Vibration Analysis of Structures, 6 credits

Strukturdynamik, 6 hp

TMME40

Course starting semester

Main field of study

Mechanical Engineering

Course level

Second cycle

Course type

Programme course

Examiner

Jonas Stålhand

Director of studies or equivalent

Peter Schmidt

Education components

Preliminary scheduled hours: 50 h
Recommended self-study hours: 110 h

Available for exchange students

Yes

Possible deviation from course syllabus/programme syllabus

ECV = Elective / Compulsory / Voluntary

Course offered for		Semester	Period	Timetable module	Language	Campus	ECV
6MAER	Aeronautical Engineering, Master's Programme	3 (Autumn 2019)	1	3	English	Linköping, Valla	E
6CMMM	Mechanical Engineering, M Sc in Engineering	7 (Autumn 2019)	1	3	English	Linköping, Valla	E
6CMMM	Mechanical Engineering, M Sc in Engineering (Aeronautical Engineering)	7 (Autumn 2019)	1	3	English	Linköping, Valla	E
6CMMM	Mechanical Engineering, M Sc in Engineering (Engineering Mechanics)	7 (Autumn 2019)	1	3	English	Linköping, Valla	E
6MMEC	Mechanical Engineering, Master's Programme	3 (Autumn 2019)	1	3	English	Linköping, Valla	E
6MMEC	Mechanical Engineering, Master's Programme (Applied Mechanics)	3 (Autumn 2019)	1	3	English	Linköping, Valla	E

Main field of study

Mechanical Engineering

Course level

Second cycle

Advancement level

A1X

Course offered for

Master's Programme in Aeronautical Engineering
Master's Programme in Mechanical Engineering
Mechanical Engineering, M 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.

Prerequisites

Mechanics, as well as basic courses in mathematics, mechanics of materials and structural engineering.

Intended learning outcomes

The objective of the course is to familiarize the student with fundamental laws in mechanics of vibration, and to give the student the proficiency needed to independently apply these laws to vibration problems. After completed the course, the student is able to:

model simple and more complex mechanical systems;
understand definitions and fundamental concepts used in mechanics of vibrations, e.g. velocity, acceleration, energy, frequency, period and damping factor;
use modal analysis, solve eigenvalue problems and determine frequencies and eigenmodes for different structural elements;
use Lagrange’s equations to derive the governing equations for a vibrating system;
solve the governing equations analytically and numerically;
perform simpler analyses for stability of non-linear systems;
derive simpler theorems used within mechanics of vibration.

Course content

Modelling of vibrating systems. Derivation of the governing equations using Newton’s laws and Lagrange’s equations for linear systems. Systems with one or multiple degrees of freedom. Analytical solution of free and damped oscillations including harmonic and general forcing. Methods for determining eigenfrequencies. Modal analysis. Discrete and continuous systems. Approximation methods and finite elements.

Teaching and working methods

The teaching comprises lectures, tutorials and computer laborations.

Examination

UPG2

Hand-in exercises

6 credits

U, 3, 4, 5

Grades

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

Department

Institutionen för ekonomisk och industriell utveckling

Director of Studies or equivalent

Peter Schmidt

Examiner

Jonas Stålhand

Course website and other links

Education components

Preliminary scheduled hours: 50 h
Recommended self-study hours: 110 h

Course literature

Books

Inman, J.D., Engineering Vibrations 4

Code	Name	Scope	Grading scale
UPG2	Hand-in exercises	6 credits	U, 3, 4, 5

Student rights and obligations (login required)
Linköping University common rules and regulations (in Swedish)

Books

Inman, J.D., Engineering Vibrations 4

Download

Download course literature list as PDF

Note: The course matrix might contain more information in Swedish.

I = Introduce, U = Teach, A = Utilize

		I	U	A	Modules	Comment
1. DISCIPLINARY KNOWLEDGE AND REASONING
	1.1 Knowledge of underlying mathematics and science (G1X level)		X	X		Linear Algebra, Calculus
	1.2 Fundamental engineering knowledge (G1X level)		X	X		Solid Mechanics
	1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)
	1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level)
	1.5 Insight into current research and development work
2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES
	2.1 Analytical reasoning and problem solving		X		UPG2	Problem formulation, modelling and problem solving
	2.2 Experimentation, investigation, and knowledge discovery
	2.3 System thinking
	2.4 Attitudes, thought, and learning
	2.5 Ethics, equity, and other responsibilities
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
	3.1 Teamwork	X
	3.2 Communications			X	UPG2	Written report
	3.3 Communication in foreign languages			X		English
4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT
	4.1 External, societal, and environmental context
	4.2 Enterprise and business context
	4.3 Conceiving, system engineering and management
	4.4 Designing
	4.5 Implementing
	4.6 Operating
5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS
	5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development
	5.2 Economic conditions for knowledge development
	5.3 Identification of needs, structuring and planning of research or development projects
	5.4 Execution of research or development projects
	5.5 Presentation and evaluation of research or development projects

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