Contents

## **Preface XI**


Chapter 8 **Vibration Analysis of Cracked Beams Using the Finite Element Method 181**

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


Andrade, Pedro Colmar Gonçalves da Silva Vellasco, Luciano Rodrigues Ornelas de Lima, Elvis Dinati Chantre Lopes and Sidclei Gomes Gonçalves

Preface

engineering and structural dynamics.

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

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

