Study Guide@lith

Linköping Institute of Technology

Valid for year : 2017
TMME40 Vibration Analysis of Structures, 6 ECTS credits.

For:   AER   I   Ii   M   MEC  


Prel. scheduled hours: 48
Rec. self-study hours: 112

  Area of Education: Technology

Main field of studies: Mechanical Engineering

  Advancement level (G1, G2, A): A

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.After the course, the student should be able to:
  • Modeling simple and more complex mechanical systems.
  • Define the basic concepts in structural dynamics as velocity,acceleration,force,couple,energy,frequence,period,damping factor,excitation,system characteristics,response.
  • Be able to perform simple derivations of theorems and expressions used in the cource.
  • Use modal analysis,approximate and exact methods to solve the eigenvalueproblem,and to be able to solve for frequences and eigenmodes for different element of structures.
  • Use the principle of Hamilton and Lagranges equations to obtain the govering equations for a structure,and solve these analytically or numerically by using MATLAB.
  • Determine the type of stability for simple non-linear systems.

Prerequisites: (valid for students admitted to programmes within which the course is offered)
Mechanics, as well as basic courses in mathematics, mechanics of materials and structural engineering.

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.

Instruction is carried out in the form of large seminars.

Course contents:
Brief review of Newton‚?Ts 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‚?TAlembert‚?Ts principle, Lagrange‚?Ts 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".

Hand-in exercises

Course language is English.
Department offering the course: IEI.
Director of Studies: Peter Schmidt
Examiner: Jonas Stålhand
Link to the course homepage at the department

Course Syllabus in Swedish

Linköping Institute of Technology


Contact: TFK ,
Last updated: 03/21/2017