Course syllabus


TME146 Structural dynamics control lp2 HT23 (7.5 hp)

Course is offered by the department of Mechanics and Maritime Sciences

Contact details

Håkan Johansson, Bitr. ProfessorCourse responsible, Examiner, Lectures, Exercises

E-mail:, Phone:  031-772 8575

Yu-Hung Pai, PhD student – Instructor, Computer Assignments, Labprojects


Hans Lindell, Lic. Eng., RISE – Guest lecture


Email is generally the best contact to teachers. Håkan Johansson and Yu-Hung Pai have office on floor 3 in M-building.

Course purpose

The course aims at providing knowledge on modern methods and concepts of passive, semi-active and active vibration control, to cross the bridge between the structural dynamics and control engineering, while providing an overview of the potential of smart materials, (magnetorheological fluids, magnetostrictive materials, and piezoceramics), for sensing and actuating purposes in active vibration control. Vibration control applications appear in vehicle engineering, high precision machines and mechanisms, robotics, biomechanics and civil engineering. The focus of the project part of the course is on experimental validation of practical methods, i.e., methods that were found to actually work efficiently for passive and/or active vibration control. The course prepares students to use data acquisition hardware and software tools for measurement, signal processing and vibration control. 



In brief - some deviations (see detailed schedule in TimeEdit):

Tuesdays 8:00-11:45: Lecture 2h, followed by 2h computer class

Wednesday 8:00-9:45: Lecture 2h

Fridays 8:00-11:45: Lecture 2h, followed by 2h computer class

Self-studies from Dec 18.

Course literature

eBook "Structural Dynamics and Control" by V. Berbyuk will be available to download for registered students at Canvas.

Limited number of printed version of the textbook "Structural Dynamics and Control" by V. Berbyuk will be available at course start (pending on printing service).

Hands-On for Computer Assignments and lab projects, Department of Mechanics and Maritime Sciences, Chalmers University of Technology, 2023.

Course design

Course will comprise the following parts.

Introduction: Supplementary mathematics and mechanics for structural dynamics control. Vibration dynamics modelling and analysis. State space approach. Smart structures and active control of structural dynamics.

Passive control in structural dynamics: Vibration control by parameter optimization. Tuned mass damper technology. Vibration isolation. Dynamic vibration absorbers.

Feedback control and stability of structural dynamics: Review of different control strategies. Lyapunov stability of dynamical systems. Lyapunov equation. Routh-Hurwitz criterion.

Semi-active control in structural dynamics: Controllable stiffness/damping based semi-active vibration control. Continuous and on-off skyhook control strategies for semi-active structural control. Smart materials technology for active structures. Magneto-rheological fluid technology for semi-active structural dynamics control.

Active control in structural dynamics: The LQR optimization and active vibration control. The variational calculus for optimal structural dynamics control. The first integrals method and active vibration control. The Pontryagin maximum principle for optimal structural dynamics control.

Useful vibration: Magnetostrictive and piezoelectric materials technologies for vibration to electrical energy conversion (power harvesting from vibration). Models, simulations, experimental validation.

Applications: Vibration control in automotive engineering (vehicle suspensions, engine mounting systems, driveline vibration, vehicle comfort, motion stability and safety); Wind turbine drive train structural dynamics; Vibration control in rotor systems; Vibration control in high speed trains (primary and secondary car-body suspensions); Magnetostrictive sensors, actuators and electric generators for active structures, self-powered structural health monitoring systems, others.

Computer assignments and lab project: The topics will be closed related to the course lectures as well as to the ongoing research projects at the Division of Dynamics with industrial partners.

The course comprises the following type of activities:

  • Lectures (incl. problem solving) sessions (6 hours weekly)
  • Own work on (Matlab) computer assignments (4 hours weekly - with supervision)
  • Lab projects on validation of vibration control methods (a separate lab schedule)
  • Reporting on computer assignments and lab projects (own work)
  • Written exam

All sessions are planned to be held physically in room, with combination of blackboard and computer presentations.

Changes made since the last occasion

Updated labs.

Learning objectives and syllabus

Learning objectives:

-Derive the equations and solve vibration dynamics problems for controlled multibody systems with springs, dampers and bushings;

-Create mathematical and computational models suitable for structural dynamics control applications;

-Analyze vibration dynamics, dynamic responses of structural systems for different damping concepts and external control;

-Explain in detail the basic principles on which the structural dynamics control methods rely and choose appropriate control strategy for particular applications;

-Formulate and solve passive, semi-active as well as active structural dynamics control problems for vibrating mechanical systems;

-Evaluate vibration control solutions experimentally by test rigs with modern data acquisition hardware (CompactDAQ, CompactRIO) and software (LabVIEW, Matlab/Simulink);

-Understand, explain and apply the physics behind semi-active and active structural dynamics control solutions based on smart materials sensor and actuator technologies (magnetorheological fluids, magnetostrictive and piezoelectric materials);

-Carry out structural dynamics analysis and design vibration control strategies for vibrating systems having applications in automotive industry (chassis and powertrain suspensions), railway industry (high speed train bogie and car-body suspensions), wind power industry (turbine drive train systems), civil engineering;

-Understand that vibrations can be also used for advantage in some applications. Know the basic principles and the state of the art on vibration to electrical energy conversion by using smart materials (power harvesting technology);

-Show ability to work in project team and collaborate in groups with different compositions.

Link to the syllabus on Studieportalen.

Study plan

Examination form

Approved Computer Assignments and Lab projects work will give 3,0 hec. The written exam (4,5 hec) consists of four problems of the type solved on the problem solving sessions and during the lectures. Each problem on the exam can give maximum 5 points. The total course mark will be based on results of the reporting of Computer Assignments & lab projects work and the results of written exam. The grades are: 9-13 points give “3”, 14-17 points give “4”, and 18 or more points give “5”.

Aids during the examination            

Students can bring to the exam the textbook “Structural Dynamics Control” by Viktor Berbyuk, Math tables (e.g. standard math, Beta; ask examiner before exam if unsure if a certain book is permissible) and Chalmers approved calculator.


Course summary:

Date Details Due