TMME40	Vibration Analysis of Structures, 6 ECTS-points /Strukturdynamik/ Advancement level: D
	Aim: The purpose of the course is to provide the students with greater knowledge of vibration, necessary for many applications within industry which are associated with dynamic processes, for example. Many vessels are exposed to vibrations; also, transverse vibrations occur in airplane wings when the airplane descends for a landing. These vibrations can result in high stress on materials, which could result in material failure in the worst case situation. Therefore it is important for the future civil engineer to be able to analyze and dimension structures which are subjected to dynamic loads. A large number of methods for analysis of vibrating structures are given in the course. One important objective is to give the student insight into the applicability, use, and limitations of the methods. Further, that they can be used critically and in such a way that the numerical performance of the methods can be explained with well supported and formulated theory. Prerequisites: Mechanics, as well as basic courses in mathematics, mechanics of materials and structural engineering. Course organization: Instruction is carried out in the form of large seminars. Course content: Brief review of Newton’s laws. Systems with one and several degrees of freedom. Methods for determining natural frequencies. Modal analysis. Discrete and continuous systems (damped and undamped), orthogonal and normal coordinates. D&#180Alembert’s principle, Lagrange’s equations for linear systems. Approximative methods for continuous systems. Finite element method. Non linear systems, stability criteria, geometric methods, perturbation methods. Various computation techniques, transfer matrices, discrete time systems. Runge-Kutta methods. Course literature: Meirovitch, L. "Elements of Vibration Analysis".
TEN1	Written examination, 4 p.
UPG1	Hand-in exercises, 0 p.

Course language is English.