Free Surface Slosh Modes
by Robert N. Coppolino,
Kristin B. Zimmerman
The Integrated Test Analysis Process for Structural Dynamic Systems
- Preface
- Overview of the Integrated Test Analysis Process (ITAP)
- Definition of Test Article Finite Element Models
- Part 1: Variational Foundations of Modern Structural Dynamics
- Introduction
- Economy in Nature and Basic Variational Formulations
- Mathematical Physics and Hamilton's Principle
- The Contributions of Ritz, Galerkin, and Trefftz
- The Ritz Method
- Galerkin's Method
- Trefftz's Method
- Automated Formulations in Structural Dynamics
- The Finite Element Method
- Assembly of Linear Structural System Models
- System Models with Localized Nonlinearities
- Matrix Structural Analysis
- Free Vibration and Modal Analysis
- Uncoupled Structural Dynamic Equations
- Closure
- Part 2: Guidelines for Systematic Model Development
- Introduction
- Linear Single-Degree-of-Freedom Equations
- Linear Multi-Degree-of-Freedom Equations
- Normal Modes of Undamped MDOF Systems
- Response to Impulsive and Transient Force Excitations
- Response Spectrum and Shock Spectrum
- Illustrative Example: Half-Sine Pulse Force
- Illustrative Example: 1940 El Centro CA Ground Motion Data
- Definition of Relevant Structural Dynamic Models
- Illustrative Example: Aluminum Launch Vehicle and Spacecraft Components
- Illustrative Example: Aluminum Launch Vehicle Feedline
- Modal Density and the Effectiveness of Finite Element Models
- Illustrative Example: Fluid-Filled Circular Cylindrical Shell
- Free Surface Slosh Modes
- Interface Flexibility in Structural Assemblies—A Retrospective
- Damping in Structural Assemblies
- Closure
- References
- Part 1: Variational Foundations of Modern Structural Dynamics
- Systematic Modal Test Planning
- Part 1: Understanding Modal Dynamic Characteristics
- Part 2: Target Mode Selection
- Introduction
- Structure Excited by Boundary Accelerations and Applied External Loads
- Modal Effective Mass and Target Mode Selection
- Illustrative Example: ISS P5 Short Spacer
- Modal Gains and Target Mode Selection
- The Mode Acceleration Method and Target Mode Selection
- Illustrative Example: Axisymmetric Shell Finite Element Model
- Closure
- Part 3: Response DOF Selection for Mapping Experimental Modes
- References
- Measured Data Analysis
- Part 1: Preliminary Measured Data Analysis
- Introduction
- Key Preliminary Measured Data Analysis Functions, Mean, Variance, and Standard Deviation
- Normalized Probability Density and Ideal Gaussian Distribution
- Total Normalized Probability Function
- Autospectrum or Power Spectral Density Function
- Cross-Spectrum or Cross-Power Spectral Density Function
- The Spectrogram Function
- Illustrative Example: Sinusoidal Time History with Background Random Noise
- Illustrative Example: SDOF Linear System Response to Random Excitation
- Illustrative Example: ISPE Modal Test
- Illustrative Example: Wire Rope Test Article
- Illustrative Example: ISS P5 Modal Test
- Closure
- Part 2: Frequency Response Function Estimates from Measured Data
- References
- Part 1: Preliminary Measured Data Analysis
- Experimental Modal Analysis
- Systematic Test Analysis Correlation
- Part 1: Conventional Mass Weighted Correlation of Test and FEM Modes
- Part 2: Correlation of Test and FEM Modes Using Left-Hand Eigenvectors
- Introduction
- Modal Test Data Resulting from Estimated State-Space Models
- Theoretical System Modes in State-Space Form
- Correlation of Experimental and Theoretical Modes (Complex Least Squares)
- Illustrative Example: ISPE Modal Test
- Roadmap for a Highly Improved Integrated Test Analysis Process
- Closure
- References
- Reconciliation of Finite Element Models and Modal Test Data
- Author's Biography
- Blank Page (1/3)
- Blank Page (2/3)
- Blank Page (3/3)
28 2. DEFINITION OF TEST ARTICLE FINITE ELEMENT MODELS
Table 2.4: Modal density and sensitivity of empty shell natural frequencies to ullage pressure
Circumferential Harmonic (n), P
0
= 30 psi
m
m
Circumferential Harmonic (n), P
0
= 0 psi
Table 2.5: Modal density and sensitivity of fluid-filled shell natural frequencies to ullage pressure
m
m
Circumferential Harmonic (n), P
0
= 0 psi
Circumferential Harmonic (n), P
0
= 30 psi
-
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