Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment

in Physica D: Nonlinear Phenomena (2005), 204(1-2), 41-69

We study the dynamics of a two-degree-of-freedom (DOF) nonlinear system consisting of a grounded linear oscillator coupled to a light mass by means of an essentially nonlinear (nonlinearizable) stiffness ... [more ▼]

We study the dynamics of a two-degree-of-freedom (DOF) nonlinear system consisting of a grounded linear oscillator coupled to a light mass by means of an essentially nonlinear (nonlinearizable) stiffness. We consider first the undamped system and perform a numerical study based on non-smooth transformations to determine its periodic solutions in a frequency-energy plot. It is found that there is a sequence of periodic solutions bifurcating or emanating from the main backbone curve of the plot. We then study analytically the periodic orbits of the undamped system using a complexification/averaging technique in order to determine the frequency contents of the various branches of solutions, and to understand the types of oscillation performed by the system at the different regimes of the motion. The transient responses of the weakly damped system are then examined, and numerical wavelet transforms are used to study the time evolutions of their harmonic components. We show that the structure of periodic orbits of the undamped system greatly influences the damped dynamics, as it causes complicated transitions between modes in the damped transient motion. In addition, there is the possibility of strong passive energy transfer (energy pumping) from the linear oscillator to the nonlinear attachment if certain periodic orbits of the undamped dynamics are excited by the initial conditions. (c) 2005 Elsevier B.V. All rights reserved. [less ▲]

Transient dynamics of a dispersive elastic wave guide weakly coupled to an essentially nonlinear end attachment

in Wave Motion (2005), 41(2), 109-132

We consider the dynamics of a dispersive semi-infinite linear rod weakly connected to an essentially nonlinear end attachment. Using a Green's function formulation we reduce the dynamics to an integro ... [more ▼]

We consider the dynamics of a dispersive semi-infinite linear rod weakly connected to an essentially nonlinear end attachment. Using a Green's function formulation we reduce the dynamics to an integro-differential equation, which we express in the form of an infinite set of ordinary differential equations using Neumann expansions. We examine resonant interactions of the attachment with incident traveling waves propagating in the pass band of the rod, as well as resonance capture phenomena where the attachment engages in transient 1:1 internal resonance with the in-phase mode of the rod, at the bounding frequency of its pass and stop bands. The studied resonant interactions of the nonlinear attachment with traveling waves are similar to resonance capture cascades occurring in finite-chain nonlinear attachment configurations; these are the transient dynamics of the attachment as it engages in a series of instantaneous resonances with a continuous spectrum of frequencies in the pass band of the medium. As the energy of the attachment decreases due to damping and energy radiation back to the rod, the attachment engages in 1:1 resonance capture with the in-phase mode of the rod; this resonance capture occurs due to the dispersion property in the linear medium. It is shown that the transient dynamics of resonance capture can be reduced to a set of two 'slow flow' amplitude and phase modulation equations. The analytical results are in agreement with direct numerical simulations. (C) 2004 Elsevier B.V. All rights reserved. [less ▲]

Generation of accurate finite element models of nonlinear systems - Application to an aeroplane-like structure

in Nonlinear Dynamics (2005), 39(1-2), 129-142

Model updating and validation is currently a central issue in the fields of computational structural mechanics and dynamics. The vast majority of applications however concerns linear structures. On the ... [more ▼]

Model updating and validation is currently a central issue in the fields of computational structural mechanics and dynamics. The vast majority of applications however concerns linear structures. On the other hand, updating nonlinear models is something the structural dynamicist prefers to avoid mainly because tools such as modal analysis are no longer available. The objective of the present study is to propose a two-step methodology for dealing with nonlinear systems. Its most appealing feature is that it decouples the estimation of the linear and nonlinear parameters. A numerical application consisting of an aeroplane-like structure is used to assess the efficiency of the procedure. [less ▲]

A model updating strategy of non-linear vibrating structures

in International Journal for Numerical Methods in Engineering (2004), 60(13), 2147-2164

The objective of this paper is to present a model updating strategy of non-linear vibrating structures. Because modal analysis is no longer helpful in non-linear structural dynamics, a special attention ... [more ▼]

The objective of this paper is to present a model updating strategy of non-linear vibrating structures. Because modal analysis is no longer helpful in non-linear structural dynamics, a special attention is devoted to the features extracted from the proper orthogonal decomposition and one of its non-linear generalizations based on auto-associative neural networks. The efficiency of the proposed procedure is illustrated using simulated data from a three-dimensional portal frame. Copyright (C) 2004 John Wiley Sons, Ltd. [less ▲]

Feature extraction using auto-associative neural networks

in Smart Materials & Structures (2004), 13(1), 211-219

Modal analysis is now mature and well accepted in the design of mechanical structures. It determines the vibration mode shapes and the corresponding natural frequencies. However, the validity of modal ... [more ▼]

Modal analysis is now mature and well accepted in the design of mechanical structures. It determines the vibration mode shapes and the corresponding natural frequencies. However, the validity of modal analysis is limited to structures showing a linear behaviour. In non-linear structural dynamics, it is well known that mode shapes are no longer useful for the characterization of the dynamic response. The purpose of the present paper is to define new features which efficiently capture the dynamics of a non-linear structure. The proposed methodology takes advantage of auto-associative neural networks to compute one-dimensional curves which allow for non-linear dependences between the coordinates. Synthetic data sampled from a non-linear normal mode motion are used to illustrate the method and to develop intuition about its implementation. [less ▲]

Passive energy transfer and dissipation for isolation from transcient broadband disturbances

in US-Korea Joint Seminar/Workshop on Smart Structures Technologies, Seoul, 2004 (2004)

We discuss passive nonlinear energy pumping from a linear (main) mechanical structure to a weakly coupled, local, passive nonlinear energy sink (NES). We show that the NES can be designed to effectively ... [more ▼]

We discuss passive nonlinear energy pumping from a linear (main) mechanical structure to a weakly coupled, local, passive nonlinear energy sink (NES). We show that the NES can be designed to effectively absorb vibrational energy from the main structure in a one-way, irreversible fashion. We demonstrate the occurrence of pumping cascades, where an appropriately designed NES passively extracts energy sequentially from a number of modes of the main (linear) structure, interacting individually with each mode before moving to the next. Experimental results confirm our theoretical findings. The applications of the nonlinear energy pumping phenomenon to the problem of vibration and shock isolation will be discussed [less ▲]

Sensor Validation for On-line Vibration Monitoring

in 2nd European Workshop on Structural Health Monitoring, Munich, 2004 (2004)

For a reliable on-line vibration monitoring of structures, it is necessary to have accurate sensor information. However, sensors may sometimes be faulty or may even become unavailable due to failure or ... [more ▼]

For a reliable on-line vibration monitoring of structures, it is necessary to have accurate sensor information. However, sensors may sometimes be faulty or may even become unavailable due to failure or maintenance activities. The problem of sensor validation is therefore a critical part or structural identification. The objective of the present study is to present a procedure based on principal component analysis, which is able to perform detection, isolation and reconstruction of a faulty sensor. Its e ciency is assessed using an experimental application. [less ▲]

Structural damage diagnosis under changing environmental conditions

in 7th International Conference on Motion and Vibration Control, Saint Louis, 2004 (2004)

A method is proposed to perform structural health monitoring under varying environmental and operational conditions. The method is based on principal component analysis (PCA) applied to a data set ... [more ▼]

A method is proposed to perform structural health monitoring under varying environmental and operational conditions. The method is based on principal component analysis (PCA) applied to a data set containing vibration characteristics identified during the monitoring of the structure. The advantage of the method is that it does not require the measurement of environmental parameters that are taken into account as embedded variables. As the influence of environmental effects may be effectively eliminated, the residual error of the PCA prediction model remains small if the structure is healthy, and increases significantly when structural damage occurs. Novelty analysis on the residual errors provides a statistical indication of damage. The PCA-based damage detection method is illustrated using experimental data. It will also be shown that when the relationship between the vibration characteristics becomes nonlinear, PCA is advantageously replaced by one of its nonlinear generalizations. [less ▲]

On the development of a model updating strategy of nonlinear vibrating structures

in ASME International Design Engineering Technical Conferences, Chicago, 2003 (2003, September)

The objective of this paper is to present a model updating strategy of non-linear vibrating structures. Because modal analysis is no longer helpful in non-linear structural dynamics, a special attention ... [more ▼]

The objective of this paper is to present a model updating strategy of non-linear vibrating structures. Because modal analysis is no longer helpful in non-linear structural dynamics, a special attention is devoted to the features extracted from the proper orthogonal decomposition and one of its non-linear generalisations based on auto-associative neural networks. The efficiency of the proposed procedure is illustrated using simulated data from a three-dimensional portal frame. [less ▲]

Identification of a continuous structure with a geometrical non-linearity. Part I: Conditioned reverse path method

in Journal of Sound & Vibration (2003), 262(4), 889-906

Particular effort has been spent in the field of identification of multi-degree-of-freedom non-linear systems. The newly developed methods permit the structural analyst to consider increasingly complex ... [more ▼]

Particular effort has been spent in the field of identification of multi-degree-of-freedom non-linear systems. The newly developed methods permit the structural analyst to consider increasingly complex systems. The aim of this paper and a companion paper is to study, by means of two methods, a continuous non-linear system consisting of an experimental cantilever beam with a geometrical non-linearity. In this paper (Part I), the ability of the conditioned reverse path method, which is a frequency domain technique, to identify the behaviour of this structure is assessed. The companion paper (Part II) is devoted to the application of proper orthogonal decomposition, which is an updating technique, to the test example. (C) 2002 Elsevier Science Ltd. All rights reserved. [less ▲]