### Analysis of Wave Propagation in Structures and Solids MME(2014)

Welcome to Analysis of Wave Propagation in Structures and Solids

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, boundary integral equations and boundary-element schemes for wave propagation in solids and structures are derived in the time as well as the frequency domain, and an alternative solution for stratified materials, e.g. layered soil, is given in the wavenumber-frequency domain. Furthermore, the wave based method is introduced, which adopts a Trefftz approach to solve efficiently the frequency domain equations for structural dynamics and vibro-acoustics. A discussion on the properties of the method and a performance comparison with finite element solution strategies is discussed. Finally, lumped-parameter models (LPMs) are introduced as a means of representing the dynamic stiffness of continuous structures and soil in a computationally efficient manner. As an example, the application of LPMs for wind-turbine or machine foundations is illustrated.

Prerequisites: The participant must have a solid background in continuum mechanics and partial differential equations. Experience with numerical methods and programming is strongly recommended. The participants are expected to read the texts in the literature list before the course. The literature will be available upon registration.

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 Andersen, Associate Professor (phone: +45 9940 8455; e-mail: la@civil.aau.dk) and Sergey Sorokin, Professor (phone: +45 9940 9332; e-mail: svs@me.aau.dk)

Time: 21-28 October, 2014