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Syllabus for

Academic year
TME146 - Structural dynamics control
Syllabus adopted 2015-02-15 by Head of Programme (or corresponding)
Owner: MPAME
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: Second-cycle
Major subject: Automation and Mechatronics Engineering, Mechanical Engineering, Civil and Environmental Engineering
Department: 42 - APPLIED MECHANICS

Teaching language: English
Open for exchange students
Block schedule: C
Maximum participants: 40

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0112 Examination, part A 4,5 c Grading: TH   4,5 c   12 Jan 2016 am M,  07 Apr 2016 am M,  19 Aug 2016 am M
0212 Laboratory, part B 3,0 c Grading: UG   3,0 c    

In programs

MPAME APPLIED MECHANICS, MSC PROGR, Year 1 (compulsory elective)


Professor  Viktor Berbyuk


TME145   Vibration control

  Go to Course Homepage


In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement: Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.

Course specific prerequisites

Basic knowledge in mechanics, in particular dynamics of particles and rigid bodies¿ plane motion, some familiarity with state space models and automatic control.


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 industry-leading data acquisition hardware and software tools for measurement, signal processing and vibration control.

Learning outcomes (after completion of the course the student should be able to)

-Derive the equations and solve vibration dynamics problems for controlled multibody systems with springs, dampers and bushings, as well as with active functional components like electromagnetomechanical dampers and actuators;

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

-Analyze vibration dynamics, dynamic responses of structural systems (response ratio, response spectra, etc.) 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 using LabVIEW, Matlab/Simulink and test rigs with modern data acquisition hardware (CompactDAQ, CompactRIO);

-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.


Course content comprises the following parts.

Introduction: Supplementary mathematics and mechanics for structural dynamics control. Vibration dynamics modeling 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. Mounts and mounting systems. Dynamic vibration absorbers. Optimal tuned mass dampers and dynamic absorbers.

Feedback control and stability: Controllability. Observability. 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. Smart tuned mass damper for vibration control. 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. Hybrid control in structural dynamics.

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; wind turbine drive train structural dynamics; vibration control in high speed trains; magnetostrictive sensors, actuators and electric generators for active structures, self-powered structural health monitoring systems, others.

Computer assignments and labproject: 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 (AB Volvo, Scania, SKF, ABB CR, Bombardier Transportation, Swedish Wind Power Technological Centre, CHARMEC, others).


The course will comprise the following type of activities: lectures, problem solving sessions, computer assignment on vibration dynamics and control with LabVIEW and MATLAB/Simulink and labproject on experimental validation of vibration control methods at the Vibrations and Smart Structures Lab of the division of Dynamics.


1. Berbyuk V., Structural Dynamics and Control, Lecture Notes, Department of Applied Mechanics, Chalmers University of Technology, Göteborg, 2014.

2. LabProject in Vibration Control, Hands-On, Department of Applied Mechanics, Chalmers University of Technology, 2015.

3. Introduction to LabVIEW and Computer-Based Measurements, National Instruments, 2013.

All course literatures will be available before course start for the reasonable student price.


Laboratory (Project report) (3,0 hec), written exam (4,5 hec).

Page manager Published: Mon 28 Nov 2016.