Course will cover the theory and practical aspects of the processes involved in testing of structural components with the objective of obtaining a mathematical description of their dynamic behavior. Main ingredients of the course will be the study of the theoretical basis of vibrations, details and functioning of vibration measuring instruments, digital processing of measurements, and detailed analysis of measured data. Laboratory sessions will provide instructive guidelines for dynamic testing, selection/placement considerations of sensors and actuators, and for system identification using modal parameter extraction methods. The course will motivate solutions for testing, monitoring and diagnosis of common structural components found in the machine tool/automotive/aerospace/ship building/civil industries.


  • PG/UG students interested in applied vibrations.

  • Students keen on exploring work opportunities related to vibration testing, monitoring and diagnosis in the machine tool/automotive/aerospace/ship building/civil industries.  


  • To teach the basics of the theory and practice of modal analysis

  • To introduce experimental methods in modal analysis

  • To teach digital signal processing of measurements

  • To teach estimation and extraction of modal parameters (natural frequencies, damping and mode shapes) from measured data

  • To teach construction of mathematical models from extracted modal parameters

  • To introduce advanced topics on dynamic substructuring, modal reduction, modal expansion, model updating, and vibration testing of weakly nonlinear structures


Students will, on completion of the course:

  • Get familiar with theoretical and practical aspects of structural dynamics

  • Develop the ability to plan for experimental testing of structural vibrations

  • Gain understanding of sensor and actuator selection and placement

  • Gain understanding of the importance of digital signal processing of measurements, and its impact on quality of measured data

  • Gain the ability to reconstruct mathematical models describing the structure based on experimental modal analysis

  • Appreciate role of modal analysis in system identification, model updating, and condition monitoring


(1) Modal testing: theory, practice and application by D. J. Ewins;

(2) Theoretical and experimental modal analysis by N. Maia and J. Silva


1. Theoretical basis for modal analysis (6 lectures)

  • Overview of modal analysis

  • Vibrations of single and multiple degree of freedom (SDOF, MDOF)  systems

  • Frequency response functions (FRFs) for SDOF/MDOF systems. Types of FRFs.

  • Orthogonality of modes and their application in modal analysis

  • Theory of undamped, proportionally damped, and non-proportionally damped SDOF/MDOF systems

  • Analyses for complex modes and sensitivity analysis of modal models

2. FRF measurement considerations (6 lectures)

  • Introduction to test planning

  • Excitation of structures (electromagnetic and electrohydraulic shakers, hammers, etc.)

  • Transducers and amplifiers for measurements (force transducer, accelerometers, laser vibrometers, signal conditioners, amplifiers etc.)

  • Actuator/sensor placement considerations

  • Revision of Fourier analysis and Fourier transforms

  • Discussions on aliasing, leakage, windowing, filtering and averaging

  • Role of excitations signals in structural testing

3. Modal parameter extraction and derivation of mathematical models (6 lectures)

  • Preliminary checks of FRF data (spectrum, coherence, asymptotic behavior, assessment using singular value decomposition (SVD))

  • Mode indicator functions

  • SDOF modal analysis methods (peak-picking, circle-fit)

  • Treatment of residuals

  • MDOF modal analysis in the frequency domain  (least square methods, rational fraction polynomial methods)

  • Extraction of natural frequencies, damping ratios and shapes.

  • Discussion on modal models, response models and spatial models

4. Applications and advanced topics (6 lectures)

  • Model correlation. Concepts of modal assurance criterion and some of its variants

  • Dynamic substructuring

  • Modal reduction and expansion

  • Model updating

  • Advanced curve fitting for modal parameter extractions

  • Testing of weakly nonlinear structures