching 627; 631; Flat duct with bulk reacting lining, isotropic 552;

sets of mode solutions 555; anisotropic 554;

Flat duct with unsymmetrical lining, locally reacting 558; bulk reacting 560;

flow-induced nonlinearity 676; Flow-induced nonlinearity of perforated sheets 681;

M modal angle 535; 620; mode charts 564; mode coupling coefficients 592; 594; 645; Mode excitation coefficients 651; mode hopping 574; Mode mixtures 647;

with equal amplitude 649; with equal sound power 649; with equal energy density 650;

mode orthogonality 594; mode profile 535; 538; 603; 612; 624; mode solutions 535; modes 538; Modes in rectangular ducts with locally reacting lining

538; Morse charts 539; Muller's procedure 536;

N Nonlinearities by amplitude and/or flow 675;

o orthogonality relation 553;

p pine-tree silencers 590; poro-elastic foil 552; porous material 552;

R radiation directivity 614; radiation impedance 632; radiation loss 631; ray formation 654; Reciprocity at duct joints 683; Round duct

with locally reacting lining 561; with bulk reacting lining 577;


S secular equation 534; 554; Sets of modes in rectangular ducts 545; silencer modes 612; Single step of duct 591; Sound radiation from duct orifice 630; source contributions 607; spatial harmonics 585; 611; 615; 620; Splitter type silencer,

wide, with locally reacting splitters 611; in a duct, with locally reacting splitters 614; in a duct, with bulk reacting splitters 620; in a duct, with bulk reacting splitters, covered with foil 623;

static pressure drop 675; Stationary flow resistance of splitter silencers 675; substantial derivative 665; surface wave range 549; 573;

K Muffler Acoustics :

A absorber variable 735; acoustic filters 692; Acoustic power in a flow duct 690; Acoustically lined circular duct 735; Annular airgap lined duct 732; annular cavity resonator 699; annular duct 724;

B Bellows 729; bypass 731;

C capillary tube monolith 727; Catalytic converter elements 726; common perforated section 733; compliant walls 701; concentric tube resonator 703; 705; 734; Conical tube 700; convected quantities 689; convective radiation flow impedance 691; cross-flow contraction element 706; cross-flow expansion element 706; cross-flow, closed-end, extended peroration element

720; cross-flow, open-end, extended-perforation element

718; cross-flow, three-duct, closed-end element 713; cross-flow, three-duct, open-end element 715;

T temperature wave 572; T -joints 629; transmission coefficient 614; transmission loss 536; T-shaped Helmholtz resonator 610; Turning-vane splitter silencer 683;

V velocity profile 529; viscosity wave 572;

W wave equations 528; wave impedance 528; 531; 532;

D discontinuities 689; downsound cross sections 689; drop in stagnation pressure 698;

E eigenmatrix 712; end correction 691; end-correction effect 696; Exponential horn 700; extended inlet 698; Extended Inlet/Outlet 698; extended outlet 698; extended perforated pipes 718; extended-tube three-pass perforated element 725;

F flow impedance 689; flush tube three-pass perforated element 724; forward wave 690; fundamental-mode analysis 735;

G grazing flow impedance 715; 733; 734;

H Helmholtz Resonator 728; Hose 701; hose-wall impedance 702;


I impedance mismatch 697; In-line cavity 728; insertion loss 693; inviscid stationary medium 695;

L level difference 693; lined duct 730;

M Mach number 690; matrix formulations 689; meanflow velocity 690; Micro-perforated Helmholtz panel parallel baffle

muffler 734; modal matrix 723; Muffler performance parameters 693;

N noise reduction 693; not co-axial junction 697;

p Parallel baffle muffler 737; 734; partition impedance 704; 735; 736; pellet block element 726; perforate 704; perforated extended inlet 710; perforated extended outlet 709; perforated plate 736; Pod silencer 730; pressure drop 715; protective cover 735;

Q Quincke tube 731;

R radiation flow impedance 691; Radiation from the open end ofa flow duct 691; radiation impedance 702; reflected/rearward wave 690; reflection factor 691; 697; reversal contraction 698; reversal expansion 698; reversal-contraction, two-duct, open-end perforated

element 709; reversal-expansion, two-duct, open-end, perforated

element 708; reverse-flow contraction element 707; reverse-flow expansion element 707; reverse-flow, open-end, extended-perforated element

721; reverse-flow, open-end, three-duct element 716; reverse-flow, three-duct, closed-end element 714;

S specific flow resistance 727; stagnation pressure drop 696; Sudden Area Changes 696;

T Three-duct perforated elements 711; Three-duct perforated elements with extended

perforations 717; Three-pass perforated elements 722; transfer matrix 695; 696; 698; 700; 701; 711; 715;

718;720;721;724;728;729;730;731;735; Transfer matrix representation 692; transformation matrix 689; 692; transmission loss 693; 697; Two-duct perforated elements 703;

U Uniform tube with flow and viscous losses 695; upsound cross sections 689;

V volume flow impedance 702;


L Capsules and Cabins:

A Absorbent sound source in a capsule 745;

B boundary conditions 743; 746; 752; 761; 771;

C Cabin with plane walls 764; Cabin with rectangular cross section 770; Cabins, semicylindrical model 760; capsule efficiency 741; coherent sound incidence 768;

D diffuse sound incidence 744;

E efficiency of a cabin 760; Energetic approximation for capsule efficiency 741; equivalent network method 764;

H Helmholtz's source theorem 745; Hemispherical source and capsule 755;

I incoherent sound incidence 768; insertion coefficient 743; insertion loss 741; insertion power coefficient 753; 757;

M Room Acoustics:

A average absorption coefficient 781; average reflection rate 781;

C centre time 843; characteristic equation 775; clarity 843; concave model room 794; cone, beam, or pyramid approach 839; continued fraction expansion 776; convex model room 803; comer source 812;

D decay curve 842; decay rate 780; 782; definition 843;

M modal partition impedance 761; modal radiation impedance 753; 757; mode coupling coefficients 771; multi-modal excitation 757;

N narrow capsule 748;

p partition impedance 743; 746; 756; 771; pressure source 748;

S Semicylindrical source and capsule 751; sound protection measure 760; 763; 767; sound transmission coefficient 742; sound transmission loss 742;

V velocity source 748;

Density of eigen frequencies in rooms 777; diffuse sound field 780;

E early decay time 842; early-to-Iate energy ratio 843; effective mirror sources 786; 796; eigen frequencies 776; Eigen functions in parallelepipeds 774; energy balance 781: energy density 781; equivalent absorption area 782;

F field angle of a mirror source 786;

G Geometrical room acoustics in parallelepipeds 778; geometrical sub-tasks in mirror source method 832;


I intensity of a reflection 781; intensity of the reverberant field 779; interaural cross correlation coefficient 844; interaural cross correlation function 844; interrupt criteria in mirror source generation 789;

L Lambert's law 837; late lateral sound level 844; lateral energy fraction 843;

M mean free path length,

energetic average 779; geometrical average 779;

mirror source approximation 785;

1166

p probability density 778;

R radius of reverberant field 783; ray sources 840; Ray tracing models 837;

Index

reciprocity in the mirror source model 815; reverberant field 778; reverberation time 780; 842; reverberation time with results of mirror source

method 828; reverberation times 782;

Eyring 782;

mirror source method and 2nd principle of superposition

Sabine 783; Millington-Sette 783; Pu jolle 783;

Room acoustical parameters 842; Room impulse responses 841; room transfer function 778;

818; Mirror source model 784; mirror sources 779; mirror sources of wall couples 807; mode overlap 778; modes 774; Monte Carlo method 838;

N needed number of mirror sources 797; number of reflections 779;

N Flow Acoustics:

A acoustic analogy 866; 878; 881; 890; Acoustic analogy

in terms of entropy 895; in terms of vorticity 880; with effects of solid boundaries 890; with mean flow effects 874; with source terms 871;

acoustic efficiency 911; acoustic intensity 910; acoustic power 911; acoustic-aerodynamically efficiency 920; acoustical intensity spectrum 912; acoustical power spectrum 912; Acoustics of moving sources 901; aeroacoustics 846; Aerodynamic sound sources 908; autocorrelation function 912;

S secular equation 775; shading of mirror sources 801; sound strength 842; Statistical room acoustics 780;

T temporal density of reflections 779; transfer function 777;

averaging 850;

B

spatial 851; time 851; ensemble 8S 1; phase 851; Reynolds 851; mass-weighted or Favre 851;

basic equations 852; 856; blade thickness noise 915; boundary layer flow 850; bulk modulus 847; cylindrical co-ordinates 865;


C coefficient of expansion 847; coherent source region 909; combustion noise 897; compactness 920; compressibility 847; computational aeroacoustics 861; continuity equation 852; 856; 859; 861; 8621; 863;

864;866;867;875;881;882;886;890;900; convected wave equation 853; 865; 877; 886; 906; correlation function 908; correlations 854; cylindrical co-ordinates 865;

D decomposition 852; 861; 864; 869; 876; density 846; dilatation 877; dipole 901; 917; 921; dipole source 892; 868; 881; 896; 897; 902; 903; 920; Doppler amplification factor 905; Doppler factor 910;

E energy conservation 857; energy density 860; energy equation 856; 859; 887; enthalpy 857; 877; 880; 880; 883; 886; 887; 895; entropy 857; 895; entropy fluctuations 874; equation of motion 863; 867; equation of state 858; 863; Equations of linear acoustics 863' Euler equation 856; 858; 861; 864;

F far-field noise 912; far-field solution 869; Ffowcs Williams-Hawkings equation 891; 904; 914; fluid energy 857; fluid flows 848;

real flow 848; ideal flow 848; inviscid flow 847; viscous flow 847; incompressible flow 848; compressible 848; adiabatic flow 848; isentropic flow 848; 883; homentropic flow 848; 883; 888; isothermal flow 848; steady flow 848; stationary flow 848; 888; unsteady flow 848; uniform flow 848; rotationsal flow 848; irrotational flow 848; 864; 888; laminar flow 849; turbulent flow 849;

fluid mechanics 850;

fluids,

G

ideal 846; Newtonian 846; non-Newtonian 846;

gas constant 858; Green's function 885;

H heat release 898; Heaviside function 890; homogeneous wave equation 864;

I ideal gas 858; inhomogeneous convected wave equation 887; 878; Inhomogeneous wave equation 866;

Lighthill's form 866; in general form 867; solutions 868; Lilley's form 875; Goldstein's form 877; Goldstein-Howes form 877; with stream function 879' Ffowcs Williams-Hawkin~s form 890;

inhomogeneous wave equation 872; 873; 874; 881; 882;895;896;900;908;

internal energy 857; 882;

J jet 878; jet noise 896; 897; 908;

K Kirchhoffformulation 893; 905; Kirchhoff surfaces 905; Kirchhoff's equation 868; 894;

L Lamb vector 882; 884; Lighthill tensor 867; 876; 891; 903; 908; 917; loading noise 915;

M Mach number 865; 867; 872; 874; 881; 883; 885; 893;

901;905;907;910;915; Mohring's equation with source term 885; momentum equation 853; 856; 859; 861; 862; 863;

864;875;881;886;891;900; monopole 900; 917; 921; monopole source 867; 892; 896; 897; 901; 902; 920; moving sources 890; 922; moving surface 906;

subsonically 906; supersonically 906; arbi traril y 907;


N Navier-Stokes-equation 854; 863;

o octupole source 867; 871; 896; 904;

P perturbation equations 858; Poisson's equation 872; 873; power law 921; Power law of the aerodynamic sound sources 920; pressure 847; pressure-source theory 871; 872; pseudo-sound 871;

Q quadrupole 901; 918; 921; quadrupole noise 917;

1168

S scales 855; self noise 862; 871; 875; 880; 913; sexdecupole source 904; shear flow 875; 876; 879; shear noise 862; 871; 875; 880; 913; shear stress 847; specific heat ratio 847; specific heats 847; 858; speed of sound 858; spherical co-ordinates 865; stator vanes 919; subscript summation rule 846;

T

Index

quadrupole source 867; 868; 881; 891; 896; 897; 902;

thermal conductivity 847; thermoacoustic source mechanisms 896; thermodynamic relationships 857;

903; 904; 920;

R retardation time 868; retarded source strength 868; retarded time 907; 909; Reynolds number 849; 867; 877; 883; Reynolds stress 850; rotor blades 919; rotor dipole sound 918; rotor monopole sound 918; rotor noise 914; 917;

turbulence 849; 862; 870; 899; 909; 910; 913; turbulence level 849; 910; turbulent flame 898; turbulent fluctuation 898; 861; turbulent kinetic energy 899; two-phase flow 895; 900;

V velocity potential 864; viscosity 847; vortex sound 880; vorticity 848; 880; 883; 884; 885;

W wave equation 853; 875; 879; 884; 885; 893; 905;

o Analytical and Numerical Methods in Acoustics:

A absorbing boundary condition operators 995; absorbing material 994; absorption coefficient 931; acoustic equilibrium equation 989; acoustic loading 952; acoustic-structural analogy 989; approximating the radiation condition 996; artificial boundary 995; asymptotic far field solution 996; automatic optimisation 966; averaged square error 932; axisymmetric bodies 977;

B backscattering maximum 969; backward scattering 969; benchmark models 997; 1006; boundary element method (BEM) 972; boundary equations 956; boundary equations of 2nd kind 974; boundary error or residual 956; Boundary integral equations 972; 986; 988; Burton and Miller method 981;


C cat's-eye structure 969; 997; cavities 990; 996; collocation method 976; combined finite element and spectral approach 995; combined integral equation formulation (CHIEF)

979; combined layer potential 981; completeness 961; Computational optimisation of sound absorbers 930; Computing with mixed numeric-symbolic expressions

942; condition number 967; constant elements 967: coupled FEIBE approach 994; Coupled fluid-elastic interaction problem 952; coupled fluid-structure problem 953; 995; coupled integral equations 987; coupled interior-exterior problems 986; coupling 952; coupling parameter 981; 982; critical frequencies 961; 973; 979; critical wave number 982; cubic polynomial functions 993;

D dipole and monopole matrices 995; dipole self terms 983; Dirichlet condition 950; Dirichlet problem 949; discretisation 976; discretised functional 991; double-layer potential 974; 975;

E effective sound power 949; eigenfrequencies 990; eigenmodes 990; eigenmodes of a rectangular room 985; eigenvalue parameter 993; enclosures 993; equation for equilibrium of stresses 989; equivalent radiation problem 955; equivalent source method 964; equivalent source system 956; equivalent sources 959; error wave 960; Euclidean condition number 967; Euler-Lagrange equation 990;

F Finite element method (FEM) 989; 956; finite element model 976; fluid-structure coupling 993; 994; Fredholm integral equation 973; Frobenius norm 967; full-field equations 954; 961; 963; functional 990; functions with local support 991;

G Galerkin method 960; Gaussian distribution 959; generalised eigenvalue problem 993; generalized full-field equations 964; generalized minimum residual method 978; generalized null-field equations 964; global shape functions 991; Green's function 972; Green's function of half space 984;

H half spaces 983; Hamilton's principle 990; Helmholtz equation 948; 950; 953; Helmholtz integral equation 972; 975; hypersingular integral equation 982;

I idealised structures 969; impedance boundary condition 950; impedance scatterer 987; integral equation of scattering problem 945; integral equation of the first kind 973; interior Helmholtz integral 984; interior problem 983; interior spaces 951; interpolation property 991; iterative solver 978; iterative systems 944;

J Jacobi iteration 978;

L Lagrange function 990; least squares method 962; 963; least squares minimisation 962; least -squares orthonorrnalising 980; Levenberg-Marquardt algorithm 966;

M mass matrix 992; matrix equation of motion 994; matrix norm 967; method of moments 976; methods of weighted residuals 971; minimum search 932; mirror sources 985; modified double-layer potential 982; monopole terms 983; monopoles 966; m-th order operator 996; multigrid method 979; multi-point multipole method 963; multipole method 954; 958; multi pole radiator synthesis 958;


N natural boundary conditions 990; Neumann boundary value problem 948; Neumann condition 950; nodal points 992; nodal variables 991; non-convex structures 969; nonlinear least squares problem 966; non-uniqueness problem 981; normalised functions 967; null-field equations 954; 960; 963; 980; numerical acoustics 948; numerical implementation 966;

o one-point multi pole method 963; optimal numbering procedures 993; optimal source locations 965; optimisation of absorber parameters 930; optimisation of frequency response curve 930; orange model 1006;

p parallel absorber 939; parameters,

fixed 932; variable 933;

perfect absorption condition 995; Picard iteration 978; plane wave approximation 969; plate and acoustic finite elements 996; polynomial shape functions 992; porous absorber 994; post-processing 940; potential-layer approach 973; prolate spheroidal coordinates 959; pulsating sphere 967;

Q quadratic triangular elements 992;

R radiation and scattering problem 972; radiation condition 950; 953; radiation efficiency 949; radiation problem 948; 949; 951; reflector 969; regular wave functions 961; resonance phenomenon 979; Robin or impedance problem 949;

S scattered effective intensity 951; scattering problem 950; 986; self-adjoint formulation 978; shape functions 991; 913; single layer potential 964; 973; 974; 975; singular integral equation 974; singular kernel 973;

1170

singular values 968; singularities 983; singular-value decomposition 968; six elements per wavelength rule 977; Sommerfeld radiation condition 949; sound intensity 949; sound power 968; sound radiation 954; sound scattering 969; sound transmission 996; Source simulation technique 954; sparse matrices 993; sphere-like radiators 963; spherical wave functions 957; 963; 995; spherical wave synthesis 954; staibility 967; star-like 965; start configuration 933; stiffness matrix 992; strain tensor 953; stress tensor 952; structural damping matrix 994; structural impedance matrix 994; structural mass matrix 994; structural stiffness matrix 994; structural velocities 995; successive over relaxation 978; superposition method 954; 964; surface velocity error 968; symmetry 971; 977; symmetry relations 957; 958; system of sources 955;

T target quantity 933; target strength 951; 969; termination conditions 946;

Index

tetrahedral and cuboid finite elements 993; T-matrix approach 960; transmission condition 953; 987; transmission problem 987; triangular elements 990; triangularisation 990; two-grid method 979;

U unit triangle 992;

V variational principle 990; 994; velocity potential 953; viscoelastic material 952;

W wave equation 989; weight function 932; weighted residual equation 956; 959; weighted residuals 956; weighting functions 963;


P Variational Principles in Acoustics:

B boundary condition,

"natural" 1030; 1034; 1036; 1039; 1040; "forced" 1030; 1031;

boundary conditions, Dirichlet 1026; 1030; Neumann 1026; 1030;

boundary layer thickness, thermal 1031 ; viscous 1031 ;

boundary layers, thermal 1030; viscous 1030;

C cavity, rigid-walled 1026; 1027; characteristic impedance 1034; characteristic wavenumber 1034; compressibility, isentropic 1025; coupled eigenvalue problem 1048; coupled mode 1034; 1036; 1039; 1043; 1045; 1046;

1047; cut-on frequencies 1026; 1028;

D density, complex 1035; dispersion relation 1035; 1037; 1041; 1044; duct,

E

arbitrary cross-section 1034; 1038; 1042; flat-oval 1026; 1027; flexible walls 1042; 1044; 1045; 1046; square 1045; 1046;

eigenfrequencies 1026; 1027; equivalent fluid 1034; 1038; Eulerequations 1025; 1030; 1034; 1036; 1039; 1040;

1043; 1047;

F finite element discretization 1026; 1049; flexural rigidity 1043; functional 1025; 1030; 1034; 1036; 1039; 1040; 1042;

1043; 1044; 1047; 1048;

G Green's formula 1030; Green's theorem 1026;

H Hamilton's Principle 1025;

L Lagrange density 1025; Lagrange's equations 1025; Lagrangian 1025; lining,

M

bulk-reacting 1034; 1042; isotropic 1034; 1042; anisotropic 1035; 1038; 1046; inhomogeneous 1039;

mean flow 1035; 1039; 1042; 1044;

N Navier-Stokes equation 1029;

p Prandtl number 1030;

R Rayleigh-Ritz method 1038; 1047;

S specific heat, at constant pressure 1029; structural resonance 1045;

T thermal conductivity 1029; thermal energy equation 1029; trial function 1025; 1027; 1028; 1030; 1031; 1034;

1036; 1040; 1042; 1044; 1047; 1049; tube,

V

narrow 1029; circular 1033; hexagonal 1033; rectangular 1033; square 1033; triangular 1033;

variational principle 1026; viscosity,

kinematic 1029; dynamic 1029;

W wall admittance 1044;


Q Elasto-Acoustics :

A Anderson localization 1067; Anisotropic media 1073; Anisotropy and isotropy 1054;

B

cubic 1056; hexagonal 1056; monoclinic 1055; orthotropic 1055; triclinic 1055;

bar bending modulus 1091; bending mode 1080; bending stiffness 1083; bending wave equation 1093; Bergmann-Viktorov equation 1082; Bernoulli-Euler model 1088; Bloch wave 1066; 1068; 1069; boundary conditions at the plate 1097; Bounds on effective moduli 1070; bulk modulus 1057;

C causality 1061; Christoffel's equation 1073; clamped 1094; classical supports 1093; coincidence 1092; coincidence frequency 1092; 1098; Cole-Cole equation 1063; complex notation 1065; compliance tensor 1055; 1071; composite sphere 1071; compressibility 1058; compression modulus 1091; constraints 1056; correspondence principle 1062; creep compliance 1061; Cremer-Heckllimit 1085; critical frequency 1086; 1092; cylinder 1087; 1088; Cylindrical shell III 0;

D D'Alembert's principle 1054; Density of eigenfrequencies 1102; deviators 1060; Diffusion 1067; Dilatation modulus 1091; disorder 1066; dispersion relation 1086; 1089;

1172

E effective medium theories 1066; eigenvalues 1094; elastic stability 1056; 1057; elastic tensor 1053; energy balance 1064; energy dissipation 1097; energy flux density 1064; energy velocity 1066; engineering notation 1055; 1071; equipartition 1065; equivalent piston radiator 1116; evanescent wave 1060;

F fiber reinforcement 1072; fibers 1072; Foot point impedance 1102;

examples 1103, 1104; of corrugated sheet I 105; ofribbed plate 1106; of plate on elastic bed 1106; of strip 1106; of tube 1106; of bar 1107;

Fresnel equations 1059;

G group velocity 1066; 1074; 1075; 1078;

H Halpin-Tsai equations 1072; Hamilton's principle 1053; Hashin-Shtrikman bounds 1070; homogenization 1066; 1069; 1070; 1073; Hooke's law 1053; 1055; hysteretic model 1062;

I inertial impedance 1098; in-plane waves 1083; intensity 1065; 1074; 1085;

complex 1065; reactive 1065;

Interface conditions 1059; loffe-Regel criterion 1067;

K Kelvin-Voigt model 1061; Kirchhoff vector 1064; Kramers-Kronig relations 1062;

Index


L Lagrange-Euler equations 1054; Lagrangian density 1053; Lamb modes 1082; Lamb waves 1077; Lame constants 1053; 1057; 1090; Lame wave 1080; lateral contraction 1059; lattice vector 1067; localization 1067; logarithmic decrement 1061; longitudinal waves 1075; loss modulus 1061; loss tangent 1061;

M Material damping 1060; Maxwell model 1061; mean free path 1066; Modes of plates 1093; modulation function 1069; Moduli 1089; moment of inertia 1087; monoclinic 1072; 1083;

N nearfields 1084;

o orthogonality relation 1078; orthotropic 1084; p Partition impedance,

of plates 1096; of shells 1099; lloo; 1l01;

Periodic media 1067; plate bending modulus 1091; Plate waves 1077; Poisson's ratio 1057; 1090; polarization 1073; 1075; polycrystals 1071; polymer 1062; Poynting vector 1064; pressure far field of a plate ll17; 'Pure modes' 1073; PVC foam 1063;

Q quality factor 1061; quasi-longitudinal mode 1079;

R radiated sound power of a finite plate 1117; radiation efficiency IllS; 1116; 11l7; radiation impedance IllS; Random media 1066; Rayleigh wave 1082; 1080; 1081; Rayleigh-Lamb frequency equations 1078; Rayleigh's principle 1065; 1079; reactive intensity 1076; reciprocal lattice 1067;

1173 Index

refraction 1059; relaxation function 1061; relaxation modulus 1061; relaxation time 1063; Reuss averages 1070; 1071;

S scattering cross section 1066; shear modulus 1057; 1090; shell,

circular cylindrical 1099; spherical 1100;

simply supported 1094; slip assumption 1059; slowness 1060; 1074; 1075; Snell's law 1059; Sound radiation from plates IllS; spherical inclusions 1071; Spherical shells, similarity relations 1114; storage modulus 1061; strain deviator 1053; stress deviator 1053; supported plate 1093; Surface intensity 1064;

T thin plate theory 1098; time average 1065; Timoshenko bar 1l05; Timoshenko model 1089; Timoshenko-Mindlin model 1086; Timoshenko-Mindlin plate 1098; torsional stiffness 1087; total reflection 1060; trace velocity 1060; 1086; 1092; transmission coefficient ll08; Transmission loss at steps 1108; 1109; transversal waves 1075; transversely isotropic 1056; 1073; transversely isotropic fibers 1071;

U unit cell 1067;

V viscoelastic 1060; Voigt averages 1070; 1071; Voigt's notation 1055;

W 'warping' 1088; y Young's modulus 1090; 1057;

Z Zener model 1060; 1062;


R Ultrasound Absorption in Solids:

A Amorphous Solids and Glasses 1136; anisotropy 1133; anisotropy factor 1128; Arrhenius process 1137; attenuation 1125;

B backscattering 1129;

C collision time 1135; cyclotron resonance 1135;

D damping coefficient 1125; Debye average 1133; diffraction losses 1126; Dislocations 1129;

E electric polarization 1123; excitation, by surface field 1123;

by thin films 1124; by piezoelectric disk 1124;

F Fermi surface 1135; Fermi velocity 1134;

G Generation of ultrasound 1123; geometrical losses 1126; group velocity 1132; Grlineisen constant 1134;

H Haas van Alphen effect 1136; inelastic scattering 1136;

I Interaction with electrons in metals 1134;

K Kramers-Kroning relation 1138;

L logarithmic decrement 1125; p phase velocity 1132; phonon and electron bath 1130; phonon interactions 1133; Phonon scattering 1132; piezoelectric constant 1123; piezoelectric coupling factor 1124; piezoelectric equations 1123; piezoelectric,

crystal 1123; transducer 1123;

polycrystals 1133;

Q Q-value 1126;

R radiated energy 1123; relaxation absorption 1131; relaxation frequency 1137; relaxation time 1133; resonance of dislocation 1130;

S scattering cross-section 1127; scattering in polycrystalline materials 1128; scattering losses 1126; shear modulus 1130; superconductor 1136; suszeptibility 1123;

T thermal diffusivity 1133; Thermoelastic effects 1132;

U Ultrasonic attenuation 1124;

V viscous drag 1130;

W Wave in piezoelectric semiconducting solids 1136;


s Nonlinear Acoustics:

A acoustic Mach number 1142; acoustic Reynolds number 1146;

B Bessel-Fubini solution 1145; bipolar pulse 1149; Burger's equation 1145; 1151;

C concentrator 1151; cylindrical wave 1151;

D decaying wave 1146; dissipative medium 1145;

E elastic modules 1143; equation of state 1142;

F Fay solution 1147;

G Goldberg's number 1146; 1151; Green's function 1146;

H hydrodynamic equations 1144;

I intensity 1148; isotropic solid 1143;

K Khokhlov's solution 1147;

M monopolar pulse 1149; nonlinear distortion 1144;

N nonlinear parameter 1142; 1143; Nonlinear waves in a dissipative medium 1150; normalized distance 1I44; N-waves 1150; p perfect gas 1142; Plane nonlinear waves 1145;

R retarded time 1144; Riemann waves 1144; 1145;

S shear elasticity 1143; shock formation 1145; 1147; 1152; spherical wave 1151;

V volume elasticity 1143;

index [link.springer.com]978-3-662-07296-7/1.pdfformulas of acoustics 1153 index index the material...

Documents