Basics of Vibration Dynamics

This chapter intends to introduce the reader to the theoretical basics of vibration dynamics analysis. Every well designed active vibration control (AVC) system requires at least a fundamental understanding of the underlying vibration phenomenon. The simple point mass oscillator is used as an example to build more and more complicated systems gradually. After the free response of undamped and damped one degree of freedom systems is discussed, forced response from a harmonic source is considered as well. The basics of engineering vibration analysis of lumped mass multiple degree of freedom systems is investigated with a concise account on the eigenvalue problem and modal decomposition. The transversal vibration of a clamped-free cantilever beam is used as an example to show, how exact solutions for distributed parameter systems may be developed. The chapter is finished with a section discussing modeling techniques used in vibration control, such as first principle transfer function models, state-space models, FEM based models and experimental identification. The aim of this chapter is to introduce the mathematical description of vibration phenomena briefly, in order to characterize the nature of the mechanical systems to be controlled by the model predictive control (MPC) strategy presented in the upcoming chapters of this book.

[1]  Hemanshu R. Pota,et al.  Modelling, system identification, and control of acoustic–structure dynamics in 3-D enclosures , 2004 .

[2]  Jing-Huei Lee,et al.  Simulation study on active noise control for a 4-T MRI scanner. , 2008, Magnetic resonance imaging.

[3]  S. O. Reza Moheimani,et al.  Model Predictive Control Applied to Constraint Handling in Active Noise and Vibration Control , 2008, IEEE Transactions on Control Systems Technology.

[4]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[5]  Andy J. Keane,et al.  Active vibration control (AVC) of a satellite boom structure using optimally positioned stacked piezoelectric actuators , 2006 .

[6]  Daniel J. Inman,et al.  Vibration with Control: Inman/Vibration with Control , 2006 .

[7]  Ioan Doré Landau,et al.  Adaptive narrow band disturbance rejection applied to an active suspension - an internal model principle approach , 2005, Autom..

[8]  Brett Ninness,et al.  AN IDENTIFICATION TOOLBOX FOR PROFILING NOVEL TECHNIQUES , 2006 .

[9]  D. Inman.  Vibration control , 2018, Advanced Applications in Acoustics, Noise and Vibration.

[10]  Xinong Zhang,et al.  The actuated performance of multi-layer piezoelectric actuator in active vibration control of honeycomb sandwich panel , 2008 .

[11]  T. Rossing,et al.  The Science of Sound , 1998 .

[12]  Gergely Takács,et al.  Newton-raphson based efficient model predictive control applied on active vibrating structures , 2009, 2009 European Control Conference (ECC).

[13]  Alberto Cavallo,et al.  Gray-Box Identification of Continuous-Time Models of Flexible Structures , 2007, IEEE Transactions on Control Systems Technology.

[14]  Glauco Feltrin,et al.  Assessment of long-term behavior of tuned mass dampers by system identification , 2010 .

[15]  Oddvar Hallingstad,et al.  Vibration parameters identification in a spacecraft subjected to active vibration damping , 1998 .

[16]  José Luis Guzmán,et al.  ITSIE: An Interactive Software Tool for System Identification Education , 2009 .

[17]  S. Van Huffel,et al.  SLICOT system identification software and applications , 2002, Proceedings. IEEE International Symposium on Computer Aided Control System Design.

[18]  Brett Ninness,et al.  Maximum-likelihood parameter estimation of bilinear systems , 2005, IEEE Transactions on Automatic Control.

[19]  Boris Rohal,et al.  NEWTON- RAPHSON MPC CONTROLLED ACTIVE VIBRATION ATTENUATION , 2009 .

[20]  Jinhao Qiu,et al.  Two-mode vibration control of a beam using nonlinear synchronized switching damping based on the maximization of converted energy , 2010 .

[21]  Clarence W. de Silva,et al.  Vibration: Fundamentals and Practice , 1999 .

[22]  J. Bruch,et al.  Piezo patch sensor/actuator control of the vibrations of a cantilever under axial load , 2003 .

[23]  Sabine Van Huffel,et al.  High-performance numerical algorithms and software for subspace-based linear multivariable system identification , 2004 .

[24]  Roger Ohayon,et al.  Active vibration control of a thin rectangular plate in air or in contact with water in presence of tonal primary disturbance , 2008 .

[25]  Kefu Liu,et al.  A tunable electromagnetic vibration absorber: Characterization and application , 2006 .

[26]  J. C. Bruch,et al.  Vibration damping in beams via piezo actuation using optimal boundary control , 2000 .

[27]  Guang Meng,et al.  Vibration control of piezoelectric smart structures based on system identification technique: Numerical simulation and experimental study , 2006 .

[28]  Haym Benaroya,et al.  Mechanical Vibration: Analysis, Uncertainties, and Control , 1997 .

[29]  S. C. Pradhan.  Vibration suppression of FGM shells using embedded magnetostrictive layers , 2005 .

[30]  Brett Ninness,et al.  The university of Newcastle identification toolbox (UNIT) , 2005 .

[31]  A. Preumont.  Vibration Control of Active Structures , 1997 .

[32]  Nader Jalili,et al.  An experimental investigation of nonlinear vibration and frequency response analysis of cantilever viscoelastic beams , 2008 .

[33]  Yixin Diao,et al.  Feedback Control of Computing Systems , 2004 .

[34]  T. C. Manjunath,et al.  Modeling, Control and Implementation of Smart Structures: A FEM-State Space Approach , 2007 .

[35]  Cornel Mihai Nicolescu,et al.  Active vibration control in palletised workholding system for milling , 2006 .

[36]  Brett Ninness,et al.  On Gradient-Based Search for Multivariable System Estimates , 2008, IEEE Transactions on Automatic Control.

[37]  C F Beards,et al.  STRUCTURAL VIBRATION: ANALYSIS AND DAMPING , 1996 .

[38]  Michel Verhaegen,et al.  Optimal and robust feedback controller estimation for a vibrating plate , 2004 .

[39]  Kazuto Seto,et al.  Active Control of Structures , 2008 .

[40]  Manfred Morari,et al.  Feedback control of sound transmission through a double glazed window , 2003 .

[41]  Harley H. Cudney,et al.  A piezoelectric array for sensing vibration modal coordinates , 2001 .

[42]  Boris Lohmann,et al.  H∞ Feedback control and Fx-LMS feedforward control for car engine vibration attenuation , 2005 .

[43]  Mehdi Ahmadian,et al.  Experimental application of orthogonal eigenstructure control for structural vibration cancellation , 2010 .

[44]  Jan Swevers,et al.  Sprayer boom motion, Part 1 : Derivation of the mathematical model using experimental system identification theory , 2000 .

[45]  Brett Ninness,et al.  Maximum Likelihood estimation of state space models from frequency domain data , 2009, 2007 European Control Conference (ECC).

[46]  Thomas B. Schön,et al.  System identification of nonlinear state-space models , 2011, Autom..