Modal Analysis Course

Lesson 1 • Damping Models and Their Effects

Compares viscous, structural, and Coulomb damping formulations. Establishes how damping model choice affects predicted response and modal parameters.

Lesson 2 • Single-Degree-of-Freedom Systems

Derives the equation of motion for a mass-spring-damper system. Provides the core analytical model that underpins multi-DOF and continuous-system theory.

Lesson 3 • Free and Forced Response Analysis

Solves SDOF equations for transient and steady-state responses. Connects mathematical solutions to observable physical behaviour under various excitations.

Lesson 4 • Energy Methods in Vibration

Applies Lagrangian and Rayleigh energy principles to derive equations of motion. Prepares students for efficient formulation of multi-DOF system models.

Lesson 1 • Orthogonality and Modal Properties

Proves mass and stiffness orthogonality of mode shapes. Shows how orthogonality enables decoupling of equations into independent modal coordinates.

Lesson 2 • Modal Superposition Method

Transforms physical coordinates to modal coordinates for efficient response computation. Enables analysis of complex systems by summing independent modal contributions.

Lesson 3 • Equations of Motion for MDOF Systems

Formulates coupled equations using mass and stiffness matrices. Demonstrates how matrix notation compactly represents complex structural interactions.

Lesson 4 • Eigenvalue Problem Formulation

Derives the generalised eigenvalue problem from free-vibration equations. Connects eigenvalues to natural frequencies and eigenvectors to mode shapes.

Lesson 1 • FRF-Based Structural Modification

Uses measured FRFs to predict how mass or stiffness changes alter dynamic behaviour. Introduces structural modification as a practical application of FRF theory.

Lesson 2 • FRF Definitions and Types

Introduces receptance, mobility, and accelerance FRFs and their mathematical relationships. Establishes the standard measurement quantities used in experimental modal analysis.

Lesson 3 • FRF Visualisation and Interpretation

Reads Bode, Nyquist, and real/imaginary plots to identify resonances and anti-resonances. Develops the visual pattern recognition essential for experimental data review.

Lesson 4 • Analytical FRF Derivation

Derives FRFs from MDOF equations of motion in modal and physical coordinates. Connects pole-residue representation to modal parameters.

Lesson 1 • Test Planning and Setup

Covers boundary condition selection, sensor placement, and excitation point strategy. Proper planning prevents data quality issues that cannot be corrected in post-processing.

Lesson 2 • FRF Matrix Completeness

Explains row and column FRF measurement strategies for full modal identification. Demonstrates how measurement coverage affects the completeness of extracted mode shapes.

Lesson 3 • Sensors and Signal Conditioning

Describes accelerometers, force transducers, and conditioning electronics. Sensor selection and mounting directly affect the accuracy of measured FRFs.

Lesson 4 • Excitation Methods

Compares impact hammer, shaker, and multi-point excitation techniques. Matching excitation method to test objectives ensures adequate frequency range and force level.

Lesson 1 • MDOF Frequency-Domain Estimators

Introduces rational fraction polynomial and global curve-fitting methods. Handles closely spaced modes and multiple FRFs simultaneously for improved accuracy.

Lesson 2 • Stabilisation Diagrams and Model Order

Uses stabilisation diagrams to distinguish physical poles from mathematical artefacts. Selecting correct model order is critical for reliable modal parameter extraction.

Lesson 3 • Time-Domain Identification Methods

Covers Ibrahim Time Domain and Eigensystem Realisation Algorithm approaches. Time-domain methods are advantageous for broadband or transient response data.

Lesson 4 • Modal Parameter Uncertainty and Validation

Quantifies confidence intervals on extracted frequencies, damping, and mode shapes. Validation against independent measurements confirms parameter reliability.

Lesson 1 • Geometric Model and Animation

Builds wireframe geometry models and animates mode shapes for visual inspection. Animation reveals spatial deformation patterns that numerical tables cannot convey.

Lesson 2 • Mode Shape Representation

Describes real normal modes, complex modes, and their physical meaning. Understanding mode shape character guides correct interpretation of structural behaviour.

Lesson 3 • Modal Assurance Criterion

Computes MAC values to quantify similarity between mode shape vectors. MAC is the standard metric for comparing test results to analytical predictions.

Lesson 4 • Coordinate Modal Assurance Criterion

Applies COMAC to identify spatial locations where mode shapes disagree. Localises measurement or model errors to specific degrees of freedom.

Lesson 1 • FE Model Correlation Workflow

Compares FE natural frequencies and mode shapes against test results systematically. Establishes a structured process before any parameter updating is attempted.

Lesson 2 • Updating Parameter Selection

Identifies physically meaningful parameters with high sensitivity for updating. Choosing appropriate parameters prevents non-physical solutions and improves robustness.

Lesson 3 • Validation of Updated Models

Tests updated model predictions against data not used in the updating process. Independent validation confirms that improvements are genuine, not overfitted.

Lesson 4 • Uncertainty in Model Updating

Accounts for measurement noise and modelling errors in the updating process. Probabilistic updating methods yield parameter distributions rather than point estimates.

Lesson 1 • Vibro-Acoustic Modal Analysis

Extends modal concepts to coupled structural-acoustic systems. Addresses noise and vibration problems where fluid-structure interaction is significant.

Lesson 2 • Structural Health Monitoring with Modal Data

Uses tracked changes in modal parameters to detect, locate, and quantify damage. Establishes the link between modal analysis and continuous structural assessment.

Lesson 3 • Rotating Machinery Modal Analysis

Addresses gyroscopic effects, speed-dependent stiffness, and Campbell diagrams. Rotating systems require specialised modal approaches beyond standard structural analysis.

Lesson 4 • Operational Modal Analysis

Extracts modal parameters from output-only data under ambient or operational excitation. Enables testing of structures where controlled excitation is impractical.