Description: The course concerns the physics and modelling of wave propagation in structures and solids. The theories and formulations covered by the course are applicable within structural and mechanical engineering as well as earthquake and geotechnical engineering. Firstly, an introduction is given to the basic properties of body waves in an elastic continuum. Phenomena such as geometrical and material dissipation, dispersion, impedance, reflection and refraction are discussed. Furthermore, the formulation of theories for wave propagation in one-dimensional structures, including straight and curved beams, plates and cylindrical shells, is considered. The Floquet theory for periodic structures is introduced and exemplified. Secondly, the finite element method is introduced as a computational tool for the analysis of wave propagation in soil and structures. Special attention is paid to its wave format for modelling one- and two-dimensional piecewise homogeneous/periodic structures. Time and frequency-domain solutions are considered, and guidelines are given for the treatment of artificial boundaries in numerical models. Thirdly, the use of Green’s functions for analysis of wave propagation in the three-dimensional solid is discussed. Homogeneous as well as stratified materials are considered. Also, lumped-parameter models (LPMs) are introduced as a means of representing the dynamic stiffness of continuous structures and soil in a computationally efficient manner. Finally, the course participants will contribute with a presentation of their own work, especially regarding wave propagation and dynamics.

Form: Each part of the course consists of a lecture followed by a workshop. The lectures are given in English.
Evaluation: As part of the course work, the participant must hand in a portfolio containing answers to exercises as well as computer codes elaborated by the participant during and after the course. Some of this work may be carried out in the workshops.

Organizer: Lars Vabbersgaard Andersen, Associate Professor, Department of Civil Engineering, Aalborg University, Denmark (phone: +45 9940 8455; e-mail:

Lecturers: Lars Vabbersgaard Andersen, Associate Professor, Department of Civil Engineering, Aalborg University, Denmark (phone: +45 9940 8455; e-mail:; Sergey Sorokin, Professor, Department of Mechanical Engineering, Aalborg University, Denmark (phone: +45 9940 9332; e-mail: and Elisabetta Manconi, Associate Professor, Department of Industrial Engineering, University of Parma, Italy (e-mail:


Time: 19-21 and 26-28 October, 2015

Place: Aalborg University

Zip code: 9220

City: Aalborg

Number of seats: 20

Deadline: 28 September, 2015