Structural Dynamics Control
Bok, 2012

The objective in writing this textbook was to help students wishing to get deeper knowledge on structural dynamics and vibration control, while providing an overview of the potential of smart materials based sensor and actuator technologies for active vibration control. The textbook consist of four main parts: Vibration dynamics (Part 1), Passive and semi-active vibration control (Part 2), Active and hybrid vibration control (Part 3), and Applications (Part 4). The textbook ends with the supplementary mathematics, list of Matlab codes and answers and hints for the exercises. The Part 1 consists of Chapter 2 and Chapter 3. In Chapter 2 we present three approaches, which are usually used for developing of mathematical models of vibration dynamics of mechanical systems. These approaches are: free-body diagram, energy method and Lagrange formalism. Chapter 3 is devoted to elements of vibration dynamics analysis. The focus is set primarily on simple and widely recognizable vibrating mechanical systems. Attention is paid to analysis of vibration dynamics under harmonic excitations, transmissibility and vibration isolation. Vibration dynamics of a mechanical system can be affected by changing the initial state, or/and by changing the system’s structural/design parameters, or/and by varying the external force/torque excitations acting on the system. This type of problems is considered in the Part 2 of the textbook which is called “Passive and semi-active vibration control”. In many cases mechanical systems are inherently stable to begin with, and external control is applied to improve the performance. But, unfortunately, the introducing the active control, let say for vibration control by using feedback control, can often make the system unstable. In Chapter 5 the elements of the theory of stability to be used for designing of active vibration control strategies making the closed loop vibrating system stable, are presented. Chapter 6 presents several details of physical and mathematical representations of feedback control. Some important properties of a system to be controlled such as controllability and observability are defined and discussed.In Chapter 7 semi-active vibration control problems are considered. Some well-known semi-active control strategies based on skyhook approach are presented. A brief overview of magnetorheological (MR) fluids technology including modelling of MR dampers is presented and their applications for semi-active control are discussed. The Part 3 of the textbook is called “Hybrid and active vibration control”. It consists of Chapters 8 - 9. Chapter 8 presents several approaches and methods for designing of optimal control laws and algorithms for vibration attenuation and vibration suppression. Focus is put on linear quadratic regulator (LQR) optimization technique, the calculus of variations approaches, the methods which are used first integrals of a vibrating system to be controlled, and the method for optimal vibration control based on Pontryagin maximum principle. Chapter 9 presents the elements of theory of hybrid control techniques. A mathematical statement of the optimal control problem which is suitable for modelling of controlled motion and optimization of semi-passively actuated mechanical systems is proposed. A methodology and numerical algorithms for solving the control and optimization problems for semi-passively actuated mechanical systems are described. Special emphasis is put on the study of controlled mechanical systems having different degrees and types of actuation (underactuated and overactuated systems, external powered drives, unpowered spring-damper like drives, etc.). The Part 4 of the textbook is called “Applications” and comprises Chapters 10 –13. The Chapter 10 deals with application of smart materials, namely giant magnetostrictive materials, for power harvesting from vibration. In the Chapter 11 the engineering and computational models of a washing machine are described and structural dynamics analysis of the system is presented and briefly discussed. The dynamical behavior of railway vehicles is an active area of research. Recent activities are focused on improvements of train-set performance with focus on cost efficiency of railway operation, safety, comfort and environment impact. In Chapter 12 we give a brief overview of the results obtained and on-going research on structural dynamics and control of railway vehicles at the Mechanical systems group at Chalmers. In recent years wind energy has been a fast growing source of electrical power. In the Chapter 13 we outline challenges and motivations in research and developing in wind turbine technology as well as present some results on structural dynamics of drive train system of wind turbines. The textbook ends with the Supplementary mathematics, List of Matlab codes and Answers and hints for the exercises.

wind turbine drive train

semi-active vibration control

structural dynamics

active vibration control

active structure

power harvesting from vibration

vibration dynamics

hybrid vibration control

vibration control

passive vibration control

active structures and smart materials technology

bogie system optimisation


Viktor Berbyuk




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