by J. Biggs and C. Tang, Maidenhead, England,
Open University Press, 2007, 360 pp., £29.99, ISBN-13: 978-0-335-22126-4

Teaching for quality learning at university

Nonlinear system identification in structural dynamics: 10 more years of progress

The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems

The harmonic balance (HB) method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems. The objective of this paper is to exploit the method for bifurcation analysis, i.e., for the detection and tracking of bifurcations of nonlinear systems. To this end, an algorithm that combines the computation of the Floquet exponents with bordering techniques is developed. A new procedure for the tracking of Neimark–Sacker bifurcations that exploits the properties of eigenvalue derivatives is also proposed. The HB method is demonstrated using numerical experiments of a spacecraft structure that possesses a nonlinear vibration isolation device.

Dynamic testing of nonlinear vibrating structures using nonlinear normal modes

Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques

The power law relation between the mean population count and its variance (Taylor’s Power Law, TPL) is among the few general patterns in population ecology. While the TPL has been described to be pervasive across taxa, the causes of variation of the exponent describing this relation is not well understood. We compare the TPL exponents for two species with different social systems and behavior: Pinon jays (Gymnorhinus cyanocephalus) and Western scrub-jays (Aphelocoma californica). We analyze the underlying processes that generate the expected values of population size and its variance. Using a probabilistic model, we identify and estimate important processes involved in the generation of the TPL exponents. While both species show a scaling relationship between their mean and abundance, share a common negative relation between mean abundance and colonization–extinction rates, they differ greatly in the statistical distributions of colonization, extinction, the mean number of colonists, the probability of zero abundance and population sizes. We show how different aspects of the processes that generate abundance affect the TPL exponent, thereby providing empirical guidelines to interpret differences in the scaling relation between mean and variance of population size.

Analyzing Taylor’s Scaling Law: qualitative differences of social and territorial behavior on colonization/extinction dynamics

Leukocyte- and Platelet-Rich Fibrin Have Same Effect as Blood Clot in the 3-Dimensional Alveolar Ridge Preservation. A Split-Mouth Randomized Clinical Trial

Structural Dynamics Research GroupAerospace and Mechanical Engineering DepartmentUniversity of Liege, Li` `ege, Belgiumm.peeters,r.viguie,g.serandour,g.kerschen,jc.golinval@ulg.ac.beAbstractThe concept of nonlinear normal modes (NNMs) isdiscussed in the present paper and its companion, PartII. Because there is virtually no application of theNNMs to large-scale engineering structures, these pa-pers are an attempt to highlight one aspect that mightdrive their development in the future. Speciﬁcally, weargue that numerical methods for the continuation ofperiodic solutions pave the way for an effective andpractical computation of NNMs. In this context, weshow that the NNM computation is possible with lim-ited implementation effort. The proposed algorithm,implemented in MATLAB, relies on two main tech-niques, namely a shooting procedure and a method forthe continuation of NNM motions. The algorithm isdemonstrated using a 2DOF nonlinear system. A com-parison with the results given by the AUTO software isachieved in Part II.Key wordsNonlinear normal modes, periodic solution, numericalcomputation, shooting, continuation techniques.1 IntroductionNonlinear normal modes (NNMs) offer a solid the-oretical and mathematical tool for interpreting a wideclass of nonlinear dynamical phenomena, yet they havea clear and simple conceptual relation to the LNMs[Vakakis et al., 1996; Vakakis, 1997; Kerschen et al.,2008]. However, most structural engineers still viewNNMs as a concept that is foreign to them, and they donot yet consider NNMs as a useful concept for struc-tural dynamics. One reason supporting this statementis that most existing constructive techniques for com-puting NNMs are based on asymptotic approaches andrely on fairly involved mathematical developments.There have been very few attempts to compute NNMsusing numerical methods [Slater, 1996; Pesheck, 2000;Lee et al., 2005; Arquier, 2007]. Algorithms for thecontinuation of periodic solutions are really quite so-phisticated and advanced (see, e.g., [Seydel, 1994;Doedel, 2007]), and they have been extensively usedfor computing the forced response and limit cycles ofnonlinear dynamical systems (see, e.g., [Touze et al.,´2007]). Interestingly, they have not been fully ex-ploited for the computation of nonlinear modes.The objective of this paper and its companion, PartII, is to support that these numerical algorithms pavethe way for an effective and practical computation ofNNMs. In the present paper, we show that the NNMcomputation is possible with limited implementationeffort. The proposed algorithm, implemented in MAT-LAB, relies on two main techniques, namely a shootingprocedure and a method for the continuation of NNMmotions. The algorithm is demonstrated using a 2DOFnonlinear system. In Part II, the same study is carriedout using the AUTO software.2 Nonlinear Normal Modes (NNMs)A detailed description of NNMs and their fundamen-tal properties (e.g., frequency-energy dependence, bi-furcations and stability) is given in [Vakakis et al.,1996; Vakakis, 1997; Kerschen et al., 2008]. For com-pleteness, the two main deﬁnitions of an NNM arebrieﬂy reviewed in this section.The free response of discrete conservative mechanicalsystems with

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Computation of nonlinear normal modes, part i: numerical continuation in matlab

Este articulo presenta una plataforma de software para la evaluacion de a ctividades de trabajo en equipo. Esta herramienta se enfoca en la evaluacion de competencias actitudinales, soportando la e valuacion desde cuatro perspectivas diferentes. La automatizacion de la gran parte del trabajo necesario para hacer evalua ciones libera al docente del sobretrabajo que esta actividad usualmente implica. La plataforma presenta resultados tanto al docente como al estudiante con el fin de constituir una herramienta que aporte a la retroalimentacion de las competencias actitu dinales. El despliegue de resultados se realiza de manera resumida y mediante graficos, lo que facilita su interpretacion. Los resultados son entregados en tiempo real, lo que permite a los docentes seguir de cerca la actividad del grupo e intervenir oportunamente en caso de necesidad. Esta herramienta se utilizo en 7 asignaturas, obteniendo resultados positivos, los cuales son presentados en este articulo.

Guillaume Sérandour

Papers

Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques

Analyzing Taylor’s Scaling Law: qualitative differences of social and territorial behavior on colonization/extinction dynamics

Leukocyte- and Platelet-Rich Fibrin Have Same Effect as Blood Clot in the 3-Dimensional Alveolar Ridge Preservation. A Split-Mouth Randomized Clinical Trial

Computation of nonlinear normal modes, part i: numerical continuation in matlab

Una Herramienta de Apoyo a la Auto, co, Hetero y Ecoevaluación