Course syllabus
Course-PM
TME141 TME141 Structural dynamics lp2 HT25 (7.5 hp)
Course is offered by the Dynamics Division of Department of Mechanics and Maritime Sciences (soon to be known as Department of Mechanical Engineering).
Contact details
The course administration is based at the Dynamics Division of the Department of Mechanics and Maritime Sciences, Hörsalsvägen 7A, 3rd floor.
| Role | Name | Position | Contact Number | |
| Teacher & Examiner | Shivesh Kumar | Assistant Professor | shivesh.kumar@chalmers.se | +46 31 772 22 95 |
| Teaching Assistant | Henrik Vilhelmson | PhD Student | henrik.vilhelmson@chalmers.se | |
| Course Administrator | Carina Schmdit | Student administrator | carina.schmidt@chalmers.se | +46 31 772 15 15 |
Course purpose
This course will bring knowledge about linear structural dynamics methods of contemporary industrial relevance. It will also bring user experience to some of these methods. It gives a solid foundation for computer aided engineering within the field, especially relevant when a tight integration between test and analysis for prediction and problem solving is utilized. Time and frequency domain methods for vibration analysis are treated. Model reduction methods for efficient analysis of large problems are within the scope of the course, as for dynamic problems involved in dynamics of roller coaster structure as depicted below. Connections to linear system theory will be made. A computer assignment that will require some programming in MATLAB will be given to give hands-on experience.
Schedule
Course prerequisites
- Mathematics (Linear Algebra)
- Mechanics
- Strength of Materials
- Basic course on Finite Element Methods
- Basic knowledge of MATLAB/Python
Course literature
The theory part of the course is treated in the book available for free in the Course’s Canvas: T Abrahamsson, Structural Dynamics and Linear Systems - Compute, Test, Calibrate and Validate, Chalmers University of Technology, 2019. Only selected topics from Part 1 (Chapters 1-7) of the book are relevant. Please note that lectures do not follow the book chronologically. Optionally, the students may additionally refer to the textbook R.R. Craig, A.J. Kurdila: Fundamentals of Structural Dynamics, 2nd edition, Wiley.
Learning objectives and syllabus
The intended learning outcomes (ILOs) of the course include:
- explain in detail the basic principles on which the structural dynamics methods rely,
- derive the structural dynamics equations (SDE) via several approaches,
- solve stationary and transient problems for multi degree of freedom (DOF) systems,
- apply and explain most used numerical eigenvalue algorithms,
- apply and explain most used direct integration methods,
- use the model reduction methods for large-scale structural dynamics problem,
- use the finite element method to solve structural dynamics problems,
- derive equations of motion for rods, shaft and beams,
- solve stationary and transient continuous problems using modal analyses.
Link to the syllabus on Studieportalen.
Computer Assignments
Three computer assignments (worth 5 points each) which will contain some tasks related to the course content will be released during the course. A separate report concerning each CA should be handed in to detail the procedures used and describe your findings. The reports will be evaluated for quality and will hold a weightage of 20% in your final grade. See the computer assignment schedule below for the release and submission dates. Resubmissions are not allowed.
Examination
The written examination is a 5 hour exam on 13th January 2026 starting at 08:30 am. It will consist of 5 problems and will give up to 3 credit points each. The final written exam has a weightage of 80% in your final grade. All aids are allowed on the exam (however, it is not permitted to cooperate with or take help from another person so mobile phones and cameras must be turned off).
Your final grade is calculated as a combination of your performance in the written exam (80%) and computer assignment (20%). At least 6, 9 and 12 credit points are needed for grades 3, 4 and 5 respectively.
Course design
The learning activities in this course include:
- 15x lectures: Lectures are intended for delivery of the course content (theory, methods, applications) which primarily involves blackboard teaching aided with a few MATLAB based examples.
- 12x tutorials: Tutorials are intended for problem solving with the help of the teaching assistant. They are usually scheduled right after the lectures and the selected problems are aligned with the content covered already in the lectures previously.
- 5x computer assignment (CA) sessions: Students may use the CA sessions to work on the computer assignment composed of three tasks A, B and C. TA will be available to help students with any questions.
- 3x consultancy hours: Students may use these sessions to clarify any questions they might have regarding the theory, tutorials or computer assignment. Both teacher and TA are available in these sessions.
- 2x guest lectures:
- Jonathan Westlund at Volvo cars will give a lecture titled "Applied structural dynamics at Volvo Cars – Road Noise, Vibration and Harshness".
- Jaseung Lee, PhD student at Dynamics Division, M2 will give a lecture titled “Structural dynamics in wind engineering - Design principles for wind towers”
Course material (lecture notes, tutorial problems & their solutions, computer assignment, and previous exams etc.) are made available to students via canvas. Any communications/announcements related to the course will be made via canvas. Deadline for computer assignment is to be respected strictly. Delayed submissions are only accepted in proven exceptional circumstances provided the teaching staff is informed well in advance.
Timetable
The following table shows the timetable of the lectures (including guest lecture). Note that L2 is a double lecture slot.
| Date | Time | Session ID | Topic | Course Book | Room | Responsible |
| 03/11 (Monday) | 15-17 | L1 | Linear structural mechanics, Setting up structural dynamics equations (SDE) | 2.1 - 2.3 | EB, EDIT | Shivesh Kumar |
| 06/11 (Thursday) | 8-12 | L2 | Vibrations of multi DOF systems. Free vibrations, Eigen modes, Mode Orthogonality. Forced Harmonic Vibration. Transfer Functions. Resonance and Anti-Resonance | 4.1, 4.2, 6.1 | EB, EDIT | Shivesh Kumar |
| 10/11 (Monday) | 13-15 | L3 | Transient Excitation, Mode Displacement Method | 5.1, 7.2.1 | EB, EDIT | Shivesh Kumar |
| 13/11 (Thursday) | 8-10 | L4 | Mode acceleration method. Support Motion | 7.2.2, 6.2 | EB-EDIT | Shivesh Kumar |
| 17/11 (Monday) | 13-15 | L5 | Dynamic Condensation and Reduction Methods (Guyan and Craig Bampton) | 6.2.1, 7.1 | EB-EDIT | Shivesh Kumar |
| 20/11 (Thursday) | 8-10 | L6 | Continuous Rod Elements | 6.2.2 | EB-EDIT | Shivesh Kumar |
| 24/11 (Monday) | 13-15 | L7 | Rayleigh Quotient, Rayleigh's and Courant's Minimax Theorems, Inverse Iteration with Shift | 4.1.2 | EB-EDIT | Shivesh Kumar |
| 27/11 (Thursday) | 8-10 | L8 | Sturm Sequence | 4.2.2 | EB-EDIT | Shivesh Kumar |
| 27/11 (Thursday) | 16-18 | GL |
1. Applied structural dynamics at Volvo Cars – Road Noise, Vibration and Harshness 2. Structural dynamics in wind engineering - Design principles for wind towers |
Not Applicable | SB-L516 | 1. Jonathan Westlund, 2. Jaseung Lee |
| 01/12 (Monday) | 13-15 | L9 | Eigenvalue problem of condensed systems. Wittrick-Williams Algorithms | 4.2.3 | EB-EDIT | Shivesh Kumar |
| 04/12 (Thursday) | 8-10 | L10 | Damping. Damping in frequency domain | 6.1 | EB-EDIT | Shivesh Kumar |
| 08/12 (Monday) | 13-15 | L11 | Modal Damping, Rayleigh Damping, Caughey Damping and Augmented Damping | 4.1.3, 5.1 | EB-EDIT | Shivesh Kumar |
| 11/12 (Thursday) | 8-10 | L12 | State Space Formulation, State space in frequency domain | 4.1.3, 3.1 | EB-EDIT | Shivesh Kumar |
| 15/12 (Monday) | 13-15 | L13 | Decoupling of state space differential equations. Complex Eigen values and Eigen modes | 6.1.4, 4.1.5 | EB-EDIT | Shivesh Kumar |
| 18/12 (Thursday) | 08-10 | L14 | Numerical time integration. Exponential integrator, zero order hold method. Newmark Method | 5.4.1-2 | EB-EDIT | Shivesh Kumar |
The following table shows the timetable of the tutorial schedule.
| Date | Time | Session ID | Problems in Course Book | Room | Responsible |
| 10/11 (Monday) | 15-17 | X1 | P2.1, P2.2a-e | EB, EDIT | Henrik Vilhelmson |
| 13/11 (Thursday) | 10-12 | X2 | P2.5, P2.3c-d | EB-EDIT | Henrik Vilhelmson |
| 17/11 (Monday) | 15-17 | X3 | P6.2, P6.3, P6.7ab | EB-EDIT | Henrik Vilhelmson |
| 20/11 (Thursday) | 10-12 | X4 | P6.5, P2.4 | EB-EDIT | Henrik Vilhelmson |
| 24/11 (Monday) | 15-17 | X5 | P7.4, P7.5 | EB-EDIT | Henrik Vilhelmson |
| 27/11 (Thursday) | 10-12 | X6 | P5.1a-b | EB-EDIT | Henrik Vilhelmson |
| 01/12 (Monday) | 15-17 | X7 | P4.3a-c | EB-EDIT | Henrik Vilhelmson |
| 04/12 (Thursday) | 10-12 | X8 | P4.4, P4.5, P4.9 | EB-EDIT | Henrik Vilhelmson |
| 08/12 (Monday) | 15-17 | X9 | P4.8, P6.8a-b | EB-EDIT | Henrik Vilhelmson |
| 11/12 (Thursday) | 10-12 | X10 | P4.10 | EB-EDIT | Henrik Vilhelmson |
| 15/12 (Monday) | 15-17 | X11 | P3.2, P3.3 | EB-EDIT | Henrik Vilhelmson |
| 18/12 (Thursday) | 10-12 | X12 | P5.3, P5.4, P5.5 | EB-EDIT | Henrik Vilhelmson |
The timetable of computer assignment sessions along with the assignment release and submission dates is given in the following table.
| Date | Time | Session ID | Topic | Room | Responsible |
| 7/11 (Friday) | Release of Computer Assignment Task A | ||||
| 14/11 (Friday) | 15-17 | CA1 | Computer Assignment | EB-EDIT | Henrik Vilhelmson |
| 21/11 (Friday) | Release of Computer Assignment Task B | ||||
| 28/11 (Friday) | 15-17 | CA2 | Computer Assignment & Meeting with Student Representatives | EL41+ES61 | Henrik Vilhelmson, Shivesh Kumar |
| 28/11 (Friday) | 23:59 | Submission Deadline for CA Task A | |||
| 05/12 (Friday) | Release of Computer Assignment Task C | ||||
| 05/12 (Friday) | 15-17 | CA3 | Computer Assignment | HB105 | Henrik Vilhelmson |
| 12/12 (Friday) | 15-17 | CA4 | Computer Assignment | EB-EDIT | Henrik Vilhelmson |
| 12/12 (Friday) | 23:59 | Submission Deadline for CA Task B | |||
| 19/12 (Friday) | 15-17 | CA5 | Computer Assignment | HB105 | Henrik Vilhelmson |
| 22/12 (Monday) | 23:59 | Submission Deadline for CA Task C |
The following is the schedule for consultancy hours (including meeting with student representatives).
| Date | Time | Lecture | Topic | Room | Responsible |
| 21/11 (Friday) | 15-17 | CH1 | Consultancy Hours | EB-EDIT | Shivesh Kumar, Henrik Vilhelmson |
| 04/12 (Thursday) | 16-18 | CH2 | Consultancy Hours | SBL516 | Shivesh Kumar, Henrik Vilhelmson |
| 11/12 (Thursday) | 16-18 | CH3 | Consultancy Hours | SB-L516 | Shivesh Kumar, Henrik Vilhelmson |
Student Representatives
If you have any concerns or feedback regarding the execution of the course, you are welcome to bring it up to us directly or via the assigned student representatives for this course. The following students have been randomly selected as the student representatives for the TME141 Structural Dynamics course.
MPSEB alaabadi@student.chalmers.se Ahmed Ala-Abadi
MPSEB wilmaer@student.chalmers.se Wilma Eriksson
MPAME hugoot@student.chalmers.com Hugo Ottosson
UTBYTE silvan.andrea00@gmail.com Andrea Silvan
MPAME antoniollouzada@gmail.com António Vitor Louzada de Almeida
The teaching team will meet with the student representatives for a mid-term and end of the course meetings.
Course summary:
| Date | Details | Due |
|---|---|---|