ITAP Toolbox Integrated Test Analysis Processor Toolbox User’s Guide © UNIVERSAL ANALYTICS, INC. Torrance, California USA All Rights Reserved January 1999 UNIVERSAL ANALYTICS, INC. 3625 Del Amo Blvd, Suite 370 Torrance, CA 90503 Tel: (310) 214-2922 FAX: (310) 214-3420 ii Table of Contents Foreword viii Preface ix What is ITAP? x The ITAP-A Toolbox xi The ITAP-T Toolbox xii UAI/NASTRAN in the Laboratory xiii Installation xiv 1.0 ITAP-A Theory 1 1.1 Introductory Remarks 2 1.2 Dynamics of Linear Single Degree-of-Freedom Systems 3 1.2.1 Fundamental Single-Degree-of-Freedom Equations 3 1.2.2 Response to Simple Harmonic Excitation 4 1.2.3 Response to Impulsive and Transient Excitations 6 1.2.4 Response Spectrum and Shock Spectrum 8 1.2.5 Response to Random Excitation 9 1.2.6 Nonlinear Single-Degree-of-Freedom Systems 11 1.3 Structural and Mechanical System Dynamic Models 12 1.3.1 Guidelines for Definition of Relevant Finite Element Models 12 1.3.2 Modal Density and the Effectiveness of Finite Element Models 13 1.3.3 Fundamental Dynamic Formulations 14 1.3.4 Constraints and Model Condensation 15 1.3.5 Description of Normal Modes 16 1.3.6 Useful Normal Mode Relationships 17 1.3.7 ITAP-A Normal Mode Calculations 18 1.3.8 Description of Complex Modes for a Structural Dynamic System 18 1.3.9 ITAP-A Complex Structural Dynamic Mode Calculations 20 1.3.10 Truncated Mode Set Descriptions 20 1.3.11 Residual Mode Vectors 21 1.3.12 The Mode Acceleration Method 23 iii 1.4 Response of Multi-Degree of Freedom Systems 24 1.4.1 Normal Modes and Complex Modes 24 1.4.2 Response to Base Motion Excitation 25 1.4.3 Response to Simple Harmonic Excitation 26 1.4.4 Response to Random Excitation 28 1.4.5 Response to Transient Excitation (Orthonormal Real Mode Case) 29 1.4.6 Response to Transient Excitation (Complex Mode Case) 30 1.4.7 Summary of Key Linear Dynamic System Analysis Modules 31 1.4.8 Response of Nonlinear Dynamic Systems 32 1.5 Model Quality, Content and Correlation Analysis 33 1.5.1 Rigid Body Relationships 33 1.5.2 Modal Participation Factors and Modal Effective Mass 34 1.5.3 Modal Orthogonality Evaluation 35 1.5.4 Modal Cross-Orthogonality and Coherence Evaluation 36 1.5.5 Mode Set Orthogonalization 37 1.5.6 Apparent Mass and Stiffness Matrices 39 1.6 DOF Selection for Mapping of Experimental Normal Modes 40 1.6.1 Overview 40 1.6.2 Selection of DOFs for Modal Mapping 40 1.6.3 Illustrative Examples 42 1.7 Closure 48 1.8 References 49 2.0 Model Definition and Translation 51 2.1 Accessing NASTRAN Matrix Data 52 2.2 UAI/NASTRAN Modal Analysis (Rigid Format 3 Alter) 52 2.3 Rigid Format 3 Alter Listing 54 2.4 ITAP-A Test-Analysis Model (TAM) Definition 55 2.5 Sample TAM Model Definition (a makmodl Session) 56 3.0 Modal Test Planning 61 3.1 ITAP-A Implementation Summary 62 3.2 Illustrative Test Planning Sessions 64 3.2.1 NASTRAN Output4 File Translation or ITAP-A TAM File Access 64 3.2.2 Adequacy of TAM Response “Measurement” Dofs (First Try) 65 3.2.3 Adequacy of TAM Response “Measurement” Dofs (Revised Set) 69 3.2.4 Review of TAM Modes 72 3.2.5 Allocation of Excitation Resources 76 iv 4.0 Modal Test Data Evaluation 79 4.1 Accessing Modal Test Data 80 4.2 ITAP-A Implementation Summary 81 4.3 Illustrative Modal Test Data Evaluation Sessions 83 4.3.1 SDRC Universal File Translation or ITAP-A Modal Test File Access 83 4.3.2 Modal Test Data Quality and Content 84 4.3.3 Review of Test Modes 88 4.3.4 Correlation of Test and TAM Modes 89 5.0 ITAP-A Function Modules 91 5.1 Overview of ITAP-A Function Modules by Category 92 5.2 ITAP-A Function Module Descriptions 94 6.0 ITAP-T Theory 153 6.1 Introductory Remarks 154 6.2 Preliminary Measured Data Analysis Fundamentals 155 6.2.1 Classifications of Time History Data Records 155 6.2.2 Mean, Variance and Standard Deviation 156 6.2.3 Normalized Probability Density and Ideal Gaussian Distribution 157 6.2.4 Total Probability Function 157 6.2.5 Autospectrum or Power Spectral Density Function 158 6.2.6 Response and Shock Spectrum Functions 159 6.2.7 Random Decrement Signature Function 159 6.3 Preliminary Measured Data Analysis Examples 161 6.3.1 Sinusoidal Time History Record with Background Random Noise 161 6.3.2 SDOF Linear System Response to Broad Band Random Excitation 162 6.3.3 Nonlinear SDOF System Response to Random Excitation 164 6.3.4 Nonlinear SDOF System Response to Swept Sine Excitation 166 6.3.5 Linear MDOF System Response to Broad Band Random Excitation 167 6.3.6 Preliminary Channel Pair Analysis 168 6.4 SI/SO and SI/MO Spectral and Correlation Analysis 171 6.4.1 The Cross Spectral Density Function 171 6.4.2 Optimum SI/SO Frequency Response Function Estimation 171 6.4.3 The Ordinary Coherence Function 172 6.4.4 Windowing and Overlap Processing 173 6.4.5 SI/MO Analysis 173 6.5 SI/SO and SI/MO Analysis Examples 175 6.5.1 Linear SDOF System SI/SO Analysis 175 6.5.2 Nonlinear SDOF System SI/SO Analysis 178 6.5.3 Linear MDOF System SI/MO Analysis 179 6.6 MI/SO and MI/MO Spectral and Correlation Analysis 182 6.6.1 Linear System Response due to Multiple Excitations 182 v 6.6.2 MI/SO Analysis using Triangular Decomposition 183 6.6.3 The Cumulative Coherence Function Family 185 6.7 MI/SO and MI/MO Analysis Examples 186 6.7.1 Linear MDOF System MI/MO Analysis 186 6.7.2 Nonlinear SDOF System MI/SO Analysis (Reverse Dynamic System) 191 6.7.3 MI/SO Analysis (Dynamic System with Nonlinear “Feedback”) 193 6.7.4 MI/SO Analysis (Nonlinear Tension-Displacement Relationship) 194 6.8 Modal Parameter Estimation 195 6.8.1 Preliminary Single Channel Modal Analysis 195 6.8.2 Preliminary Multi-Channel Modal Analysis 198 6.8.3 The Simultaneous Frequency Domain (SFD) Method Overview 200 6.8.4 SFD Step 0: The Global Skyline Modal Indicator Function 201 6.8.5 SFD Step 1: Dominant Vectors and Generalized FRFs 202 6.8.6 SFD Step 2: Effective Dynamic System and Associated Eigenvalues 204 6.8.7 SFD Step 3: Calculation of Modal Vectors 206 6.8.8 Complex Modes, Multiple Excitations and Base Motion Excitation 208 6.8.9 References 209 7.0 Preliminary Data Analysis 211 7.1 Introductory Remarks 212 7.2 Measured Data File Structure 213 7.2.1 The Basic Time History (.mat) Data File 213 7.2.2 Conversion of SDRC Universal File (Time History) Data 214 7.2.3 Correspondence with an ITAP-A Test-Analysis Model (TAM) File 215 7.2.4 Frequency Response Function Data 216 7.2.5 Experimental Modal Analysis Data 217 7.3 Quality and Content of Individual Time Histories 218 7.3.1 Illustrative Example “Prelim” Session 218 7.4 Preliminary Channel Pair Analysis 224 7.4.1 Illustrative Example “pairevu” Session 224 8.0 Spectral and Correlation Analysis 227 8.1 Introductory Remarks 228 8.2 Illustrative Example SI/MO and MI/MO Sessions 229 8.2.1 Illustrative Example “SI/MO” Session 229 8.2.2 Illustrative Example “MI/MO” Session 232 8.2.3 Review of SI/MO and MI/MO Analysis Results 235 vi 9.0 Experimental Modal Analysis 239 9.1 Introductory Remarks 240 9.2 Illustrative Example Modal Identification Sessions 241 9.2.1 Overview of Modal Identification Function Modules called by modexe 241 9.2.2 Example “Modexe” Session (Single Input FRFs, Real Modes) 242 9.2.3 Example “Modexe” Session (Multiple Input FRFs, Complex Modes) 247 9.2.4 Example “Modexe” Session (Base Motion Input, Complex Modes) 252 10.0 ITAP-T Function Modules 257 10.1 Overview of ITAP-T Function Modules by Category 258 10.2 ITAP-T Function Module Descriptions 260 vii Foreword The overall concept of the Integrated Test Analysis Processor (ITAP) evolved over a period of 23 years. From 1975 to 1983, while employed at The Aerospace Corporation, I was involved (with colleagues at that organization) in the planning, witnessing and evaluation of launch vehicle and spacecraft modal testing and in flight data analysis. In addition, from 1979 to 1983, Sheldon Rubin and I conducted technology studies aimed at in-situ structural health monitoring of fixed offshore oil platforms. Technical demands associated with these activities pointed to the need for a rigorous, organized and disciplined test-analysis philosophy, which is the foundation of ITAP. One key feature of ITAP, namely the Simultaneous Frequency Domain (SFD) technique for identification of vibration mode parameters from measured data was introduced in 1980. SFD has been enhanced and refined over the years as a result of its continued application in laboratory and field test activities. From 1983 to 1987, ITAP philosophy was formally introduced by a consortium led by three individuals, namely Julius Bendat, Richard Stroud and the writer. During that period, the talents and experience of these principals in Random Data Analysis (Bendat), Dynamic Test Philosophy (Stroud) and Integration of (Finite Element) Analysis and Test Disciplines (Coppolino) were combined to establish an early “incarnation” of ITAP.