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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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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
و المحتوى كما يلي :
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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