Structural Dynamics Principles in Earthquake Engineering (STRUDEE)

International Graduate Summer Course 1 – 26 June 2015


Earthquake ground acceleration acts at the base of the structure (black) which responds dynamically (red)

Earthquake ground acceleration acts at the base of the structure (black) which responds dynamically (red)

Structures are often subjected to dynamic forces of one form or the other during their lifetime. This course introduces the theory of dynamic response of structures with emphasis on physical insight into the analytical procedures and with particular application to earthquake engineering. The concepts of structural dynamics are formulated from the first principles of solid mechanics, extending the continuum hypothesis to a numerically efficient finite element approximation. . Forced and free vibration of structures at different levels of idealization such as, continuum formulation, single degree of freedom approximation, and finite degree of freedom approximation, is covered. Special emphasis is placed on the application of the theory in practical earthquake engineering problems. Basic insight into the powerful and efficient frequency domain analysis is provided. Stochastic modelling of earthquake ground motion and structural response is introduced in the framework of theory of stochastic process and random vibration theory. Damping and inelastic modelling concepts are covered in detail.

Course Description

Earthquake action on windmills

Earthquake safety and dynamics of wind farms

This course aims at training engineers, researchers, and architects in reducing seismic risk through a deep understanding of engineering structures affected by earthquakes. Basic understanding of the dynamic response of structures and advanced numerical and analytical skills in modelling and simulating seismic demands on structures is essential in formulating a safe and economical seismic design philosophy. Furthermore, the knowledge and skills in dynamic modelling and simulation of earthquake-induced structural vibrations is essential in correctly and consistently applying standard seismic design codes in practice. The main objective of the course is to educate and train the participants in understanding, modelling, and simulating structural vibrations due to earthquake-induced ground motion.

Course syllabus

1 Dynamics of deformable bodies

1.1 Dynamic equation of motion
1.2 Finite element approximation

2 SDOF dynamics

2.1 Review of response to harmonic loads
2.2 Response to arbitrary excitation
2.2.1 Unit impulse response
2.2.2 Duhamel´s integral
2.2.3 Complex frequency response function and frequency domain analysis
2.2.4 Solution by numerical integration Newmark´s method Wilson-theta method

3 Earthquake Response spectra

3.1 Elastic response spectra
3.2 Inelastic response spectra
3.2.1 Strength and ductility
3.2.2 Constant- strength response spectra
3.2.3 Constant-ductility response spectra
3.2.4 Approximate methods Equal displacement and equal energy principles Structural behaviour and force reduction Design spectra: European and American codes

4 Review of random variables and processes

4.1 Fundamentals of probability theory
4.2 Random variables, probability density and distribution
4.3 Random processes
4.3.1 Stationarity and ergodicity
4.3.2 Autocorrelation function
4.3.3 Power spectral density function
4.3.4 Simulation of random processes

5 Stochastic response of SDOF systems

5.1 Response of linear time invariant systems to random forces
5.1.1 Response statistics Mean response Autocorrelation of response Power spectral density of response
5.1.2 Level corssing analysis, peak factors, and extreme value distributions Level crossing frequency Zero-crossing rates and frequency of maxima Narrow- and wide-band processes and bandwidth parameter Statistics of extreme response

6 MDOF systems

6.1 Formulation of structural matrices

6.1.1 Lumped and consistent mass formulation
6.1.2 Damping models Proportional damping models Rayliegh damping Caughy damping Non-proportional damping

6.2 Response to ground motion

6.2.1 Formulation of basic equation for uniform support motion
6.2.2 Formulation of basic equation for variable support motion
6.2.3 Eigen-value analysis, normal modes, frequencies, and mode shapes
6.2.4 Modal superposition method
6.2.5 Direct integration method
6.2.6 Response spectrum method and combination of modal maxima
6.2.7 Introduction to random vibration of MDOF systems

7 Advanced topics

7.1 Base isolation
7.2 Supplemental damping
7.3 Structural health monitoring and control
7.4 System identification
7.5 Soil-structure interaction

Learning Outcomes

1 Knowledge

1.1 Theoretical

1.1.1 Understand the basic principles of structural dynamics
1.1.2 Formulate mathematical equations of dynamic systems under seismic excitation
1.1.3 Understand the effect of earthquakes on structures, understand methods of modelling and analysis of structures under seismic excitation
1.1.4 Knowledge of engineering simplifications and code requirements
1.1.5 Knowledge of randomness and uncertainty in quantifying seismic excitation
1.1.6 Knowdelege of theory and tools of random vibrations

1.2 Practical

1.2.1 Seismic analysis of simple structural systems
1.2.2 Data collection and processing
1.2.3 Probabilistic modelling and model calibration
1.2.4 Strong-motion data processing
1.2.5 Generation of elastic and inelastic response spectra
1.2.6 Generation of artificial ground-motion time series
1.2.7 Site response analysis
1.2.8 Analysis of practical structures in time and frequency domain

2 Skills

2.1 Conceptual/Congnitive

2.1.1 To be able to interpret a physical problem from a mathematical perspective using principles of mechanics
2.1.2 Be able to design and conduct simulation
2.1.3 To analyze data and interpret results
2.1.4 To compare scenarious and obtained results
2.1.5 To generalize concepts, formulations, and results

2.2 Practical

2.2.1 Understand and improve original ideas
2.2.2 Undertand limitations of existing models and improve them
2.2.3 Analysis of common structures in time and frequency domain
2.2.4 Computer programming and application for solving relevant dynamics of structures excited by seismic ground motion

3 Personal and professional competencies

3.1 An ability to work effectively both individually and as a team,and to understand the professional and ethical responsibility.
3.2 An ability to reach necessary information, database, and other sources, and to engage in lifelong learning.
3.3 An ability to communicate effectively, seek for advice and help, communicate difficulties and achievements, and to present studies and results to experts and general audience.
3.4 An ability to use new techniques, skills, and modern engineering tools, and to examine latest technologies.

Key practical information

  • This is an official 7.5 ECTS course of the University of Iceland, School of Engineering and Natural Sciences, Faculty of Civil and Environmental Engineering, and is fully accredited.
    Instrumented building

    Strong-motion monitoring of the Town Hall at Selfoss.

    The “Earthquake Engineering Research Center” (Rannsóknarmiðstöð í jarðskjálftaverkfræði) will supervise the overall program and is responsible for the course content and academic requirements

  • Taking advantage of Iceland´s unique natural field laboratories, the course is taught in intensive mode on location at the Earthquake Engineering Research Centre in the town of Selfoss, in the South Iceland Seismic Zone (SISZ, see figure at right)
  • This is a paid course. The course fee is 1690 euros per student. The course fee covers
    • registration to the University of Iceland
    • tuition
    • course material
    • wireless internet
    • access to required software
    • accommodation in Selfoss, South Iceland, provided by the EERC
  • The course is taught in English and students must be able to demonstrate English proficiency, both written and verbal.
  • A limited number of students (10-15) will be accepted to the course. Each student’s application will be considered and evaluated before a decision is made on acceptance to the course. All applications are evaluated on the basis of academic qualifications and expected fit to the subject, and without regard to race, color, religion, gender, national origin, age, etc.
    6-DOF HexaPod at the EERC lab

    A 6-DOF hexapod at the EERC lab capable of simulating 6-component ground motion.

  • This is a graduate course. Thus an undergraduate university degree (B.S., B.Sc., B.A. etc) is a minimum requirement.
  • Students will receive a grade for the course upon completion. The grade will be constructed from the evaluation of student projects, class participation and a final test.
  • Students are expected to bring a personal computer (laptop) for use during the course.


The course instructors are Dr. Rajesh Rupakhety and Dr. Símon Ólafsson.

The course supervisor is Dr. Rajesh Rupakhety.