Vibrations and Fatigue in Mechanical Structures, 6 credits (TMMI09)

Mekaniska svängningar och utmattning, 6 hp

Main field of study

Mechanical Engineering


First cycle

Course type

Programme course


Robert Eriksson

Director of studies or equivalent

Peter Schmidt

Available for exchange students

Course offered for Semester Period Timetable module Language Campus VOF
6IMAS Mechanical Engineering, B Sc in Engineering 5 (Autumn 2019) 2 3 Swedish/English Linköping v
6IMAS Mechanical Engineering, B Sc in Engineering (Design Engineering) 5 (Autumn 2019) 2 3 Swedish/English Linköping o

Main field of study

Mechanical Engineering

Course level

First cycle

Advancement level


Course offered for

  • Mechanical Engineering, B Sc in Engineering

Entry requirements

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


Basic courses in Mathematics (Analysis), Mechanics, and Solid Mechanics

Intended learning outcomes

Many failures in mechanical structures are caused by material fatigue. Fatigue may appear when a structure is loaded by a cyclic load, and in many cases this load may come from resonance vibrations of the structure. Thus, knowledge of the vibrational behaviour of mechanical systems is a prerequisite in understanding the fatigue phenomenon. The course Vibrations and Fatigue in Mechanical Structures will provide understanding and knowledge about these phenomena. After the course, the student should be familiar with the following items that are dealt with in the course:

  • the physical behaviour of vibrating mechanical systems,
  • theories used when analysing practical vibrational problems,
  • influence of different structural parameters on the vibrational behaviour of structures, material fatigue phenomena, and
  • theories used when analysing fatigue problems.

  • Course content

    On vibrations: Fundamental relationships describing the behaviour of vibrating mechanical systems. Equations of motion for vibrating systems. Influence of mass, stiffness, and damping. Resonances and its consequences for the mechanical system. Vibrations of discrete systems and continuous systems.
    On fatigue: Fundamental relationships describing the fatigue phenomenon. High-cycle fatigue and low-cycle fatigue. The Wöhler diagram and the Haigh diagram. Safety factors. Damage accumulation, the Palmgren-Miner rule. Load spectra. The Ramberg-Osgood material model. Fatigue life models according to Morrow and Coffin-Manson. Influence of stress concentration.

    Teaching and working methods

    Lectures, tutorials, laboratory work, and problem solving.


    UPG1Laboratory work and home assignmentsU, G1.5 credits
    TEN1A Written ExaminationU, 3, 4, 54.5 credits


    Four-grade scale, LiU, U, 3, 4, 5


    Institutionen för ekonomisk och industriell utveckling

    Director of Studies or equivalent

    Peter Schmidt


    Robert Eriksson

    Course website and other links

    Education components

    Preliminary scheduled hours: 48 h
    Recommended self-study hours: 112 h

    Course literature

    Dahlberg, T, (2001) Teknisk hållfasthetslära, med tillhörande formelsamling
    ISBN: 91-44-01920-3
    Dahlberg, T, Material fatigue, Kompendium


    Dahlberg, T, (2001) Teknisk hållfasthetslära, med tillhörande formelsamling

    ISBN: 91-44-01920-3


    Dahlberg, T, Material fatigue, Kompendium
    UPG1 Laboratory work and home assignments U, G 1.5 credits
    TEN1 A Written Examination U, 3, 4, 5 4.5 credits

    Course syllabus

    A syllabus has been established for each course. The syllabus specifies the aim and contents of the course, and the prior knowledge that a student must have in order to be able to benefit from the course.


    Courses are timetabled after a decision has been made for this course concerning its assignment to a timetable module. A central timetable is not drawn up for courses with fewer than five participants. Most project courses do not have a central timetable.

    Interrupting a course

    The vice-chancellor’s decision concerning regulations for registration, deregistration and reporting results (Dnr LiU-2015-01241) states that interruptions in study are to be recorded in Ladok. Thus, all students who do not participate in a course for which they have registered must record the interruption, such that the registration on the course can be removed. Deregistration from a course is carried out using a web-based form: 

    Cancelled courses

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    Regulations relating to examinations and examiners 

    Details are given in a decision in the university’s rule book:

    Forms of examination


    Written and oral examinations are held at least three times a year: once immediately after the end of the course, once in August, and once (usually) in one of the re-examination periods. Examinations held at other times are to follow a decision of the board of studies.

    Principles for examination scheduling for courses that follow the study periods:

    • courses given in VT1 are examined for the first time in March, with re-examination in June and August
    • courses given in VT2 are examined for the first time in May, with re-examination in August and October
    • courses given in HT1 are examined for the first time in October, with re-examination in January and August
    • courses given in HT2 are examined for the first time in January, with re-examination at Easter and in August.

    The examination schedule is based on the structure of timetable modules, but there may be deviations from this, mainly in the case of courses that are studied and examined for several programmes and in lower grades (i.e. 1 and 2). 

    • Examinations for courses that the board of studies has decided are to be held in alternate years are held only three times during the year in which the course is given.
    • Examinations for courses that are cancelled or rescheduled such that they are not given in one or several years are held three times during the year that immediately follows the course, with examination scheduling that corresponds to the scheduling that was in force before the course was cancelled or rescheduled.
    • If teaching is no longer given for a course, three examination occurrences are held during the immediately subsequent year, while examinations are at the same time held for any replacement course that is given, or alternatively in association with other re-examination opportunities. Furthermore, an examination is held on one further occasion during the next subsequent year, unless the board of studies determines otherwise.
    • If a course is given during several periods of the year (for programmes, or on different occasions for different programmes) the board or boards of studies determine together the scheduling and frequency of re-examination occasions.

    Registration for examination

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    Code of conduct for students during examinations

    Details are given in a decision in the university’s rule book:

    Retakes for higher grade

    Students at the Institute of Technology at LiU have the right to retake written examinations and computer-based examinations in an attempt to achieve a higher grade. This is valid for all examination components with code “TEN” and "DAT". The same right may not be exercised for other examination components, unless otherwise specified in the course syllabus.

    Retakes of other forms of examination

    Regulations concerning retakes of other forms of examination than written examinations and computer-based examinations are given in the LiU regulations for examinations and examiners,


    For examinations that involve the writing of reports, in cases in which it can be assumed that the student has had access to other sources (such as during project work, writing essays, etc.), the material submitted must be prepared in accordance with principles for acceptable practice when referring to sources (references or quotations for which the source is specified) when the text, images, ideas, data, etc. of other people are used. It is also to be made clear whether the author has reused his or her own text, images, ideas, data, etc. from previous examinations.

    A failure to specify such sources may be regarded as attempted deception during examination.

    Attempts to cheat

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    The grades that are preferably to be used are Fail (U), Pass (3), Pass not without distinction (4) and Pass with distinction (5). Courses under the auspices of the faculty board of the Faculty of Science and Engineering (Institute of Technology) are to be given special attention in this regard.

    1. Grades U, 3, 4, 5 are to be awarded for courses that have written examinations.
    2. Grades Fail (U) and Pass (G) may be awarded for courses with a large degree of practical components such as laboratory work, project work and group work.

    Examination components

    1. Grades U, 3, 4, 5 are to be awarded for written examinations (TEN).
    2. Grades Fail (U) and Pass (G) are to be used for undergraduate projects and other independent work.
    3. Examination components for which the grades Fail (U) and Pass (G) may be awarded are laboratory work (LAB), project work (PRA), preparatory written examination (KTR), oral examination (MUN), computer-based examination (DAT), home assignment (HEM), and assignment (UPG).
    4. Students receive grades either Fail (U) or Pass (G) for other examination components in which the examination criteria are satisfied principally through active attendance such as other examination (ANN), tutorial group (BAS) or examination item (MOM).

    The examination results for a student are reported at the relevant department.

    Regulations (apply to LiU in its entirety)

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    LiU’s rule book for education at first-cycle and second-cycle levels is available at 

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