Staff members at Los Alamos National Laboratory (LANL) produced a summary of the structural health monitoring literature in 1995. This presentation will summarize the outcome of an updated review covering the years 1996 2001. The updated review follows the LANL statistical pattern recognition paradigm for SHM, which addresses four topics: 1. Operational Evaluation; 2. Data Acquisition and Cleansing; 3. Feature Extraction; and 4. Statistical Modeling for Feature Discrimination. The literature has been reviewed based on how a particular study addresses these four topics. A significant observation from this review is that although there are many more SHM studies being reported, the investigators, in general, have not yet fully embraced the well-developed tools from statistical pattern recognition. As such, the discrimination procedures employed are often lacking the appropriate rigor necessary for this technology to evolve beyond demonstration problems carried out in laboratory setting.

A review of structural health monitoring literature 1996-2001

A critical review of the intrinsic nature of vortex-induced vibrations

This article reviews the development of the original modal assurance criterion (MAC) together with other related assurance criteria that have been proposed over the last twenty years. Some of the other assurance criteria that will be discussed include the coordinate modal assurance criterion (COMAC), the frequency response assurance criterion (FRAC), coordinate orthogonality check (CORTHOG), frequency scaled modal assurance criterion (FMAC), partial modal assurance criterion (PMAC), scaled modal assurance criterion (SMAC), and modal assurance criterion using reciprocal modal vectors (MACRV). In particular, the thought process that relates the original MAC development to ordinary coherence and to orthogonality computations will be explained. Several uses of MAC that may not be obvious to the casual observer (modal parameter estimation consistency diagrams and model updating are two examples) will be identified. The common problems with the implementation and use of modal assurance criterion computations will also be identified. The development of the modal assurance criterion 1-2 over twenty years ago has led to a number of similar assurance criteria used in the area of experimental and analytical structural dynamics. It is important to recognize the mathematical similarity of these varied criteria in order to be certain that conclusions be correctly drawn from what is essentially a squared, linear regression correlation coefficient. The modal assurance criterion is a statistical indicator, just like ordinary coherence, which can be very powerful when used correctly but very misleading when used incorrectly. This article will first review the historical development of the modal assurance criterion. Other similar assurance criteria will then be identified although the list is not intended to be comprehensive. Typical uses of the modal assurance criterion will be discussed and finally, typical abuses will be identified.

The modal assurance criterion–twenty years of use and abuse

Past, present and future of nonlinear system identification in structural dynamics

Introduction. 1. Nonlinear theories of elasticity of plates and shells 2. Nonlinear theories of doubly curved shells for conventional and advanced materials 3. Introduction to nonlinear dynamics 4. Vibrations of rectangular plates 5. Vibrations of empty and fluid-filled circular cylindrical 6. Reduced order models: proper orthogonal decomposition and nonlinear normal modes 7. Comparison of different shell theories for nonlinear vibrations and stability of circular cylindrical shells 8. Effect of boundary conditions on a large-amplitude vibrations of circular cylindrical shells 9. Vibrations of circular cylindrical panels with different boundary conditions 10. Nonlinear vibrations and stability of doubly-curved shallow-shells: isotropic and laminated materials 11. Meshless discretization of plates and shells of complex shapes by using the R-functions 12. Vibrations of circular plates and rotating disks 13. Nonlinear stability of circular cylindrical shells under static and dynamic axial loads 14. Nonlinear stability and vibrations of circular shells conveying flow 15. Nonlinear supersonic flutter of circular cylindrical shells with imperfections.

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Nonlinear Vibrations and Stability of Shells and Plates

This paper presents a comparative study on several approaches of structural damage diagnosis based on vibration measurements. Stochastic subspace identification method is used to identify modal parameters and to generate a Kalman prediction model, which are taken as damagesensitive features for structural damage detection. A statistical process control technique based on principal component analysis (PCA) is also presented. An improvement and enhancement of PCA is proposed. It is assumed that without damages, structural responses should remain approximately in a hyperplane defined by the principal directions of data. Damage localization is explored with these methods. As only the measured output signals are needed, the methods are convenient for on-line monitoring. The efficiency and limitation of the proposed methods are illustrated by numerical and practical applications.

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Structural Integrity Monitoring by Vibration Measurements

The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companions, Parts II and III. Because there is virtually no application of the NNMs to large-scale engineering structures, these papers are an attempt to highlight several aspects that might drive their development in the future. Specifically, we support that (i) numerical methods for the continuation of periodic solutions pave the way for an effective and practical computation of NNMs, and (ii) time-frequency analysis is particularly suitable for the analysis of the resulting dynamics. Another objective of the present paper is to describe, in simple terms, and to illustrate the fundamental properties of NNMs. This is achieved to convince the structural dynamicist not necessarily acquainted with them that they are a useful framework for the analysis of nonlinear vibrating structures. 1 NONLINEAR NORMAL MODES: A BRIEF HISTORICAL PERSPECTIVE AND CURRENT STATE-OF-THE-ART The concept of a normal mode is central in the theory of linear vibrating systems. Besides their obvious physical interpretation, the linear normal modes (LNMs) have interesting mathematical properties. They can be used to decouple the governing equations of motion; i.e., a linear system vibrates as if it were made of independent oscillators governed by the eigensolutions. Two important properties that directly result from this decoupling are: 1. Invariance: if the motion is initiated on one specific LNM, the remaining LNMs remain quiescent for all time. 2. Modal superposition: free and forced oscillations can conveniently be expressed as linear combinations of individual LNM motions. In addition, LNMs are relevant dynamical features that can be exploited for various purposes including model reduction (e.g., substructuring techniques ), experimental modal analysis , finite element model updating [3] and structural health monitoring . Clearly, though, linearity is an idealization, an exception to the rule; nonlinearity is a frequent occurrence in real-life applications . For instance, in an aircraft, besides nonlinear fluid-structure interaction, typical nonlinearities include backlash and friction in control surfaces, hardening nonlinearities in engine-to-pylon connections, saturation effects in hydraulic actuators, plus any underlying distributed nonlinearity in the structure. Furthermore, the next generations of aircraft are using materials such as glass-fiber or carbon-fiber composites to a greater extent for structural weight reduction. These materials entail new challenges for performance prediction, because they exhibit a structural behavior deviating significantly from linearity. Their increased use also creates more interfaces between different materials, which are further sources of nonlinear behavior. Any attempt to apply traditional linear analysis to nonlinear systems results, at best, in a suboptimal design. Thus, there is a need for efficient, analytically rigorous, broadly applicable analysis techniques for nonlinear structural dynamics. In this context, nonlinear normal modes (NNMs) offer a solid theoretical and mathematical tool for interpreting a wide class of nonlinear dynamical phenomena, yet they have a clear and simple conceptual relation to the LNMs, with which practicing structural engineers are familiar. Other appealing features of the NNMs are that they are capable of handling strong structural nonlinearity and that they have the potential to address the individualistic nature of nonlinear systems. The most straightforward definition of an NNM is a vibration in unison of the system (i.e., a synchronous oscillation). NNMs were pioneered in the 1960s thanks to the seminal work of Rosenberg [6−8]. They were further studied in the 1970s by Rand [9−11] and Manevitch and Mikhlin . They were regarded as a theoretical curiosity until the beginning of the 1990s when they were given a new impetus through the efforts of Vakakis et al. [13−18] and Shaw and Pierre [19−22]. Since then, a large body of literature has addressed, with notable success, the qualitative and quantitative analysis of nonlinear phenomena using NNMs (see, e.g., [23−44]). For a few typical applications and comprehensive reviews, the reader can refer to [17, 18, 45, . However, most structural engineers still view NNMs as a concept that is foreign to them, and they do not yet consider NNMs as a useful concept for structural dynamics. There are several reasons supporting this statement: 1. Nonlinear systems can exhibit extremely complex behaviors which linear systems cannot. These phenomena include jumps, bifurcations, saturation, subharmonic, superharmonic and internal resonances, resonance captures, limit cycles, modal interactions and chaos. 2. NNMs have two important limitations compared to their linear counterpart. First and foremost, the principle of superposition, which is the cornerstone of linear theory, does not apply to nonlinear systems. Second, the lack of orthogonality relations satisfied by the NNMs complicates their exploitation as bases for order reduction of the nonlinear dynamics. 3. The vast majority of the NNM literature deals with low-order lumped-mass models (systems with typically a few degrees of freedom DOFs) or focuses on specific resonances of distributed parameter systems. 4. Most existing constructive techniques for computing NNMs are based on asymptotic approaches and rely on fairly involved mathematical developments. Because NNMs have not yet been applied to large-scale engineering structures with multiple components and strong nonlinearities, this paper is an attempt to highlight several aspects that might drive their development and exploitation in the years to come: 1. There have been very few attempts to compute NNMs using numerical methods [33, 47−52]. Interestingly, algorithms for the continuation of periodic solutions are really quite sophisticated and advanced (see, e.g., [53, ), yet they have not been fully exploited for the computation of nonlinear modes. In Part II, we support that these numerical algorithms pave the way for an effective and practical computation of NNMs. 2. Time-frequency analysis is a versatile tool for analyzing nonstationary signals; i.e., signals whose spectral contents vary with time. It has been successfully exploited in structural dynamics, e.g., for linear and nonlinear system identification [55−57]. Unlike the Fourier transform, a method such as the wavelet transform models the time evolution of the dominant frequency components of a signal. Because this method can deal adequately with the frequency-energy dependence inherent to nonlinear oscillations, we believe that it is the ideal companion to the NNMs. 3. An appropriate graphical depiction of the NNMs is key to their exploitation. In this study, we show that the representation of NNMs in a frequency-energy plot is particularly convenient. It facilitates the interpretation of the dynamics and clarifies the bifurcations that connect, generate or eliminate the different NNM branches. Another objective of the present paper is to describe and to illustrate in a simple manner the fundamental properties of NNMs. This is achieved to convince the structural dynamicist not necessarily acquainted with them that they are a useful framework for the analysis of nonlinear vibrating structures. This paper is organized as follows. In the next section, the two main definitions of NNMs are provided. In addition, their fundamental properties are described, and their representation in a frequency-energy plot is introduced. In Section 3, the

Nonlinear normal modes, Part I: An attempt to demystify them

Investigations of the mechanical and tribological properties of microelectromechanical system (MEMS) components on nanoscale can provide insights into failure mechanism of material. The main goal of this paper is focused on the mechanical and tribological characterizations of MEMS mechanical components in order to improve their reliability design. The mechanical properties of interests are stiffness, modulus of elasticity, stress, strain. Dynamical investigations are performed to analyze the resonant frequency response, velocity and amplitude of oscillations of electrostatically actuated microcomponents and to estimate the quality factor. Finite element analysis is used to validate the experimental results of mechanical properties and to simulate the dynamical behaviour of investigated microcomponents. Tribological investigations are developed to estimate the stiction and friction. Testing and the individual characterization of MEMS materials and structures, performed using advanced equipments such as atomic force microscope and optical vibrometer analyzer are presented.

Nanomechanical and nanotribological characterization of microelectromechanical system

For modal analysis of large structures, it is unpractical and expensive to use artificial excitation (e.g., shakers). However, engineering structures are most often subject to ambient loads (e.g., traffic and wind) that can be exploited for modal parameter estimation. One difficulty is that the actual loading conditions cannot generally be measured, and output-only measurements are available. This paper proposes to explore the utility of blind source separation (BSS) techniques for operational modal analysis. The basic idea of BSS is to recover unobserved source signals from their observed mixtures. The feasibility and practicality of the proposed method are demonstrated using an experimental application.

Operational Modal Analysis using Second-Order Blind Identification

The electrostatic actuation devices used in MEMS are generally based on capacitive systems in which one electrode is mobile and the other one is fixed. Applying voltage between the electrodes generates an electrostatic force which tends to reduce the gap between the electrodes. Due to the non-linearity of the electrostatic force in function of the distance between electrodes, there exists a limit voltage from which there is no equilibrium between the electrostatic and mechanical forces leading to the pull-in phenomenon. In some applications, the pull-in instability is undesirable and maximizing pullin voltage is searched. The pull-in behavior involves a strong coupling between mechanical and electrostatic phenomena. Therefore the computation of the pull-in voltage for a given system requires multiphysics finite element simulations [1]. In addition, to compute efficiently the pull-in conditions, the multiphysics finite elements method is combined with a Riks-Crisfield algorithm [2]. The considered design problem consists in maximizing the pull-in voltage of a microbeam. Indeed, microbeam is the simplest example of electrostatically actuated MEMS exhibiting pull-in and consequently it is suited to serve as test to develop topology optimization of similar devices. Topology optimization is formulated as the research of the optimal distribution of a fixed volume of material. To avoid important modification of the electric field by the optimization process, this first study considers a non design electrode and uses topology optimization to design an optimal suspension structure. In this way, the structural optimization domain is separated from the electrical domain. The solution procedure of the optimization problem is based on CONLIN optimizer using a sequential convex linear programming. On each step of the optimization process, the sensitivity analysis is performed with the formulation of eigenvalue topology optimization problem on the basis of the computed pull-in conditions [3]. Two applications of this new method are finally proposed.

Jean-Claude Golinval

Papers

Structural Integrity Monitoring by Vibration Measurements

Nonlinear normal modes, Part I: An attempt to demystify them

Nanomechanical and nanotribological characterization of microelectromechanical system

Operational Modal Analysis using Second-Order Blind Identification

Improvement of pull-in voltage of electromechanical microbeams using topology optimization