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عدد المساهمات : 19001 التقييم : 35505 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
| موضوع: كتاب Vibration Simulation Using MATLAB and ANSYS الخميس 03 مايو 2012, 8:29 pm | |
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أخوانى فى الله أحضرت لكم كتاب Vibration Simulation Using MATLAB and ANSYS Michael R. Hatch
و المحتوى كما يلي :
Table of Contents Chapter 1: Introduction 1.1 Representing Dynamic Mechanical Systems 1.2 Modal Analysis 1.3 Model Size Reduction CHAPTER 2: TRANSFER FUNCTION ANALYSIS 2.1 Introduction 2.2 Deriving Matrix Equations of Motion 2.2.1 Three Degree of Freedom (tdof) System, Identifying Components and Degrees of Freedom 2.2.2 Defining the Stiffness, Damping and Mass Matrices 2.2.3 Checks on Equations of Motion for Linear Mechanical Systems 2.2.4 Six Degree of Freedom (6dof) Model − Stiffness Matrix 2.2.5 Rotary Actuator Model − Stiffness and Mass Matrices 2.3 Single Degree of Freedom (sdof) System Transfer Function and Frequency Response 2.3.1 sdof System Definition, Equations of Motion 2.3.2 Transfer Function 2.3.3 Frequency Response 2.3.4 MATLAB Code sdofxfer.m Description 2.3.5 MATLAB Code sdofxfer.m Listing 2.4 tdof Laplace Transform, Transfer Functions, Characteristic Equation, Poles, Zeros 2.4.1 Laplace Transforms with Zero Initial Conditions 2.4.2 Solving for Transfer Functions 2.4.3 Transfer Function Matrix for Undamped Model 2.4.4 Four Distinct Transfer Functions 2.4.5 Poles 2.4.6 Zeros 2.4.7 Summarizing Poles and Zeros, Matrix Format 2.5 MATLAB Code tdofpz3x3.m – Plot Poles and Zeros 2.5.1 Code Description 2.5.2 Code Listing 2.5.3 Code Output – Pole/Zero Plots in Complex Plane 2.5.3.1 Undamped Model – Pole/Zero Plots 2.5.3.2 Damped Model – Pole/Zero Plots 2.5.3.3 Root Locus, tdofpz3x3_rlocus.m 2.5.3.4 Undamped and Damped Model – tf and zpk Forms Problems CHAPTER 3: FREQUENCY RESPONSE ANALYSIS 3.1 Introduction 3.2 Low and High Frequency Asymptotic Behavior 3.3 Hand Sketching Frequency Responses 3.4 Interpreting Frequency Response Graphically in Complex Plane 3.5 MATLAB Code tdofxfer.m – Plot Frequency Responses 3.5.1 Code Description 3.5.2 Polynomial Form, For-Loop Calculation, Code Listing 3.5.3 Polynomial Form, Vector Calculation, Code Listing 3.5.4 Transfer Function Form − Bode Calculation, Code Listing 3.5.5 Transfer Function Form, Bode Calculation with Frequency, Code Listing 3.5.6 Zero/Pole/Gain Function Form, Bode Calculation with Frequency, Code Listing 3.5.7 Code Output – Frequency Response Magnitude and Phase Plots 3.6 Other Forms of Frequency Response Plots 3.6.1 Log Magnitude versus Log Frequency 3.6.2 db Magnitude versus Log Frequency 3.6.3 db Magnitude versus Linear Frequency 3.6.4 Linear Magnitude versus Linear Frequency 3.6.5 Real and Imaginary Magnitudes versus Log and Linear Frequency 3.6.6 Real versus Imaginary (Nyquist) 3.7 Solving for Eigenvectors (Mode Shapes) Using the Transfer Function Matrix Problems CHAPTER 4: ZEROS IN SISO MECHANICAL SYSTEMS 4.1 Introduction 4.2 “n” dof Example 4.2.1 MATLAB Code ndof_numzeros.m, Usage Instructions 4.2.2 Seven dof Model – z7/F1 Frequency Response 4.2.3 Seven dof Model – z3/F4 Frequency Response 4.2.4 Seven dof Model – z3/F3, Driving Point Frequency Response 4.3 Cantilever Model – ANSYS 4.3.1 Introduction 4.3.2 ANSYS Code cantfem.inp Description and Listing 4.3.3 ANSYS Code cantzero.inp Description and Listing 4.3.4 ANSYS Results, cantzero.m Problem CHAPTER 5: STATE SPACE ANALYSIS 5.1 Introduction 5.2 State Space Formulation 5.3 Definition of State Space Equations of Motion 5.4 Input Matrix Forms 5.5 Output Matrix Forms 5.6 Complex Eigenvalues and Eigenvectors – State Space Form 5.7 MATLAB Code tdof_non_prop_damped.m: Methodology, Model Setup, Eigenvalue Calculation Listing 5.8 Eigenvectors – Normalized to Unity 5.9 Eigenvectors – Magnitude and Phase Angle Representation 5.10 Complex Eigenvectors Combining to Give Real Motions 5.11 Argand Diagram Introduction 5.12 Calculating ζ , Plotting Eigenvalues in Complex Plane, Frequency Response 5.13 Initial Condition Responses of Individual Modes 5.14 Plotting Initial Condition Response, Listing 5.15 Plotted Results: Argand and Initial Condition Responses 5.15.1 Argand Diagram, Mode 2 5.15.2 Time Domain Responses, Mode 2 5.15.3 Argand Diagram, Mode 3 5.15.4 Time Domain Responses, Mode 3 Problems CHAPTER 6: STATE SPACE: FREQUENCY RESPONSE, TIME DOMAIN 6.1 Introduction – Frequency Response 6.2 Solving for Transfer Functions in State Space Form Using Laplace Transforms 6.3 Transfer Function Matrix 6.4 MATLAB Code tdofss.m – Frequency Response Using State Space 6.4.1 Code Description, Plot 6.4.2 Code Listing 6.5 Introduction – Time Domain 6.6 Matrix Laplace Transform – with Initial Conditions 6.7 Inverse Matrix Laplace Transform, Matrix Exponential 6.8 Back-Transforming to Time Domain 6.9 Single Degree of Freedom System – Calculating Matrix Exponential in Closed Form 6.9.1 Equations of Motion, Laplace Transform 6.9.2 Defining the Matrix Exponential – Taking Inverse Laplace Transform 6.9.3 Defining the Matrix Exponential – Using Series Expansion 6.9.4 Solving for Time Domain Response 6.10 MATLAB Code tdof_ss_time_ode45_slnk.m – Time Domain Response of tdof Model 6.10.1 Equation of Motion Review 6.10.2 Code Description 6.10.3 Code Results – Time Domain Responses 6.10.4 Code Listing 6.10.5 MATLAB Function tdofssfun.m – Called by tdof_ss_time_ode45_slnk.m 6.10.6 Simulink Model tdofss_simulink.mdl Problems CHAPTER 7: MODAL ANALYSIS 7.1 Introduction 7.2 Eigenvalue Problem 7.2.1 Equations of Motion 7.2.2 Principal (Normal) Mode Definition 7.2.3 Eigenvalues / Characteristic Equation 7.2.4 Eigenvectors 7.2.5 Interpreting Eigenvectors 7.2.6 Modal Matrix 7.3 Uncoupling the Equations of Motion 7.4 Normalizing Eigenvectors 7.4.1 Normalizing with Respect to Unity 7.4.2 Normalizing with Respect to Mass 7.5 Reviewing Equations of Motion in Principal Coordinates – Mass Normalization 7.5.1 Equations of Motion in Physical Coordinate System 7.5.2 Equations of Motion in Principal Coordinate System 7.5.3 Expanding Matrix Equations of Motion in Both Coordinate Systems 7.6 Transforming Initial Conditions and Forces 7.7 Summarizing Equations of Motion in Both Coordinate Systems 7.8 Back-Transforming from Principal to Physical Coordinates 7.9 Reducing the Model Size When Only Selected Degrees of Freedom are Required 7.10 Damping in Systems with Principal Modes 7.10.1 Overview 7.10.2 Conditions Necessary for Existence of Principal Modes in Damped System 7.10.3 Different Types of Damping 7.10.3.1 Simple Proportional Damping 7.10.3.2 Proportional to Stiffness Matrix – “Relative” Damping 7.10.3.3 Proportional to Mass Matrix – “Absolute” Damping 7.10.4 Defining Damping Matrix When Proportional Damping is Assumed 7.10.4.1 Solving for Damping Values 7.10.4.2 Checking Rayleigh Form of Damping Matrix Problems CHAPTER 8: FREQUENCY RESPONSE: MODAL FORM 8.1 Introduction 8.2 Review from Previous Results 8.3 Transfer Functions – Laplace Transforms in Principal Coordinates 8.4 Back-Transforming Mode Contributions to Transfer Functions in Physical Coordinates 8.5 Partial Fraction Expansion and the Modal Form 8.6 Forcing Function Combinations to Excite Single Mode 8.7 How Modes Combine to Create Transfer Functions 8.8 Plotting Individual Mode Contributions 8.9 MATLAB Code tdof_modal_xfer.m – Plotting Frequency Responses, Modal Contributions 8.9.1 Code Overview 8.9.2 Code Listing, Partial 8.10 tdof Eigenvalue Problem Using ANSYS 8.10.1 ANSYS Code threedof.inp Description 8.10.2 ANSYS Code Listing 8.10.3 ANSYS Results Problems CHAPTER 9 TRANSIENT RESPONSE: MODAL FORM 9.1 Introduction 9.2 Review of Previous Results 9.3 Transforming Initial Conditions and Forces 9.3.1 Transforming Initial Conditions 9.3.2 Transforming Forces 9.4 Complete Equations of Motion in Principal Coordinates 9.5 Solving Equations of Motion Using Laplace Transform 9.6 MATLAB Code tdof_modal_time.m – Time Domain Displacements in Physical/Principal Coordinates 9.6.1 Code Description 9.6.2 Code Results 9.6.3 Code Listing Problems CHAPTER 10: MODAL ANALYSIS: STATE SPACE FORM 10.1 Introduction 10.2 Eigenvalue Problem 10.3 Eigenvalue Problem – Laplace Transform 10.4 Eigenvalue Problem – Eigenvectors 10.5 Modal Matrix 10.6 MATLAB Code tdofss_eig.m: Solving for Eigenvalues and Eigenvectors 10.6.1 Code Description 10.6.2 Eigenvalue Calculation 10.6.3 Eigenvector Calculation 10.6.4 MATLAB Eigenvectors – Real and Imaginary Values 10.6.5 Sorting Eigenvalues / Eigenvectors 10.6.6 Normalizing Eigenvectors 10.6.7 Writing Homogeneous Equations of Motion 10.6.7.1 Equations of Motion – Physical Coordinates 10.6.7.2 Equations of Motion – Principal Coordinates 10.6.8 Individual Mode Contributions, Modal State Space Form 10.7 Real Modes – Argand Diagrams, Initial Condition Responses of Individual Modes 10.7.1 Undamped Model, Eigenvectors, Real Modes 10.7.2 Principal Coordinate Eigenvalue Problem 10.7.3 Damping Calculation, Eigenvalue Complex Plane Plot 10.7.4 Principal Displacement Calculations 10.7.5 Transformation to Physical Coordinates 10.7.6 Plotting Results 10.7.7 Undamped/Proportionally Damped Argand Diagram, Mode 2 10.7.8 Undamped/Proportionally Damped Argand Diagram, Mode 3 10.7.9 Proportionally Damped Initial Condition Response, Mode 2 10.7.10 Proportionally Damped Initial Condition Response, Mode 3 Problems CHAPTER 11: FREQUENCY RESPONSE: MODAL STATE SPACE FORM 11.1 Introduction 11.2 Modal State Space Setup, tdofss_modal_xfer_modes.m Listing 11.3 Frequency Response Calculation 11.4 Frequency Response Plotting 11.5 Code Results – Frequency Response Plots, 2% of Critical Damping 11.6 Forms of Frequency Response Plotting Problem CHAPTER 12: TIME DOMAIN: MODAL STATE SPACE FORM 12.1 Introduction 12.2 Equations of Motion – Modal Form 12.3 Solving Equations of Motion Using Laplace Transforms 12.4 MATLAB Code tdofss_modal_time_ode45.m – Time Domain Modal Contributions 12.4.1 Modal State Space Model Setup, Code Listing 12.4.2 Problem Setup, Initial Conditions, Code Listing 12.4.3 Solving Equations Using ode45, Code Listing 12.4.4 Plotting, Code Listing 12.4.5 Functions Called: tdofssmodalfun.m, tdofssmodal1fun.m, tdofssmodal2fun.m, tdofssmodal3fun.m 12.5 Plotted Results Problem CHAPTER 13: FINITE ELEMENTS: STIFFNESS MATRICES 13.1 Introduction 13.2 Six dof Model – Element and Global Stiffness Matrices 13.2.1 Overview 13.2.2 Element Stiffness Matrix 13.2.3 Building Global Stiffness Matrix Using Element Stiffness Matrices 13.3 Two-Element Cantilever Beam 13.3.1 Element Stiffness Matrix 13.3.2 Degree of Freedom Definition – Beam Stiffness Matrix 13.3.3 Building Global Stiffness Matrix Using Element Stiffness Matrices 13.3.4 Eliminating Constraint Degrees of Freedom from Stiffness Matrix 13.3.5 Static Solution: Force Applied at Tip 13.4 Static Condensation 13.4.1 Derivation 13.4.2 Solving Two-Element Cantilever Beam Static Problem Problems CHAPTER 14: FINITE ELEMENTS: DYNAMICS 14.1 Introduction 14.2 Six dof Global Mass Matrix 14.3 Cantilever Dynamics 14.3.1 Overview – Mass Matrix Forms 14.3.2 Lumped Mass 14.3.3 Consistent Mass 14.4 Dynamics of Two-Element Cantilever – Consistent Mass Matrix 14.5 Guyan Reduction 14.5.1 Guyan Reduction Derivation 14.5.2 Two-Element Cantilever Eigenvalues Closed Form Solution Using Guyan Reduction 14.6 Eigenvalues of Reduced Equations for Two-Element Cantilever, State Space Form 14.7 MATLAB Code cant_2el_guyan.m – Two-Element Cantilever Eigenvalues/Eigenvectors 14.7.1 Code Description 14.7.2 Code Results 14.8 MATLAB Code cantbeam_guyan.m – User-Defined Cantilever Eigenvalues/Eigenvectors 14.9 ANSYS Code cantbeam.inp, Code Description 14.10 MATLAB cantbeam_guyan.m / ANSYS cantbeam.inp Results Summary 14.10.1 10-Element Beam Frequency Comparison 14.10.2 20-Element Beam Mode Shape Plots, Modes 1 to 5 14.11 MATLAB Code cantbeam_guyan.m Listing 14.12 ANSYS Code cantbeam.inp Listing Problems CHAPTER 15: SISO STATE SPACE MATLAB MODEL FROM ANSYS MODEL 15.1 Introduction 15.2 ANSYS Eigenvalue Extraction Methods 15.3 Cantilever Model, ANSYS Code cantbeam_ss.inp, MATLAB Code cantbeam_ss_freq.m 15.4 ANSYS 10-Element Model Eigenvalue/Eigenvector Summary 15.5 Modal Matrix 15.6 MATLAB State Space Model from ANSYS Eigenvalue Run – cantbeam_ss_modred.m 15.6.1 Input 15.6.2 Defining Degrees of Freedom and Number of Modes 15.6.3 Sorting Modes by dc Gain and Peak Gain, Selecting Modes Used 15.6.4 Damping, Defining Reduced Frequencies and Modal Matrices 15.6.5 Setting up System Matrix “a” 15.6.6 Setting up Input Matrix “b” 15.6.7 Setting up Output Matrix “c” and Direct Transmission Matrix “d” 15.6.8 Frequency Range, “ss” Setup, Bode Calculations 15.6.9 Full Model – Plotting Frequency Response, Step Response 15.6.10 Reduced Models – Plotting Frequency Response, Step Response 15.6.11 Reduced Models – Plotted Results – Four Modes Used 15.6.12 Modred Description 15.6.13 Defining Sorted or Unsorted Modes to be Used 15.6.14 Defining System for Reduction 15.6.15 Modred Calculations – “mdc” and “del” 15.6.16 Reduced Modred Models – Plotting Commands 15.6.17 Plotting Unsorted Modred Reduced Results – Eliminating High Frequency Modes 15.6.18 Plotting Sorted Modred Reduced Results – Eliminating Lower dc Gain Modes 15.6.19 Modred Summary 15.7 ANSYS Code cantbeam_ss.inp Listing CHAPTER 16: GROUND ACCELERATION MATLAB MODEL FROM ANSYS MODEL 16.1 Introduction 16.2 Model Description 16.3 Initial ANSYS Model Comparison – Constrained-Tip and Spring-Tip Frequencies/Mode Shapes 16.4 MATLAB State Space Model from ANSYS Eigenvalue Run – cantbeam_ss_shkr_modred.m 16.4.1 Input 16.4.2 Shaker, Spring, Gram Force Definitions 16.4.3 Defining Degrees of Freedom and Number of Modes 16.4.4 Frequency Range, Sorting Modes by dc Gain and Plotting, Selecting Modes Used 16.4.5 Damping, Defining Reduced Frequencies and Modal Matrices 16.4.6 Setting Up System Matrix “a” 16.4.7 Setting Up Matrices “b,” “c” and “d” 16.4.8 “ss” Setup, Bode Calculations 16.4.9 Full Model – Plotting Frequency Response, Shock Response 16.4.10 Reduced Models – Plotting Frequency Response, Shock Response 16.4.11 Reduced Models – Plotted Results, Four Modes Used 16.4.12 Modred – Setting up, “mdc” and “del” Reduction, Bode Calculation 16.4.13 Reduced Modred Models – Plotting Commands 16.4.14 Plotting Unsorted Modred Reduced Results – Eliminating High Frequency Modes 16.4.15 Plotting Sorted Modred Reduced Results – Eliminating Lower dc Gain Modes 16.4.16 Model Reduction Summary 16.5 ANSYS Code cantbeam_ss_spring_shkr.inp Listing CHAPTER 17: SISO DISK DRIVE ACTUATOR MODEL 17.1 Introduction 17.2 Actuator Description 17.3 ANSYS Suspension Model Description 17.4 ANSYS Suspension Model Results 17.4.1 Frequency Response 17.4.2 Mode Shape Plots 17.5 ANSYS Actuator/Suspension Model Description 17.6 ANSYS Actuator/Suspension Model Results 17.6.1 Eigenvalues, Frequency Responses 17.6.2 Mode Shape Plots 17.6.3 Mode Shape Discussion 17.6.4 ANSYS Output Example Listing 17.7 MATLAB Model, MATLAB Code act8.m Listing and Results 17.7.1 Code Description 17.7.2 Input, dof Definition 17.7.3 Forcing Function Definition, dc Gain Calculation 17.7.4 Ranking Results 17.7.5 Building State Space Matrices 17.7.6 Define State Space Systems, Original and Reduced 17.7.7 Plotting of Results 17.8 Uniform and Non-Uniform Damping Comparison 17.9 Sample Rate and Aliasing Effects 17.10 Reduced Truncation and Matched dc Gain Results CHAPTER 18: BALANCED REDUCTION 18.1 Introduction 18.2 Reviewing dc Gain Ranking, MATLAB Code balred.m 18.3 Controllability, Observability 18.4 Controllability, Observability Gramians 18.5 Ranking Using Controllability/Observability 18.6 Balanced Reduction 18.7 Balanced and dc Gain Ranking Frequency Response Comparison 18.8 Balanced and dc Gain Ranking Impulse Response Comparison CHAPTER 19: MIMO TWO-STAGE ACTUATOR MODEL 19.1 Introduction 19.2 Actuator Description 19.3 ANSYS Model Description 19.4 ANSYS Piezo Actuator/Suspension Model Results 19.4.1 Eigenvalues, Frequency Response 19.4.2 Mode Shape Plots 19.4.3 Mode Shape Discussion 19.4.4 ANSYS Output Listing 19.5 MATLAB Model, MATLAB Code act8pz.m Listing and Results 19.5.1 Input, dof Definition 19.5.2 Forcing Function Definition, dc Gain Calculations 19.5.3 Building State Space Matrices 19.5.4 Balancing, Reduction 19.5.5 Frequency Responses for Different Numbers of Retained States 19.5.6 “del” and “mdc” Frequency Response Comparison 19.5.7 Impulse Response 19.6 MIMO Summary Problems APPENDIX 1: MATLAB and ANSYS Programs APPENDIX 2: Laplace Transforms A2.1 Definitions A2.2 Examples, Laplace Transform Table A2.3 Duality A2.4 Differentiation and Integration A2.5 Applying Laplace Transforms to LODE’s with Zero Initial Conditions A2.6 Transfer Function Definition A2.7 Frequency Response Definition A2.8 Applying Laplace Transforms to LODE’s with Initial Conditions A2.9 Applying Laplace Transform to State Space References
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Admin مدير المنتدى
عدد المساهمات : 19001 التقييم : 35505 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
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