Download e-book for iPad: Acoustic Design by Duncan Templeton and David Saunders (Auth.)

By Duncan Templeton and David Saunders (Auth.)

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Table of Contents

Foreword xxi
Preface xxiii
Acknowledgments xxxi
PART I SINGLE-DEGREE-OF-FREEDOM structures 1
1 Equations of movement, challenge assertion, and Solution Methods 3
1. 1 basic constructions 3
1. 2 Single-Degree-of-Freedom approach 7
1. three Force—Displacement Relation 8
1. four Damping strength 12
1. five Equation of movement: exterior strength 14
1. 6 Mass—Spring—Damper approach 19
1. 7 Equation of movement: Earthquake Excitation 23
1. eight challenge assertion and point Forces 26
1. nine Combining Static and Dynamic Responses 28
1. 10 tools of resolution of the Differential Equation 28
1. eleven research of SDF structures: association 33
Appendix 1: Stiffness Coefficients for a Flexural Element 33
2 unfastened Vibration 39
2. 1 Undamped unfastened Vibration 39
2. 2 Viscously Damped loose Vibration 48
2. three strength in unfastened Vibration 56
2. four Coulomb-Damped unfastened Vibration 57
3 reaction to Harmonic and Periodic Excitations 65
Part A: Viscously Damped structures: uncomplicated effects 66
3. 1 Harmonic Vibration of Undamped structures 66
3. 2 Harmonic Vibration with Viscous Damping 72
Part B: Viscously Damped structures: functions 85
3. three reaction to Vibration Generator 85
3. four traditional Frequency and Damping from Harmonic Tests 87
3. five strength Transmission and Vibration Isolation 90
3. 6 reaction to flooring movement and Vibration Isolation 91
3. 7 Vibration-Measuring tools 95
3. eight power Dissipated in Viscous Damping 99
3. nine an identical Viscous Damping 103
Part C: platforms with Nonviscous Damping 105
3. 10 Harmonic Vibration with Rate-Independent Damping 105
3. eleven Harmonic Vibration with Coulomb Friction 109
Part D: reaction to Periodic Excitation 113
3. 12 Fourier sequence illustration 114
3. thirteen reaction to Periodic strength 114
Appendix three: Four-Way Logarithmic Graph Paper 118
4 reaction to Arbitrary, Step, and Pulse Excitations 125
Part A: reaction to Arbitrarily Time-Varying Forces 125
4. 1 reaction to Unit Impulse 126
4. 2 reaction to Arbitrary strength 127
Part B: reaction to Step and Ramp Forces 129
4. three Step strength 129
4. four Ramp or Linearly expanding strength 131
4. five Step strength with Finite upward push Time 132
Part C: reaction to Pulse Excitations 135
4. 6 resolution equipment 135
4. 7 oblong Pulse strength 137
4. eight Half-Cycle Sine Pulse strength 143
4. nine Symmetrical Triangular Pulse strength 148
4. 10 results of Pulse form and Approximate research for
Short Pulses 151
4. eleven results of Viscous Damping 154
4. 12 reaction to flooring movement 155
5 Numerical assessment of Dynamic reaction 165
5. 1 Time-Stepping equipment 165
5. 2 equipment in response to Interpolation of Excitation 167
5. three principal distinction approach 171
5. four Newmark’s approach 174
5. five balance and Computational mistakes 180
5. 6 Nonlinear platforms: primary distinction technique 183
5. 7 Nonlinear platforms: Newmark’s process 183
6 Earthquake reaction of Linear structures 197
6. 1 Earthquake Excitation 197
6. 2 Equation of movement 203
6. three reaction amounts 204
6. four reaction background 205
6. five reaction Spectrum inspiration 207
6. 6 Deformation, Pseudo-velocity, and Pseudo-acceleration Response Spectra 208
6. 7 height Structural reaction from the Response Spectrum 217
6. eight reaction Spectrum features 222
6. nine Elastic layout Spectrum 230
6. 10 comparability of layout and reaction Spectra 239
6. eleven contrast among layout and Response Spectra 241
6. 12 pace and Acceleration reaction Spectra 242
Appendix 6: El Centro, 1940 floor movement 246
7 Earthquake reaction of Inelastic structures 257
7. 1 Force—Deformation relatives 258
7. 2 Normalized Yield energy, Yield power Reduction Factor, and Ductility issue 264
7. three Equation of movement and Controlling Parameters 265
7. four results of Yielding 266
7. five reaction Spectrum for Yield Deformation and Yield Strength 273
7. 6 Yield energy and Deformation from the Response Spectrum 277
7. 7 Yield Strength—Ductility Relation 277
7. eight Relative results of Yielding and Damping 279
7. nine Dissipated strength 280
7. 10 Supplemental power Dissipation units 283
7. eleven Inelastic layout Spectrum 288
7. 12 purposes of the layout Spectrum 295
7. thirteen comparability of layout and Response Spectra 301
8 Generalized Single-Degree-of-Freedom structures 305
8. 1 Generalized SDF structures 305
8. 2 Rigid-Body Assemblages 307
8. three structures with disbursed Mass and Elasticity 309
8. four Lumped-Mass method: Shear development 321
8. five average Vibration Frequency by means of Rayleigh’s
Method 328
8. 6 number of form functionality 332
Appendix eight: Inertia Forces for inflexible our bodies 336
PART II MULTI-DEGREE-OF-FREEDOM platforms 343
9 Equations of movement, challenge assertion, and Solution Methods 345
9. 1 easy approach: Two-Story Shear construction 345
9. 2 basic technique for Linear structures 350
9. three Static Condensation 367
9. four Planar or Symmetric-Plan platforms: Ground Motion 370
9. five One-Story Unsymmetric-Plan structures 375
9. 6 Multistory Unsymmetric-Plan constructions 381
9. 7 a number of help Excitation 385
9. eight Inelastic structures 390
9. nine challenge assertion 390
9. 10 aspect Forces 391
9. eleven equipment for fixing the Equations of Motion: Overview 391
10 loose Vibration 401
Part A: ordinary Vibration Frequencies and Modes 402
10. 1 structures with out Damping 402
10. 2 common Vibration Frequencies and Modes 404
10. three Modal and Spectral Matrices 406
10. four Orthogonality of Modes 407
10. five Interpretation of Modal Orthogonality 408
10. 6 Normalization of Modes 408
10. 7 Modal growth of Displacements 418
Part B: loose Vibration reaction 419
10. eight answer of loose Vibration Equations: Undamped Systems 419
10. nine platforms with Damping 422
10. 10 answer of unfastened Vibration Equations: Classically Damped structures 423
Part C: Computation of Vibration houses 426
10. eleven resolution tools for the Eigenvalue challenge 426
10. 12 Rayleigh’s Quotient 428
10. thirteen Inverse Vector new release approach 428
10. 14 Vector generation with Shifts: most popular approach 433
10. 15 Transformation of okayφ = ω2mφ to the Standard Form 438
11 Damping in constructions 445
Part A: Experimental info and prompt Modal Damping Ratios 445
11. 1 Vibration homes of Millikan Library development 445
11. 2 Estimating Modal Damping Ratios 450
Part B: building of Damping Matrix 452
11. three Damping Matrix 452
11. four Classical Damping Matrix 453
11. five Nonclassical Damping Matrix 462
12 Dynamic research and reaction of Linear platforms 465
Part A: Two-Degree-of-Freedom platforms 465
12. 1 research of Two-DOF structures with no Damping 465
12. 2 Vibration Absorber or Tuned Mass Damper 468
Part B: Modal research 470
12. three Modal Equations for Undamped structures 470
12. four Modal Equations for Damped structures 473
12. five Displacement reaction 474
12. 6 aspect Forces 475
12. 7 Modal research: precis 475
Part C: Modal reaction Contributions 480
12. eight Modal enlargement of Excitation Vector p(t) = sp(t) 480
12. nine Modal research for p(t) = sp(t) 484
12. 10 Modal Contribution components 485
12. eleven Modal Responses and Required variety of Modes 487
Part D: precise research methods 494
12. 12 Static Correction strategy 494
12. thirteen Mode Acceleration Superposition strategy 497
12. 14 Mode Acceleration Superposition strategy: Arbitrary Excitation 498
13 Earthquake research of Linear platforms 511
Part A: reaction heritage research 512
13. 1 Modal research 512
13. 2 Multistory structures with Symmetric Plan 518
13. three Multistory constructions with Unsymmetric Plan 537
13. four Torsional reaction of Symmetric-Plan constructions 548
13. five reaction research for a number of Support Excitation 552
13. 6 Structural Idealization and Earthquake reaction 558
Part B: reaction Spectrum research 559
13. 7 top reaction from Earthquake Response Spectrum 559
13. eight Multistory constructions with Symmetric Plan 564
13. nine Multistory structures with Unsymmetric Plan 576
13. 10 A Response-Spectrum-Based Envelope for Simultaneous Responses 584
13. eleven reaction to Multi-Component Ground Motion 592
14 research of Nonclassically Damped Linear platforms 613
Part A: Classically Damped platforms: Reformulation 614
14. 1 normal Vibration Frequencies and Modes 614
14. 2 loose Vibration 615
14. three Unit Impulse reaction 616
14. four Earthquake reaction 617
Part B: Nonclassically Damped structures 618
14. five average Vibration Frequencies and Modes 618
14. 6 Orthogonality of Modes 619
14. 7 loose Vibration 623
14. eight Unit Impulse reaction 628
14. nine Earthquake reaction 632
14. 10 platforms with Real-Valued Eigenvalues 634
14. eleven reaction Spectrum research 642
14. 12 precis 643
Appendix 14: Derivations 644
15 relief of levels of Freedom 653
15. 1 Kinematic Constraints 654
15. 2 Mass Lumping in chosen DOFs 655
15. three Rayleigh—Ritz process 655
15. four choice of Ritz Vectors 659
15. five Dynamic research utilizing Ritz Vectors 664
16 Numerical overview of Dynamic reaction 669
16. 1 Time-Stepping equipment 669
16. 2 Linear structures with Nonclassical Damping 671
16. three Nonlinear structures 677
17 structures with allotted Mass and Elasticity 693
17. 1 Equation of Undamped movement: utilized Forces 694
17. 2 Equation of Undamped movement: Support Excitation 695
17. three ordinary Vibration Frequencies and Modes 696
17. four Modal Orthogonality 703
17. five Modal research of compelled Dynamic reaction 705
17. 6 Earthquake reaction historical past research 712
17. 7 Earthquake reaction Spectrum research 717
17. eight hassle in reading useful platforms 720
18 advent to the Finite aspect procedure 725
Part A: Rayleigh—Ritz strategy 725
18. 1 formula utilizing Conservation of strength 725
18. 2 formula utilizing digital paintings 729
18. three risks of Rayleigh—Ritz process 731
Part B: Finite aspect approach 731
18. four Finite aspect Approximation 731
18. five research strategy 733
18. 6 point levels of Freedom and Interpolation Functions 735
18. 7 point Stiffness Matrix 736
18. eight point Mass Matrix 737
18. nine aspect (Applied) strength Vector 739
18. 10 comparability of Finite point and Exact Solutions 743
18. eleven Dynamic research of Structural Continua 744
PART III EARTHQUAKE reaction, layout, AND EVALUATION OF MULTISTORY constructions 751
19 Earthquake reaction of Linearly Elastic constructions 753
19. 1 structures Analyzed, layout Spectrum, and Response Quantities 753
19. 2 effect of T1 and Á on reaction 758
19. three Modal Contribution components 759
19. four effect of T1 on Higher-Mode reaction 761
19. five impact of Á on Higher-Mode reaction 764
19. 6 Heightwise version of Higher-Mode reaction 765
19. 7 what percentage Modes to incorporate 767
20 Earthquake research and reaction of Inelastic structures 771
Part A: Nonlinear reaction heritage research 772
20. 1 Equations of movement: formula and resolution 772
20. 2 Computing Seismic calls for: Factors To Be thought of 773
20. three tale float calls for 777
20. four energy calls for for SDF and MDF structures 783
Part B: Approximate research methods 784
20. five Motivation and easy suggestion 784
20. 6 Uncoupled Modal reaction heritage research 786
20. 7 Modal Pushover research 793
20. eight assessment of Modal Pushover research 798
20. nine Simplified Modal Pushover Analysis
for sensible program 803
21 Earthquake Dynamics of Base-Isolated structures 805
21. 1 Isolation platforms 805
21. 2 Base-Isolated One-Story constructions 808
21. three Effectiveness of Base Isolation 814
21. four Base-Isolated Multistory structures 818
21. five purposes of Base Isolation 824
22 Structural Dynamics in construction Codes 831
Part A: construction Codes and Structural Dynamics 832
22. 1 overseas construction Code (United States), 2009 832
22. 2 nationwide development Code of Canada, 2010 835
22. three Mexico Federal District Code, 2004 837
22. four Eurocode eight, 2004 840
22. five Structural Dynamics in development Codes 842
Part B: assessment of establishing Codes 848
22. 6 Base Shear 848
22. 7 tale Shears and an identical Static Forces 852
22. eight Overturning Moments 854
22. nine Concluding feedback 857
23 Structural Dynamics in development evaluate directions 859
23. 1 Nonlinear Dynamic technique: present perform 860
23. 2 SDF-System Estimate of Roof Displacement 861
23. three Estimating Deformation of Inelastic SDF structures 864
23. four Nonlinear Static tactics 870
23. five Concluding feedback 876
A Frequency-Domain approach to reaction research 879
B Notation 901
C solutions to chose difficulties 913
Index 929

 
      

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Additional info for Acoustic Design

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Fibrous layer covered with thin impervious membrane These are used in wet and/or corrosive environments, in ducts with high flow velocity and in areas where contamination of the air supply must be avoided. The fibrous absorbent blankets are enclosed in very thin impervious membranes; this has the effect of improving the low frequency performance of the material but reduces its absorption at the higher frequencies compared with the same thickness of uncovered material. Fibrous layer covered with perforated panel To give protection to the absorbent and to improve its appearance it is often covered with a perforated material of some kind, such as textiles, wood or metal sheet.

Each hole or perforation acts with an effective volume behind it as a resonator. There is usually no need to separate the resonator cavities from one another by partitions. This type of absorber is identical with the fibrous layer covered with a perforated panel when the open area is less than 15 per cent. Its absorption characteristics will usually peak at a frequency governed by the choice of hole size and spacing but will be reasonably broad band if absorption material is included in the air space.

014) 2 '""^■IO-'W6^·0'4} fr = 250Hz Multiple resonator Such a system can be achieved by mounting a membrane of, say, thin metal or plywood with circular or slit perforations over an enclosed air space which may contain some fibrous absorbent. Each hole or perforation acts with an effective volume behind it as a resonator. There is usually no need to separate the resonator cavities from one another by partitions. This type of absorber is identical with the fibrous layer covered with a perforated panel when the open area is less than 15 per cent.

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