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The Integrated Test Analysis Process for Structural Dynamic Systems

Author Robert N. Coppolino , Kristin B. Zimmerman
Release Date: 2019/11/01
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Book Description

Over the past 60 years, the U.S. aerospace community has developed, refined, and standardized an integrated approach to structural dynamic model verification and validation.

One name for this overall approach is the Integrated Test Analysis Process (ITAP) for structural dynamic systems. ITAP consists of seven sequential tasks, namely: (1) definition of test article finite element models; (2) systematic modal test planning; (3) measured data acquisition; (4) measured data analysis; (5) experimental modal analysis; (6) systematic test-analysis correlation; and (7) reconciliation of finite element models and modal test data. Steps 1, 2, and 7 rely strictly on mathematical model disciplines, and steps 3 and 4 rely on laboratory disciplines and techniques. Current industry practice of steps 5 and 6 calls for interaction of mathematical model and laboratory disciplines, which compromises the objectivity of both modeling and laboratory disciplines. This book addresses technical content, strategies, and key relevant experiences related to all steps of ITAP, except for measured data acquisition which is the specialized domain of highly experienced laboratory professionals who contend with mechanical and electrical practicalities of instrumentation, excitation hardware, and data collection systems.

Table of Contents

  1. Preface
  2. Overview of the Integrated Test Analysis Process (ITAP)
    1. Introduction
    2. System Dynamic Model
    3. Modal Test Plan and Test-Analysis Correlation
    4. Measured Data Acquisition
    5. Measured Data Analysis
    6. Experimental Modal Analysis
    7. Model Updating (Reconciliation)
    8. General References
    9. Key Illustrative Examples
    10. Closure
  3. Definition of Test Article Finite Element Models
    1. Part 1: Variational Foundations of Modern Structural Dynamics
      1. Introduction
      2. Economy in Nature and Basic Variational Formulations
      3. Mathematical Physics and Hamilton's Principle
      4. The Contributions of Ritz, Galerkin, and Trefftz
      5. The Ritz Method
      6. Galerkin's Method
      7. Trefftz's Method
      8. Automated Formulations in Structural Dynamics
      9. The Finite Element Method
      10. Assembly of Linear Structural System Models
      11. System Models with Localized Nonlinearities
      12. Matrix Structural Analysis
      13. Free Vibration and Modal Analysis
      14. Uncoupled Structural Dynamic Equations
      15. Closure
    2. Part 2: Guidelines for Systematic Model Development
      1. Introduction
      2. Linear Single-Degree-of-Freedom Equations
      3. Linear Multi-Degree-of-Freedom Equations
      4. Normal Modes of Undamped MDOF Systems
      5. Response to Impulsive and Transient Force Excitations
      6. Response Spectrum and Shock Spectrum
      7. Illustrative Example: Half-Sine Pulse Force
      8. Illustrative Example: 1940 El Centro CA Ground Motion Data
      9. Definition of Relevant Structural Dynamic Models
      10. Illustrative Example: Aluminum Launch Vehicle and Spacecraft Components
      11. Illustrative Example: Aluminum Launch Vehicle Feedline
      12. Modal Density and the Effectiveness of Finite Element Models
      13. Illustrative Example: Fluid-Filled Circular Cylindrical Shell
      14. Free Surface Slosh Modes
      15. Interface Flexibility in Structural Assemblies—A Retrospective
      16. Damping in Structural Assemblies
      17. Closure
    3. References
  4. Systematic Modal Test Planning
    1. Part 1: Understanding Modal Dynamic Characteristics
      1. Introduction
      2. Illustrative Example: ISS P5 Short Spacer
      3. Illustrative Example: Axisymmetric Shell Finite Element Model (1/2)
      4. Illustrative Example: Axisymmetric Shell Finite Element Model (2/2)
      5. Closure
    2. Part 2: Target Mode Selection
      1. Introduction
      2. Structure Excited by Boundary Accelerations and Applied External Loads
      3. Modal Effective Mass and Target Mode Selection
      4. Illustrative Example: ISS P5 Short Spacer
      5. Modal Gains and Target Mode Selection
      6. The Mode Acceleration Method and Target Mode Selection
      7. Illustrative Example: Axisymmetric Shell Finite Element Model
      8. Closure
    3. Part 3: Response DOF Selection for Mapping Experimental Modes
      1. Introduction
      2. Selection of DOFs for Modal Mapping (the RKE Method)
      3. Illustrative Example: ISS P5 Short Spacer
      4. Allocation of Modal Excitation Resources
      5. Closure
    4. References
  5. Measured Data Analysis
    1. Part 1: Preliminary Measured Data Analysis
      1. Introduction
      2. Key Preliminary Measured Data Analysis Functions, Mean, Variance, and Standard Deviation
      3. Normalized Probability Density and Ideal Gaussian Distribution
      4. Total Normalized Probability Function
      5. Autospectrum or Power Spectral Density Function
      6. Cross-Spectrum or Cross-Power Spectral Density Function
      7. The Spectrogram Function
      8. Illustrative Example: Sinusoidal Time History with Background Random Noise
      9. Illustrative Example: SDOF Linear System Response to Random Excitation
      10. Illustrative Example: ISPE Modal Test
      11. Illustrative Example: Wire Rope Test Article
      12. Illustrative Example: ISS P5 Modal Test
      13. Closure
    2. Part 2: Frequency Response Function Estimates from Measured Data
      1. Introduction
      2. MI/MO Frequency Response Equations for Systems with Algebraic Nonlinearities
      3. SI/SO, MI/SO and MI/MO Frequency Response Function Estimation
      4. Illustrative Example: ISPE Modal Test
      5. Illustrative Example: Wire Rope MI/SO Test Data Analysis
      6. Illustrative Example: ISS P5 Modal Test
      7. Closure
    3. References
  6. Experimental Modal Analysis
    1. Part 1: Preliminary Experimental Modal Analysis
      1. Introduction
      2. Frequency Response Characteristics of Linear SDOF Systems
      3. Frequency Response Characteristics of Linear MDOF Systems
      4. Illustrative Example: ISS P5 Modal Test
      5. Illustrative Example: ISPE Modal Test
      6. Closure
    2. Part 2: The Simultaneous Frequency Domain Method
      1. Introduction
      2. Effective Dynamic Systems
      3. The SFD Method Prior to 2018
      4. Illustrative Example: ISS P5 Modal Test
      5. SFD 2018: A Fresh Look at Experimental Modal Analysis
      6. Illustrative Example: ISPE Modal Test
      7. Closure
    3. References
  7. Systematic Test Analysis Correlation
    1. Part 1: Conventional Mass Weighted Correlation of Test and FEM Modes
      1. Introduction
      2. Derivation of Mass Weighted Test-Analysis Correlation Metrics
      3. Illustrative Example: ISS P5 Modal Test
      4. Illustrative Example: ISPE Modal Test
      5. Closure
    2. Part 2: Correlation of Test and FEM Modes Using Left-Hand Eigenvectors
      1. Introduction
      2. Modal Test Data Resulting from Estimated State-Space Models
      3. Theoretical System Modes in State-Space Form
      4. Correlation of Experimental and Theoretical Modes (Complex Least Squares)
      5. Illustrative Example: ISPE Modal Test
      6. Roadmap for a Highly Improved Integrated Test Analysis Process
      7. Closure
    3. References
  8. Reconciliation of Finite Element Models and Modal Test Data
    1. Part 1: Finite Element Model Modal Sensitivity
      1. Introduction
      2. Sensitivity Analysis Strategies
      3. Residual Vector Augmentation for Local Alterations
      4. Residual Mode Augmentation (RMA) for Dispersed Alterations
      5. RMA Solution Qualities
      6. Illustrative Example: ISPE Modal Test
      7. Closure
    2. Part 2: Test-Analysis Reconciliation
      1. Introduction
      2. Modal Cost Function (C_) and Optimal Test-Analysis Reconciliation
      3. Illustrative Example: Rectangular Plate Supported by Corner Posts
      4. Illustrative Example: ISS P5 Modal Test
      5. Illustrative Example: ISPE Modal Test
      6. Illustrative Example: Wire Rope Test Article
      7. Closure
    3. References
  9. Author's Biography
  10. Blank Page (1/3)
  11. Blank Page (2/3)
  12. Blank Page (3/3)
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