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| موضوع: كتاب Design of Structure and Foundations For Vibrating Machines الخميس 30 مايو 2013, 12:16 am | |
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أخوانى فى الله أحضرت لكم كتاب Design of Structures & Foundations for Vibrating Machines Suresh C. Arya Principal Engineering Specialist, CE Lummus, Houston, Texas Michael W. O’Neill Associate Professor Civil Engineering, University of Houston George Pincus Professor Civil Engineering, University of Houston
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Contents 1. Introduction—Fundamentals 1 Structural System of Foundations,1; Theoretical Approach, 1; Fundamentals of Theory of Vibrations, 2; Single-Degree-of-Freedom System, 2; Calculation of Parameters for Mathematical Model, 2; Equivalent Mass, me, 2; Equivalent Spring Constant, kj,, 4; Equivalent Forcing Function, F(t), 4; Formulation of Mathematical Model, 4; Transient or Free Vibrations, 6; Steady-State Solution of Forced Vibrations, 8; Dynamic System Subjected to Rotating-Mass-Type Excitation, 11; Terminology, 12; Accelerating Bodies (Acceleration, Velocity, Displacement), 12; Amplitude (Displacement, Vibration), 13; Analysis (Computer, Dynamic, Matrix Method, Modal, Static), 13; Balancing (Static, Dynamic), 14; Beat, 14; Conditions (Boundary, Constraint,Initial), 14; Damping (Coefficient or Constant, Critical, Dashpot, Factor or Ratio, Viscous), 15; Coordinates (Cartesian, Generalized, Normal or Principal), 15; Differential Equations (Linear, Simultaneous), 16; Dynamic (Eigenvalues, Eigenvectors, Force, Load, Load Factor, System), 16; Excitation (impulse, Inertial, Harmonic, Sinusoidal, Periodic, Transient), 17; Foundation Structure (Block-Type, Elevated Frame or Table Top, Mat Slab, Overtuned and Undertuned), 18; Frequency (Angular or Circular, Damped Natural or Harmonic, Excitation—Forcing or Operating, Fundamental, Natural, Rayleigh's), 18; Magnification or Amplification Factor, 20; Mass (Consistent or Continuous, Equivalent Lumped or Lumped), 20; Motion (Equation of Motion, Periodic, Aperiodic, Simple Harmonic or Sinusoidal, Subharmonic, Superharmonic), 20; Modes (Coupled, Uncoupled, First, Lowest, Fundamental, Normal, PrincipalEigenvector), 21; Modes of Vibrations, 24; Node (Points, Vibrating Systems), 24; Oscillation, 24; Peak-to-Peak (Double Amplitude of Vibration), 24; Period, 24; Phase (Angle), 24; Resonance (Condition, Frequency), 25; Response (Dynamic, Steady State—Forced Part, Transient), 26; Shaft (Critical Speed, Flexible, Rigid, Stiff), 27; Spring Stiffness (Constant, Equivalent, Linear-Elastic, Nonlinear, Soil), 27; System (Continuous, Dynamic, Free, Idealized or Equivalent, Linear, Nonlinear, Lumped-Mass Spring-Dashpot, SingleDegree-of-Freedom, Multiple-Degree-of-Freedom), 28; Transmissibility Factor, 31; References, 31. 2. Development of Analytical Models for Dynamic Systems 32 Modeling Techniques, 32; The Lumping of Mass, 32; Elastic Spring Constant, 32; Damping Ratio, 32; Forcing Function, 33; Models, 33; Development of Equations of Motion, 33; Model 1—'Vibrating Machines Supported by Block-Type Foundation, 34; Model 2— Vibrating Machines Supported by Mat-Type Foundation, 34; Model 3—Machines Supported on an Inertia Block and Vibration Isolated from the Foundation, 35; Model 4— vVibrating Machines Supported by Cantilever, 35; Model 5—Vibrating Machines Supported by Fixed Beam, 35; Model 6—Typical Elevated Pedestal Foundation (Table Top), 36; Model A—Single-Lumped Mass (Uncoupled Superstructure and Foundation), 36; Model B—Multi-Lumped Mass (Uncoupled Superstructure and Foundation), 36; Rayleigh’s Frequency, 36; Modal Multidegree Lumped Mass Analysis, 37; Model C—TwoLumped Mass with Coupled Soil-Structure Interaction, 37; Model D—Multi-Lumped Mass with Coupled Soil-Structure Interaction, 38; References, 38. 3. Development of Information, Trial Sizing, and Design Checklist 46 Machine Properties and Requirements, 46; Soil Parameters, 47; Environmental Conditions, 49; Trial Sizing of a Block Foundation, 49; Trial Sizing of Elevated Foundations (Table Tops), 50;Checklist for Design, 51; Design Conditions and Procedures (Static Conditions, Limiting Dynamic Conditions, Possible Modes of Vibration, Fatigue Failures, Environmental Demands), 52; References, 56. 4. Geotechnical Considerations 57 Notation for Chapter 4, 57; Evaluation of Soil Parameters, 59; Shear Modulus, 62; Calculation of Shear Modulus for Structure-Soil Interaction Analysis, 68; Selection of Shear Strain Magnitude for Computing Approximate Shear Modulus Beneath Footings, 69; Damping Ratio, 70; Selection of Poisson’s Ratio and Soil Density, 71; Effect of Footing Embedment, 72; Effect of Stiff Underlying Stratum, 72; Effect of Stratum of Loose Granular Soil, 74; References, 76. 5. Foundations 77 Notation for Chapter 5, 77; Modification of Foundation Response, 78; Vertical Spring and Damping Constants for Flexible Mats, 79; Deep Foundations, 80; Vertical Motion, 81; Pile Groups, 82; Horizontal Motion, 86; Uncoupled Rocking Motion, 86; Testing Methods and Empirical Correlations Based on Tests, 88; Comparison of Theory and Measured Behavior, 89; References, 90. 6. Design Examples: Block Foundations 91 Example 1: Foundation Design for Reciprocating Compressor (Footing Embedment Effect Included), 92; A. Introduction, 92; B. Machine Parameters, 93; C. Soil and Foundation Parameters, 93; D. Selection of a Foundation Configuration, 93; E. Dynamic Analysis, 97; F. Check of Design Criteria—Static Conditions, 97; Limiting Dynamic Conditions, 97; Environmental Demands, 98; Nomenclature—Example 1, 98; Example 2: Design of a Foundation Block for a Centrifugal Machine, 99; A. Machine Parameters, 99; B. Soil and Foundation Parameters, 99; C. Selection of a Foundation Configuration, 100; D. Dynamic Analysis, 100; E. Check of Design Criteria, 100; Static Conditions, 100; Limiting Dynamic Conditions, 100; Possible Vibration Modes, 102; Fatigue Failures, 102; Environmental Demands, 102; Nomenclature—Example 2, 102; Example 3: Foundation Design for Centrifugal Machines with Different Operating Frequencies and Supported on an Inertia Block, 103; A. Machine Parameter, 103; B. Soil and Foundation Parameters, 105; C. Selection of a Foundation Configuration, 106; D. Dynamic Analysis, 106; Selection of Springs for Inertia Block, 106; E. Dynamic Analysis as a Multi-Mass System, 107; F. Discussion of Dynamic Analysis, 107; G. Check of Design Criteria, 110; NomenclatureExample 3, 111; References, 112. vi7. Computer Analysis and Applications: Elevated Foundation Example Problem, 114; Example—STRUDL Coding, 118; Computer Printout in ICES— STRUDL, 121; Interpretation of Results, 157; References, 158. Appendix A. Solution of Multi-Degree-of-Freedom System 113 159 Introduction, 159; Dynamic Analysis, 159; Determination of Natural Frequencies and Mode Shapes, 160; Determinant Equation Method, 160; Stodola-Vianello Method, 163; Steady-State Response Analysis, 166. Appendix B. Summary of ICES-STRUDL Commands 169 Index 187 viiIndex Compressor, reciprocating design example, 92-99 Computer analysis, 13, 113 ff. coding, 118 example, 118 ff. flow chart, 117 interpretation, 157-158 reasons for, 113— 114 Consistent mass, 20 Constant damping, 15 Constant spring stiffness, 27 Constraint conditions, 14 Continuous mass, 20 Continuous system, 28 Coordinates types of, 15— 16 Coupled modes, 21-22, 55 Critical damping, 6, 15 solution equations for, 7-8 Critical speed, 26 Crosshole tests, 63 A Accelerating bodies, 12 Acceleration, 12 Agarwal, S.L., 79 Amplification factor, 20 Amplitude, 13 Amplitude, free, 12 Analysis types of, 13—14 Analytical computer models, 113 ff. development of, 32-45 Anderson, D.G., 67 Angular frequency, 18 Aperiodic motion, 20 B Balancing, 14 Beam depth, 50 fixed (model), 35—36 resonance, 50 stiffness, 50 Beat D frequency, period, 14 Beredugo, Y.O., 84 Block foundations, 1, 18, 83 design checklist, 52—54 design examples, 91-112 model, 34 trial sizing, 49—50 Block-type foundation structure. See Block foundations Boundary conditions, 14 Damped harmonic frequency, 18 Damped natural frequency, 18 Damping, 32—33 coefficient, 15 critical, 6—7, 15 dashpot, 15 geometric, 70—71 material, 70—71 types of, 15 Damping constants, 15 for flexible mats, 79-80 Damping ratio, 6, 15, 70— 71, 80, 83 computation of, 59 geomemetric computation of, 82 in modeling, 32—33 obtaining, 78 for pile foundations, 81 Dashpot damping, 15 Deep foundations, 80-89 Design checklist, 51-54, 96, 110—111 Design conditions, 46—54 Design criteria, 54, 97, 100, 110 C Cantilever (model), 35 Cartesian coordinates, 15 Centrifugal machines design of, 49 design example, 99 ff. Circular frequency, 6, 18 Circular natural frequency, 6, 18 Clays foundations in, 65-68 Coefficient damping, 15 Column resonance, 51 Column stress, 50 187188 Design of Structures and Foundations for Vibrating Machines Determinant equation method of frequency and mode shape determination, 160-163 Differential equations types of, 16 Displacement, 12. See also Displacement amplitude Displacement amplitude, 13. See also Displacement Donovan, N.C., 89 Dynamic analysis, 14, 97, 100, 106 multi-degree-of-freedom-system, 159-168 Dynamic balancing, 14 Dynamic conditions, See also Dynamic design conditions limiting, 97—98, 100—102 soil problems of, 59—62 Dynamic design conditions, 52-53 Dynamic design factors, 5 Dynamic equations of motion types of, 16-17 Dynamic equilibrium equation, 33 Dynamic force, 17 Dynamic load, 17 Dynamic response, 26 Dynamic system, 17, 28 Field shear modulus determinations of, 62—64 Finite elements, 32, 40, 79 First mode of vibration, 22 Fixed beam (model), 35—36 Flexible mat foundations, 83 Flexible shaft, 27 Footing embedment effects of, 72, 92-99 Forced vibrations steady-state solution of, 8— 11 Forcing frequency, 19 Forcing function (F(r)), 4 equation of motion for, 11 and free vibration, 6 in modeling, 33 Foundation analysis theoretical approach to, 1—2 Foundation configuration selection of, 93, 100, 106 Foundation mass, 50 Foundation response modification of, 78—79 Foundation—soil interaction, 71—72 Foundation structure (for machine), 18 types of, 48—49 Foundations, 77-90 block, 1, 18, 83 design checklist, 52—54 design examples, 91-112 model, 34 trial sizing, 49—50 categories of, l, 78 deep, 80—89 sizing and construction of, 81 design of, 1 elevated, 1, 18, 36-38, 50, 113 elevated pedestal, 36-38, 113 embedment, 72, 92 flexible mat, 40, 83, 115 forms of, 1 machine mass ratio, 49 mat, 18, 50, 79-80, 83 model, 34—35 pile, 80—89 rigid mat, 83 structural systems, l table top structure in, 1, 18, 113 Free system, 28 Free vibrations mathematical model, 4, 6—8 Frequencies. See also Fundamental frequency; Rayleigh’s frequency circular, 18 circular natural, 6 natural, 19 determination of, 160-168 resonance, 26 types of, 18-20 of vibration, 16 Fundamental frequency, 19 Fundamental modes, 22 E Eccentricities machine, 11, 47—48 Eigenvalues, 16 Eigenvectors, 16— 17, 22—24, 117, 121 Elastic halfspace model, 58 Elastic spring stiffness, 28, 32 Elevated foundation. See also Elevated frame foundation structure; Elevated pedestal foundation example, 114— 158 trial sizing, 50 Elevated frame foundation structure, 18 Elevated pedestal foundation, 1. See also Elevated foundation typical (model), 36-38 Embedment. See Footing embedment Environmental demands, 49, 54, 98, 102. See also Geotechnical considerations Equations of motion, 20. See also Differential equations, Dynamic equations of motion development, 33— 34 for forcing function, 11 in modeling, 34—38 Equivalent forcing function (F(/)) calculation for, 4 Equivalent lumped-mass model, 20 Equivalent mass (me) calculation of, 2-4 Equivalent spring constant ( k f ) calculation of, 4 Equivalent spring stiffness, 28 Equivalent system, 28 Excitation. See also Excitation frequency rotating mass-type solution for, 11— 12 sources of, 8-11 types of, 17-18 Excitation frequency, 19 F 4 /(r), See Equivalent forcing function Factor damping, 15 Fatigue, 53—54 failures, 102 G Generalized coordinates, 15Index 189 lumping of, 20 in modeling, 32 technique for obtaining, 2-4 multi-lumped (model), 36-37, 38 single-lumped (model), 36 two-lumped (model), 37— 38 Mat foundations, 18, 50, 83 model, 34—35 vertical spring and damping constants for, 79-80 Material damping, 70—71 Mathematical model calculation of parameters for, 2— 4 formulation of, 4-11 Matrix method analysis, 14 MDOF. See Multi-degree-of-freedom system Modal analysis, 14 Modal multi-degree lumped-mass analysis, 37, 159 Mode shapes, 157 determination of, 160-168 Model elastic halfspace, 58 mathematical calculation of parameters for, 2— 4 formulation of, 4—11 Modeling alternatives, 58 Modeling techniques, 32—33 Modeling types, 33—38 Modes of vibration, 53, 92—93, 102. See also Mode shapes types of, 21—24 Motion, 6, 20-21 horizontal in pile foundations, 86 vertical in pile foundations, 81—83 Multi-degree-of-freedom (MDOF) system, 28—31, 107, 159 solution of, 159— 168 Multi-lumped mass with coupled soil-structure interaction, 38 Geometric damping, 70-71 Geotechnical considerations, 47—52, 57-76 Geotechnical requirements. See Geotechnical considerations Ghazzaly, O.I., 81 Gravels foundations in, 64—65 Grigg, R. F., 81, 84 H Hardin-Drnevich equations, 66-67 Harmonic components, 9 Harmonic excitation, 17 Harmonic motion, 21 Horizontal motion in pile foundations, 86 Hudson, W.R., 79 Hwong, S.T., 81 I ICES STRUDL commands summary of, 169— 186 Idealized system, 28 Idriss, I.M., 66-68, 70 Impulse excitation, 17 Inertia block (model), 35 use of, 103 Inertial excitation, 17 Initial conditions, 15 J Jobsis, A.C., 89 K kt. See Equivalent spring constant L Laboratory shear modulus determination of, 63-64 Lagrange’s equation, 33-34, 166, 167 Linear differential equations, 16 Linear spring stiffness, 28 Linear system, 28 Load factor, dynamic, 17 Loose granular soil (sand) stratum effect of, 74-75 Lowest modes, 22 Lumped mass, 20 analysis of, 37 technique for obtaining, 2—4 Lumped-mass spring-dashpot system, 28 Lumping of mass in modeling, 32 N Natural frequencies of motion, 19 determination of, 160—168 Natural frequencies of vibration, 16 Node, 24 Node points, 24 Node vibrating systems, 24 Nonlinear spring stiffness, 28 Nonlinear system, 28 Normal coordinates, 16 Normal modes, 22-24 Northey, R.D., 67 Novak, M., 80-81, 84, 86 OO ’Neill, M.W., 81 Operating frequency, 19 Orthogonality condition, 162, 166 Oscillation, 24. See also Oscillator tests Oscillator tests, 63 Overdamping solution equations for, 8 Overturned foundation structure, 18 M Machines properties of, 46—47 requirements for, 46-47 service factor, 54 Vibration-Severity-Data, 54 Magnification factor, 10-11, 13, 20 Mass, 20 calculations for, 2—4 consistent, 20 continuous, 20 of foundation, 50 P Particular integral, 9—10 Peak-to-peak (double amplitude of vibration), 24 Pedestal foundation, elevated (model), 36-38, 113190 Design of Structures and Foundations for Vibrating Machines Period, 24 Periodic excitation, 9, 17 Periodic motion, 20 Phase, 24-25 Phase angle, 6—12, 24-25 Physiological effects. See Environmental demands Pier foundations. See Pile foundations Pile cap, 81, 84 Pile foundations, 49-50, 80-89 Pile groups, 82—86 Poisson’s ratio selection of, 71—72 and soil density, 71-72 typical values, 72 Principal coordinates, 16 Principal modes of vibration, 22-24 Procedures, design, 54 Psychological effects. See Environmental demands laboratory determination of, 63-64 and pile foundations, 81 soil, 62-69 field procedures for, 62-64 laboratory procedures for, 64 typical values, 69 Shear strain, 69-70 Shear strain magnitude selection of, 69-70 Simple harmonic motion, 21 Simultaneous differential equations, 16 Singh, J.P., 89 Single-degree-of-freedom (SDOF) system, 2, 28 in layered soils, 73—74 model examined, 4— 12 Sinusoidal excitation, 17 Sinusoidal motion, 21 Skempton, A.W., 67 R Soil loose granular, 74-75 stiff, 72-74 Soil density and selection of Poisson’s ratio, 71—72 Soil dynamics problems of, 59-62 Soil-foundation interaction, 71—72 Soil parameters, 47—49 evaluation of, 59—62 Soil shear modulus, 62-69 Soil spring stiffness, 28 Soil Soil—tests structure , 63 interaction , 38, 71 — 72 Southwell-Dunkerley formulae, 107 Spring absorbers (model), 35 Spring constants, equivalent calculation for, 4 evaluation of, 58—59 in modeling, 32 obtaining, 78 vertical for flexible mats, 79-80 Spring-dashpot system. See Lumped-mass spring-dashpot system Spring stiffness, 27-28 Static analysis, 14 Static balancing, 14 Static conditions, 100 Static design conditions, 50, 52, 114 Steady-state response, 26— 27 method of frequency and mode shape determination, 166-168 Steady-state solution of forced vibrations solution equations for, 8-11 Stiff shaft, 27 Stiff underlying stratum effect of, 72-74 Stodola-Vianello method, 163-165 Stokoe, K.H., II, 72 Strain magnitude selection of, 69-70 Stratum loose granular soil effect of, 74-75 stiff underlying effect of, 72-74 Ratio damping, 6, 15 Rayleigh wave lengths, 63 Rayleigh’s frequency, 19—20, 114, 119 model, 36-37 Reciprocating compressor design example for, 92-99 Reciprocating machines, 92— 93 design for, 49 Resistance calculation of, 4 center of columns, 51, 116 of soil, 49—50, 116 Resonance, 12, 25-26 column, 51 condition, 25-26 frequency, 26 Resonant column test, 64 Response, dynamic, 26-27 foundation modification of, 78-79 steady state, 10, 26-27 transient, 6, 27 Richart, F.E., Jr., 72 Rigid mat foundations, 83 Rigid staff, 27 Rocking equivalent spring, 38, 111 Rocking motion in pile foundations, 86-88 Rotating-mass-type excitation dynamic system subjected to, 11-12, 17 S Sands, 74-75 foundations in, 64—65 Saturated clays foundations in, 65-68 Saul, W.E., 89 SDOF. See Single-degree-of-freedom system Seed, H.B., 66-68, 70 Shaft critical speed of, 27 Shear modulus. See also Shear strain magnitude calculation of for structure-soil interaction analysis, 68—69 correlations, 64-68 field determinations of, 62-64Index 191 Structural system of foundations, 1 Structure-soil interaction, 71-72 analysis of, 68—69 STRUDL computer coding, 118—121 commands, 169-186 Subharmonic motion, 21 Superharmonic motion, 21 Undertuned foundation structure, 18 V Velocity, 12 Vertical motion in pile foundations, 81^83 Vibrating machine supported by a cantilever (model), 35 supported by a fixed beam (model), 35-36 supported by block-type foundation (model), 34 supported by mat-type foundation (model), 34—35 supported on inertia block and vibration isolated from foundation (model), 35 Vibration amplitude, 13 Vibration analysis, 14 Vibration limits, 52-54 Vibration modes, 53, 92—94, 102 types of, 21-24 Vibration response, in multidegree model, 37 Vibration tests, 88 Vibration theory fundamentals, 2 Vibrations forced steady-state solution of, 8-11 T Table top foundation structure, 1, 18. See also Elevated foundation Terminology, 12-31 Testing methods, 63, 88—89 Theory of vibrations fundamentals of, 2 Transient excitation, 18 Transient motion, 6 Transient response, 27 • Transient vibrations mathematical model, 4, 6—8, 16 Transmissibility factor, 26, 31 Trial sizing of block foundation, 49-50 of elevated foundation, 50 Two-lumped mass, 16, 23, 37— 38 free solution of, 4, 6-8 transient, 4, 6-8 Viscous damping, 15 U Uncoupled modes, 22 Undamped system solution equations for, 6-7 Underdamped system solution equations for, 7 W Whitman, R.V., 63-64, 71 Woods, R.D., 67
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