
Topics in Modal Analysis & Testing, Volume 8
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Operational Modal & Modal Analysis Applications
Experimental Techniques
Modal Analysis, Measurements & Parameter Estimation
Modal Vectors & Modeling
Basics of Modal Analysis
Additive Manufacturing & Modal Testing of Printed Parts
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Content
- Intro
- Preface
- Contents
- 1 Modal Analysis on a Wind Turbine Blade Based on Wind Tunnel Experiments
- 1.1 Introduction
- 1.2 Modal Analysis and Operational Calculus
- 1.3 Output Only Modal Parameters Estimation
- 1.4 Wind Turbine Blade
- 1.5 Wind Tunnel Experiment
- 1.6 Application of the Time Domain Identification Scheme
- 1.7 Conclusion
- References
- 2 An Investigation of Vibrational Characteristics of Lap Joints Using Experimental and AnalyticalMethods
- 2.1 Introduction
- 2.2 Experimental Methods
- 2.3 Analytical Methods
- 2.3.1 Solid Structure FE Model
- 2.3.2 Welded Structure FE Model
- 2.3.3 Bolted Structure FE Model
- 2.3.4 Fractional Strain Energy Method
- 2.4 User Interface Development
- 2.5 Results and Discussion
- 2.5.1 Experimental Modal Comparisons
- 2.5.2 FE Model Comparisons
- 2.5.3 Strain-Energy Method Comparisons
- 2.6 Conclusions
- References
- 3 Using Strain Gages as References to Calculate Free-Free Frequency Response Functions
- 3.1 Introduction
- 3.1.1 Calculation of Free-Free FRFs Using Interface Forces as References
- 3.1.2 Numerical Example
- 3.2 Summary
- References
- 4 A Principle for Obtaining Pragmatic Uncertainty Bounds on Modal Parameters
- 4.1 Introduction
- 4.2 Theory
- 4.2.1 Multiple-Reference Ibrahim Time Domain (MITD) Method
- 4.2.2 Modified Multiple-Reference Ibrahim Time Domain (MMITD) Method
- 4.2.3 Low Order Versus High Order Method
- 4.2.4 Normalization to the Lowest or Highest Coefficient of the Matrix Polynomials
- 4.2.5 Calculating the System Matrix with Respect to Either the Original Hankel Matrix or the Time Shifted Hankel Matrix
- 4.3 Methodology
- 4.4 Results and Discussion
- 4.5 Conclusions
- References
- 5 On Partitioning of an SHM Problem and Parallels with Transfer Learning
- 5.1 Introduction
- 5.2 Problem Description
- 5.3 Problem Splitting
- 5.4 Knowledge Transfer Between the Two Problems
- 5.5 Discussion and Conclusions
- References
- 6 An Ontological Approach to Structural Health Monitoring
- 6.1 Introduction
- 6.2 Components of the Ontology
- 6.3 Main Ontology Structure
- 6.4 Connections
- 6.5 Aspects of the Ontology
- 6.6 Discussion and Conclusions
- References
- 7 Passive Aeroelastic Tailored Wing Modal Test Using the Fixed Base Correction Method
- Nomenclature
- 7.1 Introduction
- 7.2 Theory/Correction Methodology
- 7.3 Test Description
- 7.3.1 Test Article
- 7.3.2 Finite Element Model
- 7.3.3 Modal Test Setup
- 7.3.4 Modal Test Instrumentation
- 7.3.5 Modal Test Accelerometer Layout
- 7.3.6 Modal Test Shaker Layout
- 7.4 Results
- 7.4.1 Uncorrected Results
- 7.4.2 Fixed Base Corrected Results with 10 Shakers
- 7.4.3 Fixed Base Corrected Results with 12 Shakers
- 7.5 Fixed Base Corrected Results with 14 Shakers
- 7.6 Summary
- References
- 8 Nonlinear Normal Mode Estimation with Near-Resonant Steady State Inputs
- 8.1 Overview of the Basic SNRM Algorithm
- 8.2 Nonlinear Resonant Steady State Response Analysis
- 8.3 Discussion on the SNRM Algorithm Extension
- 8.4 Conclusion and Future Work
- References
- 9 Automatic Modal Parameter Identification with Methods of Artificial Intelligence
- Nomenclature
- 9.1 Introduction
- 9.2 Background
- 9.3 Peak Descriptor
- 9.4 Generation of Training Data
- 9.5 Classification
- 9.6 Measurement Setup
- 9.7 Conclusion
- References
- 10 A Single Step Modal Parameter Estimation Algorithm: Computing Residues from Numerator Matrix Coefficients of Rational Fractions
- 10.1 Introduction
- 10.2 Theoretical Background
- 10.3 Analysis
- 10.4 Conclusions
- References
- 11 Improved Expansion Results Using Regularized Solutions
- 11.1 Introduction
- 11.2 Theory
- 11.2.1 SEREP Expansion
- 11.2.2 Theory of Regularization in Direct Pseudo-Inverse Solutions
- 11.3 Models Used for Demonstrating Expansion Effects
- 11.3.1 Simple Model: Tuning Fork
- 11.3.2 Complicated Model: Coupled Components
- 11.4 Demonstration of the Effects of Gauge Location on Expansion Results
- 11.4.1 Case 1: Using Evenly Spaced Gauges to Expand the Response of Ten Modes
- 11.4.2 Case 2: Using Ten Gauges Placed with Effective Independence or Condition Number Optimization to Expand the Response of Ten Modes
- 11.4.3 Case 3: Using Forty Gauges on the Base Beam to Expand the Response of Ten Modes to the Top Beam
- 11.5 Demonstration of the Effects of Noise on Expansion Results
- 11.5.1 Model Configuration (Active Degrees of Freedom)
- 11.5.2 Noise Demonstration Test Matrix
- 11.5.3 Noise Contaminated Expansion Results
- Mode Shape Expansion
- Time Domain Expansion
- 11.6 Using Regularization to Improve Expansion Results
- 11.6.1 Mode Shape Expansion Improvement
- 11.6.2 Time Domain Expansion Improvement
- 11.6.3 Additional Considerations
- 11.7 Conclusions
- References
- 12 Expansion of Coupled Structural-Acoustic Systems
- 12.1 Motivation and Theory
- 12.2 Modal Expansion of a Coupled Structure
- 12.3 Coupled Expansion of a Transient Response
- 12.4 Discussion and Conclusions
- References
- 13 Expansion Methods Applied to Internal Acoustic Problems
- 13.1 Introduction
- 13.2 Theory
- 13.3 SEREP Expansion for Acoustic DOF in a Small Domain Model
- 13.4 Transmissibility Expansion for Acoustic DOF in a Large Domain Model
- 13.5 Discussion and Conclusions
- References
- 14 Scaling an OMA Modal Model of a Wood Building Using OMAH and a Small Shaker
- 14.1 Introduction
- 14.2 OMAH Theory
- 14.3 Structure and Instrumentation
- 14.4 Parameter Extraction by OMA
- 14.5 Mode Shape Scaling by OMAH
- 14.6 Verification of OMAH Result
- 14.7 Conclusion
- References
- 15 Quantitative Study on the Modal Parameters Estimated Using the PLSCF and the MITD Methods and an Automated Modal Analysis Algorithm
- 15.1 Introduction
- 15.2 Theory
- 15.2.1 The Poly-reference Least Squares Complex Frequency (LSCF) Algorithm
- 15.2.2 The Multi-reference Ibrahim Time Domain (MITD) Algorithm
- 15.3 Methodology
- 15.4 Results
- 15.5 Discussion
- 15.6 Conclusions
- References
- 16 Empirical Models for the Health Monitoring of High-Rise Buildings: The Case of Palazzo Lombardia
- 16.1 Introduction
- 16.2 Background
- 16.3 Empirical Model
- 16.4 The Prediction of the Eigenfrequency Values
- 16.5 Conclusion
- References
- 17 Towards Population-Based Structural Health Monitoring, Part II: Heterogeneous Populations and Structures as Graphs
- 17.1 Introduction
- 17.2 Irreducible Element Representations of Structures
- 17.2.1 Geometry
- 17.2.2 Topology
- Joints
- 17.2.3 Materials
- 17.3 Producing an Attributed Graph
- 17.4 A Note on Boundary Conditions
- 17.5 Some Formal Definitions for PBSHM
- 17.6 Conclusions
- References
- 18 Developing a Correlation Criterion (SpaceMAC) for Repeated and Pseudo-repeated Modes
- 18.1 Introduction
- 18.2 Background
- 18.2.1 Repeated Roots
- 18.2.2 Modal Vectors as Vector Spaces and Subspaces
- 18.2.3 Modal Vectors as Vector Spaces and Subspaces
- 18.2.4 Existing Correlation Methods
- 18.2.5 Extracting and Conditioning Modal Vector
- 18.3 Analysis
- 18.3.1 Implementing Existing Methods
- 18.3.2 SPACEMAC Implementation
- 18.3.3 Results
- 18.4 Conclusion
- References
- 19 Subsecond Model Updating for High-Rate Structural Health Monitoring
- 19.1 Introduction
- 19.2 Background
- 19.3 Analysis
- 19.4 Conclusion
- References
- 20 Phase Quadrature Backbone Curve for Nonlinear Modal Analysis of Nonconservative Systems
- 20.1 Introduction
- 20.2 Phase Quadrature Backbone Curve
- 20.3 Numerical Results
- 20.4 Conclusion
- References
- 21 Preliminary Results of Vibration Measurements on a Wind Turbine Test Bench
- 21.1 Introduction
- 21.2 Pretest
- 21.2.1 Conclusion from Pretest
- 21.3 Experimental Measurements
- 21.3.1 Experimental Setup
- 21.3.2 Data Processing and Analysis
- Operational Measurements
- Impact Tests
- 21.3.3 Results and Discussion
- Hammer Comparison from Impact Test
- Sensor Comparison from Impact Test
- Operational Measurements
- Comparing Impact Test to Operational Measurements
- 21.4 Conclusion
- References
- 22 Feasibility for Damage Identification in Offshore Wind Jacket Structures Through Numerical Modelling of Global Dynamics
- 22.1 Introduction
- 22.2 Background
- 22.3 Analysis
- 22.4 Results
- 22.5 Conclusion
- References
- 23 Use of Operational Modal Analysis to Identify Systems with Oscillatory Masses
- 23.1 Introduction
- 23.2 Theoretical Background
- 23.2.1 Operational Modal Analysis
- 23.2.2 Tuned Liquid Damper
- 23.3 Experimental Model
- 23.4 Results
- 23.4.1 Identification of Modal Properties
- 23.4.2 Estimation of Sloshing Frequency and Damping Ratio
- 23.5 Conclusion
- References
- 24 OMA-Based Modal Identification and Response Estimation of a Monopile Model Subjectedto Wave Load
- 24.1 Introduction
- 24.2 Theory
- 24.2.1 Operational Modal Analysis
- 24.2.2 Wave Simulation and System Response
- 24.3 Experimental Setup
- 24.4 Numerical Analysis
- 24.4.1 Finite Element Model
- 24.4.2 Loads and System Response
- 24.5 Modal Identification and FE Model Updating
- 24.6 Response Simulation Results
- 24.7 Conclusion
- References
- 25 A Concept for the Estimation of Displacement Fields in Flexible Wind Turbine Structures
- 25.1 Introduction
- 25.2 System Analysis
- 25.3 Basic Framework
- 25.4 State Estimation
- 25.5 Sensor Concept
- 25.6 Application to a Flexible Multibody System
- 25.6.1 Load Case
- 25.6.2 Results
- 25.7 Conclusion and Outlook
- References
- 26 Towards Population-Based Structural Health Monitoring, Part III: Graphs, Networksand Communities
- 26.1 Introduction
- 26.2 Matching Using the Attributed Graphs
- 26.2.1 Introduction to Graph-Matching Algorithms
- Definition
- Isomorphism
- Subgraphs
- The Modular Product Graph
- 26.2.2 Bron-Kerbosch Algorithm
- 26.2.3 C-Clique-Finding Algorithm
- C-Edges
- 26.3 Similarity Scores
- 26.4 Communities
- 26.5 Conclusion
- Appendix
- References
- 27 Utilization of Experimental Data in Elastic Multibody Simulation: Case Study on the Ampair 600 Turbine Blade
- 27.1 Introduction
- 27.2 Theoretical Background
- 27.3 Wind Turbine Blade Case Study
- 27.3.1 Test Setup
- 27.3.2 Mass Properties
- 27.3.3 Multibody Model Build-Up
- 27.4 Conclusion and Outlook
- References
- 28 On the Use of PVDF Sensors for Experimental Modal Analysis
- 28.1 Introduction
- 28.2 Piezoelectric Polyvinylidene Fluoride (PVDF) Sensor
- 28.3 Measurement Setup
- 28.3.1 Results
- References
- 29 Predicting Tool Wear Using Linear Response Surface Methodology and Gaussian Process Regression
- 29.1 Introduction
- 29.2 Experimental Set-Up
- 29.3 Results
- 29.4 Conclusions
- References
- 30 Computer Aided Measurement Uncertainty Calculation by Modern DAQs for Raw Acceleration and Force Data in Modal Analysis
- 30.1 Consideration of Measurement Deviations in the Overall Result
- 30.2 Model for a Measurement Uncertainty Budget for Vibration Transducers
- 30.3 Calculation of the Expanded Uncertainty, Urel (a), for the Acceleration Amplitude of an Accelerometer at a Single Frequency Point
- 30.4 Determination of the Measurement Uncertainty
- 30.5 Calculation of the Expanded Uncertainty, Urel (x), for the Acceleration Phase Shift of an Accelerometer at a Single Frequency Point
- 30.6 Example of an Automatic KiXact Measurement Uncertainty Calculation with the KiDAQ Data Acquisition System
- 30.6.1 Introduction To KiDAQ
- 30.6.2 Introduction To KiXact
- 30.7 Summary
- References
- 31 Towards Population-Based Structural Health Monitoring, Part VII: EOV Fields - EnvironmentalMapping
- 31.1 Introduction
- 31.1.1 Lillgrund Wind Farm
- 31.2 Environmental Mapping
- 31.2.1 Motivation
- 31.2.2 Wake Pattern in Wind Farms
- 31.2.3 Data-Based Model
- 31.3 Wind Speed Predictions
- 31.4 Conclusions
- References
- 32 Investigation of Resistive Forces in Variable Recruitment Fluidic Artificial Muscle Bundles
- 32.1 Introduction
- 32.2 Effect of Inactive Elements in a Variable Recruitment Bundle
- 32.3 Resistive Force Past Free Strain
- 32.4 Experimental Observation of Resistive Forces with Varying Pressure
- 32.5 Implications on Overall Performance of a Variable Recruitment Bundle
- 32.6 Conclusion
- References
- 33 Numerical and Experimental Study on the Modal Characteristics of a Rotor Test Rig
- 33.1 Introduction
- 33.2 Experimental Setup
- 33.2.1 Mechanical Structure
- 33.2.2 Data Acquisition
- 33.2.3 Experimental Modal Analysis Software
- 33.2.4 Measurement Repeatability
- 33.3 Experimental Modal Analysis
- 33.3.1 Excitation Variation
- 33.3.2 Experimental Modal Analysis Results
- 33.4 Correlation with Numerical Model
- 33.4.1 Numerical model
- 33.4.2 Experimental and Numerical Model Comparison
- 33.5 Conclusion
- References
- 34 A Comparison of Different Boundary Condition Correction Methods
- Nomenclature
- 34.1 Introduction
- 34.2 Demonstration Test Article
- 34.3 Summary of Test and Free-Free Modes
- 34.4 Method 1: Fixed Base Correction Method
- 34.5 Method 2: Constraint Shape Applied Directly to Mode Shapes
- 34.6 Method 3: Hybrid Approach
- 34.7 Summary
- References
- 35 Deflection Shape Balancing: An Alternative to Modal Balancing
- 35.1 Introduction
- 35.2 Background
- 35.3 Analysis
- 35.3.1 5 Weight Planes
- 35.3.2 10 Weight Planes
- 35.3.3 15 Weight Planes
- 35.3.4 20 Weight Planes
- 35.3.5 28 Weight Planes
- 35.3.6 Impact of the Number of Weight Planes
- 35.4 Conclusion
- 36 Real-Time Theoretical and Experimental Dynamic Mode Shapes for Structural Analysis Using Augmented Reality
- 36.1 Introduction
- 36.2 Experiment
- 36.2.1 Specimen
- 36.2.2 Theoretical Analysis
- 36.2.3 Experimental Analysis
- 36.3 Software Application Framework
- 36.4 Results
- 36.5 Ongoing Work
- 36.6 Conclusion
- References
- 37 A Bottom-Up Approach to FE Model Updating of Industrial Structures
- 37.1 Project Motivation and Scope
- 37.2 Theoretical Background
- 37.3 Measurement of the Test Model
- 37.3.1 Test I
- 37.3.2 Test II
- 37.3.3 Test III
- 37.4 FE Modeling and Updating
- 37.4.1 Model I
- 37.4.2 Model II
- 37.4.3 Model III
- 37.5 Conclusions and Further Work
- References
- 38 Shaft Bending to Zero Nodal Diameter Disc Coupling Effects in Rotating Structures Due to Asymmetric Bearing Supports
- 38.1 Introduction
- 38.2 Model Description
- 38.3 Numerical Results
- 38.4 Conclusions
- References
- 39 Dynamic Characterization of a Pop-Up Folding Flat Explorer Robot (PUFFER) for PlanetaryExploration
- 39.1 Introduction
- 39.2 Background
- 39.3 Initial Puffer Finite Element Model
- 39.4 Modal Test Process Validation
- 39.5 Test Procedure
- 39.6 Test Results
- 39.7 Updated Puffer Finite Element Model
- References
- 40 A Framework for the Design of Rotating Multiple Tuned Mass Damper
- 40.1 Introduction
- 40.2 Optimization of a Multiple Tuned Mass Damper Adapted to Rotating Frame
- 40.3 Conclusion
- References
- 41 Operational Modal Analysis of Wind Turbine Drivetrain with Focus on Damping Extraction
- 41.1 Introduction
- 41.2 Methodology and Theoretical Background
- 41.2.1 Reduction of the Influence of Harmonic Content
- 41.2.2 Modal Parameter Estimation
- PolyMax (p-LSCF)
- PolyMax Plus
- Stochastic Subspace Identification
- 41.3 Simulations
- 41.3.1 Comparison Between the Different Modal Parameter Estimators
- 41.3.2 Comparison Between the Different Lifter Types
- 41.4 Wind Turbine Application
- 41.5 Conclusions
- References
- 42 Investigation of Viscous and Friction Damping Mechanisms in a Cantilever Beam and Hanger System
- 42.1 Introduction
- 42.2 Background
- 42.3 Procedure
- 42.4 Results
- 42.5 Analysis
- 42.6 Conclusion and Future Work
- Reference
- 43 Detecting Nonsynchronous Heart Cells from Video - An Unsupervised Machine Learning Approach
- 43.1 Background
- 43.2 Motivation
- 43.3 Methodology
- 43.3.1 Video/Data Collection
- 43.3.2 Signal Processing
- Non-negative Matrix Factorization
- Sparse and Low-Rank Matrix Decompositions
- 43.4 Results
- 43.4.1 Non-negative Matrix Factorization on Videos
- 43.4.2 Sparse and Low-Rank Matrix Decompositions on Videos
- 43.4.3 Non-negative Matrix Factorization on Low-Rank Components
- 43.4.4 Mutual Information
- 43.5 Conclusion
- References
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