Course content

Structural dynamics 1 covers analysis of linear structural systems subject to initial conditions and deterministic loads.

The following is covered: Formulation of equation of motion for structures (continous and discrete single- and multi-degree of freedom). Free vibration. Forced vibration. Resonance. Response by analytical and numerical solution of equation of motion in time and frequency domain. Modal analysis. Reduced order modeling. Damping mechanisms and models. Time domain integration. Response of structures due to earthquakes by direct solution of equation of motion and earthquake response spectra.

Learning outcome

Structural dynamics 1 is a basic course in defining, analyzing and understanding dynamic behaviour in deformable structures common in civil engineering.

The course has the following learning objectives:

Knowledge: The candidate should be able to explain the meaning and relationship of fundamental concepts in structural dynamics, such as inertia, stiffness and damping, initial conditions and free vibration, external loads and forced vibration, natural frequencies and resonance, superposition, modal analysis and reduced order modelling. The candidate should also know how analytic and numerical methods are used in the analysis of such structures.

Skills: The candidate should be able to perform analyzes of structural systems using numerical methods in time or frequency domain and be able to check the results by analytical considerations and suggest improvements, for instance by considering the natural frequencies of the system and the frequency content of the load or considering placement of external loads and the effect on the dynamic response of the structure.

General competence: The candidate should be able to explain, assess and critically discuss dynamic problems in design of new and extension/reuse of existing structural systems.

Digital competence: Use of programming (e.g. Python or Matlab) for defining, analyzing, solving and visualizing dynamics of deformable structures common in civil engineering. Including solution of the eigenvalue problem for describing a numerical system in modal coordinates, numerical solution in time domain by convolution or direct integration, or analysis and solution in frequency domain by discrete fourier transform.

Sustainability competence: The course serves to give the students appropriate skills to design safe and cost-effective structures and assess existing structures for extension of lifetime and/or use in face of changing environmental and operational loads.

Learning methods and activities

Lectures and model illustrations. Obligatory numerical and computer exercises. Laboratory projects and demonstrations of dynamic response of structural models. The course will be given in English.

Compulsory assignments

• Exercises

Recommended previous knowledge

The course assumes basic knowledge of the finite element method for beams and frames equivalent to TKT4132 Mechanics 3.

Course materials

A.K. Chopra: Dynamics of structures, 5th ed., Prentice Hall, 2019.

S. Remseth: Structural Dynamics. Lectures notes