Vibration simulation using MATLAB and ANSYS

Vibration simulation using MATLAB and ANSYS

  • نوع فایل : کتاب
  • زبان : انگلیسی
  • مؤلف : Michael R Hatch
  • ناشر : Boca Raton : Chapman & Hall/CRC
  • چاپ و سال / کشور: 2001
  • شابک / ISBN : 9781584882053

Description

1.1 Representing Dynamic Mechanical Systems 1 -- 1.2 Modal Analysis 1 -- 1.3 Model Size Reduction 4 -- Chapter 2 Transfer Function Analysis 7 -- 2.2 Deriving Matrix Equations of Motion 8 -- 2.2.1 Three Degree of Freedom (tdof) System, Identifying Components and Degrees of Freedom 8 -- 2.2.2 Defining the Stiffness, Damping and Mass Matrices 8 -- 2.2.3 Checks on Equations of Motion for Linear Mechanical Systems 11 -- 2.2.4 Six Degree of Freedom (6dof) Model--Stiffness Matrix 11 -- 2.2.5 Rotary Actuator Model--Stiffness and Mass Matrices 12 -- 2.3 Single Degree of Freedom (sdof) System Transfer Function and Frequency Response 15 -- 2.3.1 sdof System Definition, Equations of Motion 15 -- 2.3.2 Transfer Function 15 -- 2.3.3 Frequency Response 17 -- 2.3.4 MATLAB Code sdofxfer.m Description 21 -- 2.3.5 MATLAB Code sdofxfer.m Listing 21 -- 2.4 tdof Laplace Transform, Transfer Functions, Characteristic Equation, Poles, Zeros 23 -- 2.4.1 Laplace Transforms with Zero Initial Conditions 23 -- 2.4.2 Solving for Transfer Functions 24 -- 2.4.3 Transfer Function Matrix for Undamped Model 27 -- 2.4.4 Four Distinct Transfer Functions 28 -- 2.4.5 Poles 29 -- 2.4.6 Zeros 30 -- 2.4.7 Summarizing Poles and Zeros, Matrix Format 32 -- 2.5 Matlab Code tdofpz3x3.m--Plot Poles and Zeros 32 -- 2.5.1 Code Description 32 -- 2.5.2 Code Listing 32 -- 2.5.3 Code Output--Pole/Zero Plots in Complex Plane 38 -- Chapter 3 Frequency Response Analysis 51 -- 3.2 Low and High Frequency Asymptotic Behavior 52 -- 3.3 Hand Sketching Frequency Responses 57 -- 3.4 Interpreting Frequency Response Graphically in Complex Plane 58 -- 3.5 MATLAB Code tdofxfer.m--Plot Frequency Responses 61 -- 3.5.1 Code Description 61 -- 3.5.2 Polynomial Form, For-Loop Calculation, Code Listing 62 -- 3.5.3 Polynomial Form, Vector Calculation, Code Listing 64 -- 3.5.4 Transfer Function Form--Bode Calculation, Code Listing 65 -- 3.5.5 Transfer Function Form, Bode Calculation with Frequency, Code Listing 67 -- 3.5.6 Zero/Pole/Gain Function Form, Bode Calculation with Frequency, Code Listing 70 -- 3.5.7 Code Output--Frequency Response Magnitude and Phase Plots 72 -- 3.6 Other Forms of Frequency Response Plots 73 -- 3.6.1 Log Magnitude versus Log Frequency 74 -- 3.6.2 db Magnitude versus Log Frequency 75 -- 3.6.3 db Magnitude versus Linear Frequency 76 -- 3.6.4 Linear Magnitude versus Linear Frequency 77 -- 3.6.5 Real and Imaginary Magnitudes versus Log and Linear Frequency 78 -- 3.6.6 Real versus Imaginary (Nyquist) 79 -- 3.7 Solving for Eigenvectors (Mode Shapes) Using the Transfer Function Matrix 80 -- Chapter 4 Zeros in Siso Mechanical Systems 87 -- 4.2 "n" dof Example 88 -- 4.2.1 MATLAB Code ndof_numzeros.m, Usage Instructions 89 -- 4.2.2 Seven dof Model--z7/F1 Frequency Response 89 -- 4.2.3 Seven dof Model--z3/F4 Frequency Response 91 -- 4.2.4 Seven dof Model--z3/F3, Driving Point Frequency Response 92 -- 4.3 Cantilever Model--ANSYS 94 -- 4.3.2 ANSYS Code cantfem.inp Description and Listing 95 -- 4.3.3 ANSYS Code cantzero.inp Description and Listing 99 -- 4.3.4 ANSYS Results, cantzero.m 102 -- Chapter 5 State Space Analysis 105 -- 5.2 State Space Formulation 106 -- 5.3 Definition of State Space Equations of Motion 108 -- 5.4 Input Matrix Forms 109 -- 5.5 Output Matrix Forms 111 -- 5.6 Complex Eigenvalues and Eigenvectors--State Space Form 113 -- 5.7 MATLAB Code tdof_non_prop_damped.m: Methodology, Model Setup, Eigenvalue Calculation Listing 115 -- 5.8 Eigenvectors--Normalized to Unity 119 -- 5.9 Eigenvectors--Magnitude and Phase Angle Representation 121 -- 5.10 Complex Eigenvectors Combining to Give Real Motions 122 -- 5.11 Argand Diagram Introduction 124 -- 5.12 Calculating [zeta], Plotting Eigenvalues in Complex Plane, Frequency Response 126 -- 5.13 Initial Condition Responses of Individual Modes 128 -- 5.14 Plotting Initial Condition Response, Listing 130 -- 5.15 Plotted Results: Argand and Initial Condition Responses 132 -- 5.15.1 Argand Diagram, Mode 2 133 -- 5.15.2 Time Domain Responses, Mode 2 134 -- 5.15.3 Argand Diagram, Mode 3 135 -- 5.15.4 Time Domain Responses, Mode 3 136 -- Chapter 6 State Space: Frequency Response, Time Domain 139 -- 6.1 Introduction--Frequency Response 139 -- 6.2 Solving for Transfer Functions in State Space Form Using Laplace Transforms 139 -- 6.3 Transfer Function Matrix 142 -- 6.4 MATLAB Code tdofss.m--Frequency Response Using State Space 144 -- 6.4.1 Code Description, Plot 144 -- 6.4.2 Code Listing 144 -- 6.5 Introduction--Time Domain 148 -- 6.6 Matrix Laplace Transform--with Initial Conditions 148 -- 6.7 Inverse Matrix Laplace Transform, Matrix Exponential 149 -- 6.8 Back-Transforming to Time Domain 149 -- 6.9 Single Degree of Freedom System--Calculating Matrix Exponential in Closed Form 150 -- 6.9.1 Equations of Motion, Laplace Transform 150 -- 6.9.2 Defining the Matrix Exponential--Taking Inverse Laplace Transform 151 -- 6.9.3 Defining the Matrix Exponential--Using Series Expansion 152 -- 6.9.4 Solving for Time Domain Response 152 -- 6.10 MATLAB Code tdof_ss_time_ode45_slnk.m--Time Domain Response of tdof Model 153 -- 6.10.1 Equation of Motion Review 153 -- 6.10.2 Code Description 155 -- 6.10.3 Code Results--Time Domain Responses 156 -- 6.10.4 Code Listing 157 -- 6.10.5 MATLAB Function tdofssfun.m--Called by tdof_ss_time_ode45_slnk.m 159 -- 6.10.6 Simulink Model tdofss_simulink.mdl 160 -- Chapter 7 Modal Analysis 163 -- 7.2 Eigenvalue Problem 164 -- 7.2.1 Equations of Motion 164 -- 7.2.2 Principal (Normal) Mode Definition 165 -- 7.2.3 Eigenvalues / Characteristic Equation 165 -- 7.2.4 Eigenvectors 168 -- 7.2.5 Interpreting Eigenvectors 172 -- 7.2.6 Modal Matrix 172 -- 7.3 Uncoupling the Equations of Motion 173 -- 7.4 Normalizing Eigenvectors 177 -- 7.4.1 Normalizing with Respect to Unity 177 -- 7.4.2 Normalizing with Respect to Mass 178 -- 7.5 Reviewing Equations of Motion in Principal Coordinates--Mass Normalization 182 -- 7.5.1 Equations of Motion in Physical Coordinate System 182 -- 7.5.2 Equations of Motion in Principal Coordinate System 183 -- 7.5.3 Expanding Matrix Equations of Motion in Both Coordinate Systems 183 -- 7.6 Transforming Initial Conditions and Forces 184 -- 7.7 Summarizing Equations of Motion in Both Coordinate Systems 185 -- 7.8 Back-Transforming from Principal to Physical Coordinates 186 -- 7.9 Reducing the Model Size When Only Selected Degrees of Freedom are Required 187 -- 7.10 Damping in Systems with Principal Modes 189 -- 7.10.2 Conditions Necessary for Existence of Principal Modes in Damped System 190 -- 7.10.3 Different Types of Damping 192 -- 7.10.4 Defining Damping Matrix When Proportional Damping is Assumed 195 -- Chapter 8 Frequency Response: Modal Form 201 -- 8.2 Review from Previous Results 202 -- 8.3 Transfer Functions--Laplace Transforms in Principal Coordinates 204 -- 8.4 Back-Transforming Mode Contributions to Transfer Functions in Physical Coordinates 206 -- 8.5 Partial Fraction Expansion and the Modal Form 209 -- 8.6 Forcing Function Combinations to Excite Single Mode 211 -- 8.7 How Modes Combine to Create Transfer Functions 213 -- 8.8 Plotting Individual Mode Contributions 217 -- 8.9 MATLAB Code tdof_modal_xfer.m--Plotting Frequency Responses, Modal Contributions 226 -- 8.9.1 Code Overview 226 -- 8.9.2 Code Listing, Partial 226 -- 8.10 tdof Eigenvalue Problem Using ANSYS 230 -- 8.10.1 ANSYS Code threedof.inp Description 230 -- 8.10.2 ANSYS Code Listing 230 -- 8.10.3 ANSYS Results 234 -- Chapter 9 Transient Response: Modal Form 239 -- 9.2 Review of Previous Results 239 -- 9.3 Transforming Initial Conditions ands Forces 240 -- 9.3.1 Transforming Initial Conditions 240 -- 9.3.2 Transforming Forces 241 -- 9.4 Complete Equations of Motion in Principal Coordinates 241 -- 9.5 Solving Equations of Motion Using Laplace Transform 243 -- 9.6 MATLAB Code tdof_modal_time.m--Time Domain Displacements in Physical/Principal Coordinates 247 -- 9.6.1 Code Description 247 -- 9.6.2 Code Results 248 -- 9.6.3 Code Listing 251 -- Chapter 10 Modal Analysis: State Space Form 255 -- 10.2 Eigenvalue Problem 256 -- 10.3 Eigenvalue Problem--Laplace Transform 257 -- 10.4 Eigenvalue Problem--Eigenvectors 259 -- 10.5 Modal Matrix 262 -- 10.6 MATLAB Code tdofss_eig.m: Solving for Eigenvalues and Eigenvectors 262 -- 10.6.1 Code Description 262 -- 10.6.2 Eigenvalue Calculation 262 -- 10.6.3 Eigenvector Calculation 264 -- 10.6.4 MATLAB Eigenvectors--Real and Imaginary Values 265 -- 10.6.5 Sorting Eigenvalues / Eigenvectors 266 -- 10.6.6 Normalizing Eigenvectors 269 -- 10.6.7 Writing Homogeneous Equations of Motion 273 -- 10.6.8 Individual Mode Contributions, Modal State Space Form 277 -- 10.7 Real Modes--Argand Diagrams, Initial Condition Responses of Individual Modes 279 -- 10.7.1 Undamped Model, Eigenvectors, Real Modes 280 -- 10.7.2 Principal Coordinate Eigenvalue Problem 283 -- 10.7.3 Damping Calculation, Eigenvalue Complex Plane Plot 284 -- 10.7.4 Principal Displacement Calculations 286 -- 10.7.5 Transformation to Physical Coordinates 287 -- 10.7.6 Plotting Results 288 -- 10.7.7 Undamped/Proportionally Damped Argand Diagram, Mode 2 290 -- 10.7.8 Undamped/Proportionally Damped Argand Diagram, Mode 3 292 -- 10.7.9 Proportionally Damped Initial Condition Response, Mode 2 293 -- 10.7.10 Proportionally Damped Initial Condition Response, Mode 3 295 -- Chapter 11 Frequency Response: Modal State Space Form 301 -- 11.2 Modal State Space Setup, tdofss_modal_xfer_modes.m Listing 301
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