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2012 | OriginalPaper | Chapter

2. Basics of Vibration Dynamics

Authors : Gergely Takács, Boris Rohal’-Ilkiv

Published in: Model Predictive Vibration Control

Publisher: Springer London

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Abstract

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.

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previous chapter Introduction

next chapter Smart Materials in Active Vibration Control

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Title: Basics of Vibration Dynamics
Authors: Gergely Takács
Boris Rohal’-Ilkiv
Publisher: Springer London
Book: Model Predictive Vibration Control
Print ISBN: 978-1-4471-2332-3

Electronic ISBN: 978-1-4471-2333-0

Copyright Year: 2012
DOI: https://doi.org/10.1007/978-1-4471-2333-0_2

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