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Konstruktioners dynamik: Teori og analyse (Dynamics of Structures: Theory and Analysis )



Course format On-site
Date 2021-02-01 - 2021-05-21

General course objectives

The dynamic excitation of civil engineering structures often occurs due to environmental forces from wind, waves and earthquakes, or from traffic loading, collisions and explosions. The aim of this course is to provide an understanding of dynamic effects in large structures and enable students to perform dynamic analysis of structures with a single or multiple degrees of freedom, using analytical as well as numerical methods.


The fundamental concepts of dynamics are introduced for simple systems with a single degree of freedom. Hereby, aspects such as natural frequencies, damping and resonance are introduced by determining the system’s free vibrations and its forced response to harmonic and transient loading.

The foundation of the dynamics of flexible structures is subsequently described by the theory for free vibrations of cables and beams, while the connection between these continuous elements and their corresponding discrete structural models is illustrated by applying the finite element method to solve the partial differential equations. The dynamic analysis of discrete structures with multiple degrees of freedom is then conducted by modal analysis, based on a series representation by the vibration forms of the structure. Hereby, the influence of the load’s frequency content and its spatial distribution is considered, together with the potential of quasi-static system reduction techniques.

For flexible structures, the damping of the system is crucial for the magnitude of the dynamic response, why various naturally occurring damping mechanisms are scrutinized. Furthermore, the effect of external dampers on flexible structures is treated, including the use of tuned mass dampers. For flexible structures with local dampers or advanced loading, the dynamic equations are solved by direct time integration using the Newmark method.

The theoretical content of the course is treated by MATLAB-based exercises, which are solved and reported in groups. The reports form a part of the course assessment.


Recommended prerequisites

41501 Strength of materials 1/41203 Structural mechanics/41236 Structural mechanics/(11341 Structural engineering 1.­11342 Structural engineering 2).­11305 Computational Structural Modelling 1: The Finite Element Method/41812 Introduction to Finite Element Analysis.­02631 Introduction to programming and data processing/02601 Introduction to Numerical Algorithms. Fundamental structural mechanics or strength of materials: Static analysis of structures and beams by analytical and finite element methods. Programming: Knowledge about a programming language and its principles, as the course makes use of Matlab.

Learning outcomes

A student who has met the objectives of the course will be able to:

  • Formulate the equation of motion for dynamic structures and systems.
  • Determine the solution for free and forced vibrations of systems with a single degree of freedom, and explain the meaning of a natural frequency, damping ratio and resonance.
  • Apply separation of variables and the finite element method to solve the equation of motion for vibrating cables and beams.
  • Determine natural frequencies and vibration forms for systems with multiple degrees of freedom.
  • Apply modal analysis to compute the dynamic response of systems with multiple degrees of freedom.
  • Apply quasi-static system reduction methods in modal analysis to minimize computational costs in dynamic analyses.
  • Use Newmark-based time integration methods to compute the dynamic response of systems with multiple degrees of freedom.
  • Explain the effect of the most common types of damping mechanisms.
  • Design the governing parameters of viscous dampers and tuned mass dampers (TMDs) on flexible structures.
  • Conduct a dynamic analysis and describe the results in written reports.


ISCED Categories

Near- and offshore constructions