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About this book

This book compiles recent research in the field of nonlinear dynamics, vibrations and damping applied to engineering structures. It addresses the modeling of nonlinear vibrations in beams, frames and complex mechanical systems, as well as the modeling of damping systems and viscoelastic materials applied to structural dynamics. The book includes several chapters related to solution techniques and signal analysis techniques. Last but not least, it deals with the identification of nonlinear responses applied to condition monitoring systems.

Table of Contents

Frontmatter

Chapter 1. Introduction to Scientific Computing Technologies for Global Analysis of Multidimensional Nonlinear Dynamical Systems

Abstract
To determine global behaviour of a dynamical system, one must find invariant sets (attractors) and their respective basins of attraction. Since this cannot be made extensively with analytical methods, the numerical global analysis is currently the subject of intensive research, especially for strongly nonlinear, multidimensional dynamical systems. Numerical analysis in dimensions higher than four present a challenge, since it requires significant computing resources. Numerical methods used in global analysis that can benefit from high-power computing are those that can parallelize either data or task elaboration on a large scale. Mass parallelization comes with large number of difficulties, restrictions and programming hazards. When not implemented in compliance with hardware organization, data and instruction management can lead to severe loss of parallel algorithm performance. Systematic and methodical approach to design parallel programs is, therefore, critical to get the most from expensive high-power computing systems and to avoid unrealistic speed-up expectation. Considering these difficulties, the goal of this chapter is to introduce readers to the world of high-power computing systems for science and global analysis of strongly nonlinear, multidimensional dynamical systems. Topic covered are classification and performance of hardware and software, classes of computing problems and methodical design of programs. Two major hardware platforms used for scientific computing, clusters and systems with computational GPU are considered. Functionality of widely utilized software solutions (OpenMP, MPI, CUDA and OpenCL) for high-power computing systems is described. Performance of individual computer components are addressed so that the reader can understand advantages, disadvantages, efficiency and limits of each hardware platform. With this knowledge users can judge if their computation problem is suitable for mass parallelization. If this is the case, which hardware and software platforms to use. To avoid many traps of parallel programming, one of the methodical design approaches is covered. Topic is closed with example applications in science and global analysis.
Nemanja Andonovski, Franco Moglie, Stefano Lenci

Chapter 2. Review of Synchronization in Mechanical Systems

Abstract
Synchronization of coupled sub-systems in both natural and engineered systems is a commonplace occurrence, but its existence and analysis in mechanical systems has received much less attention. This is a review, written for mechanical engineers, of some of the work done on complex machines that are in common use. Theoretical characteristics of the phenomena that are present are indicated by solutions to models based on self-excited oscillations. A variety of experiments on synchronization that have been carried out are reported, including work done by the authors on vibrations of rotor blades due to airflow and of automobile parts. A large number of references on the subject has been included so that a researcher who is new to synchronization in complex machinery can use this as a starting point.
Mihir Sen, Carlos S. López Cajún

Chapter 3. Research on Vibration Suppression of Nonlinear Energy Sink Under Dual-Frequency Excitation

Abstract
Most of modern civil turbofan engines adopt the dual-rotor layout, which introduces the typical dual-frequency excitation into the dynamic models. This work sets a single degree of freedom (SDOF) linear oscillator for the main system, and establishes the dynamic models of that coupled with the SDOF linear dynamic vibration absorber (DVA) and different configurations of nonlinear energy sink (NES). In view of the typical flutter mechanism of wing, the modal frequency of the first-order symmetric twist typical state of wing is introduced into dynamic models. With the wing, low and high characteristic frequency ratio (1:2.67:12.66) for the typical dual-rotor aero-engine in cruise, the fourth-order Runge-Kutta algorithm is employed for analysis. According to the energy criteria for the dynamic vibration absorber optimization, focusing on the effects of the characteristic frequency ratio on the kinetic energy of the primary mass, total system energy etc., numerical simulation results of comparison can indicate that reducing the torsional vibration of wing by NES is feasible, and NES has better vibration suppression effect than the traditional linear DVA with certain set of parameters under the dual-frequency excitation. In addition, the vibration suppression effects of the SDOF, two-DOF serial and parallel NES on the main oscillator system are focused on. Under the condition that the characteristic parameters of the main system and additive total mass of the vibration absorber remain unchanged, results show the two-DOF parallel NES has the best vibration energy suppression effect under dual-frequency excitation.
B. Sun, Z. Q. Wu

Chapter 4. Identification of Nonlinearities in Mechanical Systems Using Recurrence Plots

Abstract
The identification of nonlinear vibrations in mechanical systems is an unsolved problem. The structure of the measured data and waveforms have been studied for many years, and different techniques have been applied. Nevertheless, there is no single technique for identifying the nonlinear parameters. Parameter identification can be conducted either with a parametric approach or with a non-parametric approach. Among parametric approaches many researchers have work with the Hilbert transform, continuous and discrete wavelet transform, nonlinear modal analysis, phase space. Meanwhile, nonparametric procedures include fractal analysis, Hurt factor, and approximate entropy. In this paper, the recurrence plots are applied for the identification of nonlinear parameters. Recurrence plots are constructed from the phase space. To calibrate the method, the recurrence plots were obtained from two theoretical models, a Van der Pol pendulum, and a Duffing mass-lump model. Then, the recurrence plots were constructed from a mechanical gearbox. Recurrence plots are an alternative solution for the identification of nonlinearities in mechanical systems.
J. C. Jauregui-Correa

Chapter 5. Passive Vibration Control Using Viscoelastic Materials

Abstract
This chapter is devoted to the use of viscoelastic materials as a strategy intended for passive vibration control in mechanical systems. It provides a review of the theoretical foundations underlying the constitutive modeling of the viscoelastic behavior, and the association of constitutive models with modern numerical resolution procedures, especially the finite element method. This currently enables the accurate prediction of the dynamic behavior of rather complex structural systems featuring viscoelastic dampers, duly accounting for the particular characteristics of the viscoelastic behavior, namely the memory effect and the dependence of stiffness and damping properties on frequency and temperature. Other relevant aspects considered are: (i) model condensation techniques, intended to reduce the computation cost involved in the evaluation of the response of viscoelastic structures using finite element models with large numbers of degrees-of-freedom; (ii) the identification of viscoelastic constitutive models from experimental data. In addition, some applications of viscoelastic materials to structures of engineering interest are presented to illustrate the use of some techniques discussed.
D. A. Rade, J.-F. Deü, D. A. Castello, A. M. G. de Lima, L. Rouleau

Chapter 6. Dry-Friction Damping in Vibrating Systems, Theory and Application to the Bladed Disc Assembly

Abstract
The chapter deals with a dry friction damping in the dynamics of model blade systems. The main emphasis is to the solution of damping effects of dry friction contacts in tie-bosses and shrouds. Friction is considered herein from phenomenological view. The variety of modified dry-friction models and results of their equivalent linearization are presented at the beginning. Then numerical models, i.e. discrete analytical, reduced and full finite element, used in our research of non-linear dynamic behavior of the blade cascades and bladed wheel with dry friction contacts are discussed. Dynamics states, such as resonant vibration, free attenuation, self-excitation, are considered. The detailed dynamic analysis of non-linear behavior of these systems due to dry-friction contacts is presented for discrete analytical model with the stick-slip friction contact. Furthermore, the solution of the blade bundle dynamics with the tie-boss coupling by the 3D FE model with surface to surface contacts is described. Because of the rotary periodicity, the bladed wheels bring special resonant vibration mode, i.e. travelling wave mode, in dependence on a type of wheel excitation, the dynamic responses of the wheel to nozzle excitation and self-excitation are studied, too. For validation purposes, we describe the experiments and their results on blade bundles with two types of dry friction coupling. The comparisons with the numerical results show that in spite of simplifications in the modelling of the dry-friction contacts, the used numerical models can deliver very useful information about additional stiffness, damping and stabilization effect.
Ludek Pesek, Ladislav Pust, Pavel Snabl, Vitezslav Bula, Michal Hajzman, Miroslav Byrtus

Chapter 7. Bifurcation-Based Shimmy Analysis of Landing Gears Using Flexible Multibody Models

Abstract
Shimmy oscillations are undesired vibrations in aircraft landing gears. In this chapter, the onset of shimmy vibrations, marked by Hopf bifurcations, is investigated in the parameter space of high-fidelity, flexible multibody landing gear models. Such a bifurcation analysis is performed by combining the Virtual.Lab Motion multibody solver with the numerical continuation software AUTO. The resulting quasi-2-parameter bifurcation diagrams, involving aircraft velocity and normal load, are verified using conventional time-simulation methods and are shown to be computationally more efficient. A sensitivity study reveals the influence of design parameters, such as the shimmy damping coefficient, mechanical trail, and steering actuator stiffness, on the occurrence of shimmy.
C. J. J. Beckers, A. E. Öngüt, G. Verbeek, R. H. B. Fey, Y. Lemmens, N. van de Wouw

Chapter 8. Spectral Analysis of Nonlinear Vibration Effects Produced by Worn Gears and Damaged Bearing in Electromechanical Systems: A Condition Monitoring Approach

Abstract
Condition monitoring and fault identification have become important aspects to ensure the proper operating condition of rotating machinery in industrial applications. In this sense, gearbox transmission systems and induction motors are important rotating elements due to they are probably the most used in industrial sites. Thus, from an industrial perspective, the occurrence of vibrations is inherent to the working condition in any rotating machine. To overcome this issue, condition monitoring strategies have to be developed aiming to avoid unnecessary cost and downtimes; thereby, condition-based maintenance based on vibration analysis has become as the most reliable approach with condition monitoring and fault identification purposes. In this regard, this work proposes a spectral analysis of the nonlinear vibration effects produced by worn gears and damaged bearings during the condition monitoring and fault assessment in an electromechanical system. The analysis is based on the spectral estimation from the available vibration and stator current signals; furthermore, the theoretical fault-related frequency components are estimated for being located in such estimated spectra. Consequently, the identification of different levels of uniform wear is performed by comparing the amplitude increase of those theoretical frequency components. Finally, through time-frequency maps is proved that an incipient fault, such as wear in gears and damage in bearings, may produce nonlinear frequency components that affect the proper operating condition of the electromechanical system. The proposed analysis is validated under a complete experimentally dataset acquired from a real laboratory electromechanical system.
J. J. Saucedo-Dorantes, M. Delgado-Prieto, R. A. Osornio-Rios, R. J. Romero-Troncoso
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