## Structure-Borne Sound: Structural Vibrations and Sound Radiation at Audio FrequenciesStructure-Borne Sound" is a thorough introduction to structural vibrations with emphasis on audio frequencies and the associated radiation of sound. The book presents in-depth discussions of fundamental principles and basic problems, in order to enable the reader to understand and solve his own problems. It includes chapters dealing with measurement and generation of vibrations and sound, various types of structural wave motion, structural damping and its effects, impedances and vibration responses of the important types of structures, as well as with attenuation of vibrations, and sound radiation from structures. For the third edition, the author fundamentally revised and newly organized the contents of the work. Nevertheless, the intention has been to preserve the style of the previous editions, namely to focus on the fundamentals enabling the reader to analyse further problems. |

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### Contents

585 Vibration Transmission from Machinery | 325 |

References | 337 |

Attenuation of StructureBorne Sound | 340 |

611 Attenuation of Longitudinal Waves | 341 |

612 Attenuation of Bending Waves | 343 |

62 RightAngled Corners and Branches | 347 |

622 Incident Longitudinal Wave | 352 |

623 Right Angled Branches with Incident Bending and Longitudinal Waves | 353 |

26 | |

312 QuasiLongitudinal Waves on Beams and Plates | 32 |

32 Transverse Waves | 38 |

322 Torsional Waves | 43 |

33 Bending Waves | 48 |

332 Energy Relations | 57 |

34 Wave Motions on Beams of Finite Length | 59 |

341 Longitudinal Natural Vibrations | 60 |

342 Natural Vibrations in Bending | 66 |

35 The General Field Equations | 73 |

36 Wave Field at a Free Surface | 83 |

362 Excitation of an Elastic HalfSpace | 92 |

363 Surface Waves | 95 |

37 Free Plate Waves | 98 |

372 Waves with Displacements only Parallel to the Surface | 100 |

373 Waves with Displacements Perpendicular to the Surface | 102 |

374 Equations of Motion for Thin Plates from the General Field Equations | 108 |

38 Hamiltons Principle for the Derivation of the Equations of Motion | 119 |

382 Flat Plate with Shear Stiffness The Corrected Bending Wave | 120 |

383 Cylindrical Shells | 125 |

39 StructureBorne Sound Intensity | 139 |

392 Intensity in this Plates | 140 |

393 Power Transmission in ThinWalled Cylindrical Shells | 144 |

References | 146 |

Damping | 148 |

42 Complex Modulus and Wavenumbers | 152 |

43 Resonant Vibrations of Damped Beams | 160 |

431 QuasiLongitudinal Waves and Torsional Waves | 161 |

432 Bending Waves | 168 |

44 Measurement of Complex Moduli | 172 |

441 Measurements on Small Samples | 173 |

442 Measurements on Beams | 182 |

443 Measurements on Other than BeamLike Samples | 189 |

45 Experimental Data | 190 |

452 Plastics | 192 |

453 Building Materials | 195 |

46 Plates with Attached Layers | 196 |

462 Plates with MultiLayer Treatments | 200 |

463 Equations of Motion of Layered Plates | 207 |

47 Damping by means of Resonant Systems | 216 |

471 Damping by Thick Layers Ballast | 222 |

48 Damping at Joints | 224 |

481 Damping by Relative Motion Normal to the Interface | 225 |

482 Damping by Relative Motion Tangential to the Interface | 229 |

References | 231 |

Impedance and Mobility | 235 |

52 Measurement of Mobilities Impedances | 237 |

522 Comparison with Know Mobilities | 239 |

523 Other Measurement Methods | 241 |

53 Input Mobility of Infinite Rods Beams and Plates | 243 |

532 Excitation of Bending Waves in Beams | 244 |

533 Point Mobility of a Homogeneous Plate | 250 |

54 Wave Impedance Wave Mobility | 255 |

542 Examples | 256 |

543 Relation between Wave Mobility and Point Mobility | 259 |

544 Moment Mobilities | 271 |

545 Calculation of Impulse Response | 274 |

55 Power Transmission to Infinite Plane Structures | 276 |

552 Relationship with the Point Mobility | 279 |

553 Interpretations and Examples | 282 |

56 Summary of Impedance and Mobility Formulae Approximations | 285 |

57 PointExcitation of Finite Systems | 288 |

571 General Properties | 289 |

572 Some Applications | 293 |

573 Power Considerations | 297 |

58 Some Specific Applications | 305 |

582 Excitation by Sudden Release of Potential Energy | 316 |

583 Rough Surfaces as Sources of StructureBorne Sound | 318 |

584 Parametric Excitation | 321 |

63 Elastic Interlayers | 358 |

631 Attenuation of Longitudinal Waves | 359 |

632 Attenuation of Bending Waves | 362 |

64 Blocking Masses | 366 |

641 Attenuation of Longitudinal Waves | 367 |

643 Attenuation of Bending Waves Eccentric Blocking Masses | 372 |

65 Periodic Structures | 375 |

652 Attenuation of Longitudinal Waves | 379 |

653 Periodic Bending WaveGuide | 384 |

66 Hamiltons Principle for Transmission Problems | 391 |

662 An Introductory Example | 393 |

663 Bending and Longitudinal Waves at an Eccentric Blocking Mass | 396 |

67 Oblique Incidence | 401 |

672 General Consequences of the Boundary Conditions | 404 |

673 Examples | 408 |

674 Application of Hamiltons Principle | 419 |

68 Parallel Plates | 421 |

682 PointLike Sound Bridges | 426 |

69 Statistical Energy Analysis SEA | 429 |

692 Energy Flow between Linearly Coupled Oscillators | 433 |

693 Estimation of Coupling Loss Factors | 436 |

694 Application | 443 |

References | 446 |

Sound Radiation from Structures | 448 |

72 Definition and Measurement of Radiation Efficiency | 450 |

73 Radiation Loss Factor | 452 |

74 Elementary Radiators | 454 |

742 Dipole Radiators and Radiation from Forces | 457 |

743 Infinite Plates | 460 |

744 Cylindrical Radiators | 464 |

745 Impulsive Sources | 468 |

75 Plane Baffled Radiators | 471 |

751 The Plane Radiator as a Sum of Point Sources | 472 |

752 Plane Radiators as Sum of Plane Waves | 478 |

76 Radiation from Bending Waves | 482 |

763 Modal Radiation | 488 |

764 Radiation from Externally Excited Bending Waves | 491 |

765 Comparison with Experiments | 496 |

766 Additional Remarks on StructureBorne Sound Radiation | 500 |

77 FluidBorne Sound Excitation of Structures | 507 |

772 Double Walls with Sound Bridges | 511 |

78 Relation between Radiation and Response | 514 |

782 Response and Radiation in a Reverberant Room | 515 |

783 Directivity by Excitation and Radiation | 518 |

784 Sound Transmission above the Critical Frequency | 519 |

785 Transmission Loss in the Vicinity of the Critical Frequency | 523 |

79 Application of Statistical Energy Analysis | 524 |

792 Double Walls | 527 |

793 MultiLayered Walls with Several Rigid Connections | 530 |

References | 532 |

Generation and Measurement of Structure Borne Sound | 535 |

812 Comparison with Known Mobilities | 537 |

813 Mechanical Transducers as Damped MassSpring Systems | 540 |

814 Interaction of Transducer and Measurement Object | 544 |

815 Immobile Reference and Rigid Termination | 551 |

82 Controllable Sensors | 552 |

822 Optical Sensors | 557 |

83 Excitation and Measurement of StructureBorne Sound | 559 |

831 ElectroDynamic Transducers | 560 |

832 PiezoElectric Transducers | 570 |

833 ElectroStatic Transducers | 577 |

834 ElectroMagnetic Transducers | 582 |

835 Magnetostrictive Transducers | 584 |

836 Elaboration on Reciprocal Transducers | 585 |

84 Combined Quantities | 588 |

References | 590 |

List of Symbols and Notation | 592 |

Index | 597 |