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Vibration Analysis of Structures, 6 credits
Strukturdynamik, 6 hp
TMME40
Main field of study
Mechanical EngineeringCourse level
Second cycleCourse type
Programme courseExaminer
Jonas StålhandDirector of studies or equivalent
Peter SchmidtEducation components
Preliminary scheduled hours: 50 hRecommended self-study hours: 110 h
Available for exchange students
YesECV = Elective / Compulsory / Voluntary
Main field of study
Mechanical EngineeringCourse level
Second cycleAdvancement level
A1XCourse offered for
- Aeronautical Engineering, Master's Programme
- Mechanical Engineering, M Sc in Engineering
- Industrial Engineering and Management - International, M Sc in Engineering
- Industrial Engineering and Management, M Sc in Engineering
- Mechanical Engineering, Master's Programme
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, 5Department
Institutionen för ekonomisk och industriell utvecklingDirector of Studies or equivalent
Peter SchmidtExaminer
Jonas StålhandCourse website and other links
Education components
Preliminary scheduled hours: 50 hRecommended 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 |
Books
Inman, J.D., Engineering Vibrations 4
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
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X
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Linear Algebra, Calculus |
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| 1.2 Fundamental engineering knowledge (G1X level) |
|
X
|
X
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Solid Mechanics |
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
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| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
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| 1.5 Insight into current research and development work |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
|
X
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UPG2
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Problem formulation, modelling and problem solving |
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| 2.2 Experimentation, investigation, and knowledge discovery |
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| 2.3 System thinking |
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| 2.4 Attitudes, thought, and learning |
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| 2.5 Ethics, equity, and other responsibilities |
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
X
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| 3.2 Communications |
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X
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UPG2
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Written report |
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| 3.3 Communication in foreign languages |
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X
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English |
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 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 |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
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