Preface

Chapter 8 **Vibration Analysis of Cracked Beams Using the Finite**

A. S. Bouboulas, S. K. Georgantzinos and N. K. Anifantis

Chapter 10 **A Simplified Analytical Method for High-Rise Buildings 235**

Chapter 11 **An Analysis of the Beam-to-Beam Connections Effect and Steel-Concrete Interaction Degree Over the Composite Floors**

Chapter 12 **Parametric Vibration Analysis of Transmission Mechanisms**

Chapter 13 **Vibration of Satellite Solar Array Paddle Caused by Thermal**

**Shock When a Satellite Goes Through the Eclipse 333** Mitsushige Oda, Akihiko Honda, Satoshi Suzuki and Yusuke

Chapter 14 **Optimal Vibrotactile Stimulation Activates the Parasympathetic**

Katuko Ebihara, Hisako Ishii and Koichiro Ueda

Nelcy Hisao Hiraba, Motoharu Inoue, Takako Sato, Satoshi Nishimura, Masaru Yamaoka, Takaya Shimano, Ryuichi Sampei,

Nguyen Van Khang and Nguyen Phong Dien

José Guilherme Santos da Silva, Sebastião Arthur Lopes de Andrade, Pedro Colmar Gonçalves da Silva Vellasco, Luciano Rodrigues Ornelas de Lima, Elvis Dinati Chantre Lopes and Sidclei

**Element Method 181**

**VI** Contents

Chapter 9 **Vibrations of Cylindrical Shells 205**

**Dynamic Response 283**

**Using Numerical Methods 301**

Hideo Takabatake

Gomes Gonçalves

Hagiwara

**Nervous System 355**

Tiejun Yang, Wen L. Li and Lu Dai

The aim of this book is to present recent and innovative advances on research studies and engineering applications in important areas of vibration engineering and structural dynamics. The fourteen chapters of the book cover a wide range of interesting issues related to modelling, rotordynamics, vibration control, estimation and identification, modal analysis, dynamic structures, finite element analysis, numerical methods and other practical engineering applications and theoretical developments on this very broad matter. The audience of the book includes researchers, professors, engineers, practitioners, engineering students and new comers in a variety of disciplines seeking to know more about the state of the art, challenging open problems and innovative solution proposals in vibration engineering and structural dynamics.

The book is organized into 14 chapters. A brief description of every chapter follows. Chapter 1 focuses on the design, modelling, control, experimental tests and validation of all subsystems of a rotor on a five-axis active magnetic suspension system. The details of an innovative off-line electrical centering technique are exposed. Chapter 2 deals with the active control problem of unbalance-induced synchronous vibrations in variable-speed Jeffcott-like non-isotropic rotor-bearing systems. An active unbalance control scheme based on on-line compensation of rotor unbalance-induced perturbation force signals is proposed. Chapter 3 addresses the rotordynamic stabilization problem of rotors on electrodynamic bearings. A dynamic model of the entire suspension is developed to study the mechanical properties of the supports that allow guaranteeing stability. Chapter 4 introduces a study to determine the natural frequencies of machine tool spindle systems by developing its dynamic stiffness matrix and applying the proper boundary conditions. Chapter 5 presents vibration control of a flexible structure using a new type of semi-active mount operated with controllable magnetorheological fluid. Chapter 6 describes recent advances on force identification for structural dynamics using the concept of transmissibility for multiple degree-of-freedom systems. Chapter 7 proposes reduced-order models and reanalysis methodologies for accurate and efficient vibration analysis of large-scale, finite element models, and for efficient design optimization of structures for best vibratory response. Chapter 8 discusses the vibrational behavior of a beam with a non-propagating edge crack using a finite element model and Fourier and continuous wavelet transforms. Chapter 9 presents a general analytical method for vibration analysis of cylindrical shells with arbitrary boundary conditions. The proposed method can be applied to a wide range of boundary conditions with no need of modifying the solution algorithms and implementation procedures. Chapter 10 proposes an accurate analytical theory for doubly symmetric frame-tube structures by applying ordinary finite difference method to the governing equations proposed by the one-dimensional extended rod theory. Chapter 11 presents a study on the rigid, semi-rigid and flexible beam-to-beam connections effect and the influence of steel-concrete interaction degree over the non-linear dynamic behavior of composite floors when subjected to human rhythmic activities. Chapter 12 deals with the problem of dynamic modelling and parametric vibration of transmission mechanisms with elastic components governed by linearized differential equations having time-varying coefficients. Numerical procedures based on Runge-Kutta and Newmark methods are proposed and applied to find periodic solutions of linear differential equations with timeperiodic coefficients. Chapter 13 describes an approach to observe the vibrations of a low Earth orbiting satellite's solar array paddle induced by thermal shock using an onboard CMOS camera mounted on a Greenhouse gases Observing Satellite launched by the Japan Aerospace Exploration Agency (JAXA) in 2009. Chapter 14 concludes the book describing an experimental study on optimal vibrotactile stimulation to activate the parasympathetic nerve system.

Finally, I would like to express my sincere gratitude to all the authors for their excellent contributions, which I am sure will be valuable to the readers. I would also like to thank the editorial staff of InTech for their great effort and support in the process of edition and publication of the book.

I truly hope that this book can be useful and inspiring for contributing to the technology development, new academic and industrial research and many inventions and innovations in Vibration Engineering and Structural Dynamics.

> **Francisco Beltrán Carbajal** Departamento de Energía Universidad Autónoma Metropolitana, Unidad Azcapotzalco Mexico

**Chapter 1**

**Rotors on Active Magnetic Bearings: Modeling and**

In the last decades the deeper and more detailed understanding of rotating machinery dynam‐ ic behavior facilitated the study and the design of several devices aiming at friction reduction, vibration damping and control, rotational speed increase and mechanical design optimization. Among these devices a promising technology is represented by magnetic actuators used as bearings which found a great spread in rotordynamics and in high precision applications. A first classification of magnetic bearings according to the physical working principle allows to pick out two main families: a) Active Magnetic Bearings [1], [2], making use of an electronic control unit to regulate the current flowing in the coils of the actuators. They need external source of energy. b) Passive Magnetic Bearings [3], [4], [5]: they do not need any electronic equipment. The control of the mechanical structure is achieved without the introduction of any external energy source. They exploit the reluctance force or the Lorentz force due to the gener‐ ation of eddy currents developed in a conductor in a relative motion in a magnetic field.Active Magnetic Bearings require sensors an electronic equipment but, although more expensive re‐

**•** The absence of all fatigue and tribology issues due to contact: it allows the use of such bearings in vacuum systems, in clean and sterile rooms, or for the transport of aggressive

**•** Low bearing losses: at high operating speeds are 5 to 20 times less than in conventional

© 2012 Tonoli et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

© 2012 Tonoli et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

distribution, and reproduction in any medium, provided the original work is properly cited.

**•** No contamination by the dust created by friction between the rotor and the stator;

spect to classical ball bearings, they offer several technological advantages:

or very pure media, and at high temperatures;

ball or journal bearings, result in lower operating costs;

**•** No lubrication needed;

Andrea Tonoli, Angelo Bonfitto, Mario Silvagni and

Additional information is available at the end of the chapter

**Control Techniques**

http://dx.doi.org/10.5772/51298

Lester D. Suarez

**1. Introduction**
