Identification of backbone curves of nonlinear systems from resonance decay responses

Londoño, Julián M.; Neild, Simon A; Cooper, Jonathan E.

doi:10.1016/j.jsv.2015.03.015

Cited by 128 publications

(91 citation statements)

References 17 publications

(32 reference statements)

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“…Often called the Lyapunov subcenter manifold (LSM), W is known to be filled with periodic orbits of (1)-(2). In the nonlinear vibrations literature, the amplitude-frequency plot of these periodic orbits is called the (conservative) backbone curve of system (1)-(2) (see, e.g., Londono et al [13]). Reducing the full dynamics to the invariant manifold W gives an exact two-dimensional model for the nonlinear dynamics associated with the x-mode.…”

Section: Setupmentioning

confidence: 99%

Explicit third-order model reduction formulas for general nonlinear mechanical systems

Veraszto

Ponsioen

Haller

2020

Journal of Sound and Vibration

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For general nonlinear mechanical systems, we derive closed-form, reduced-order models up to cubic order based on rigorous invariant manifold results. For conservative systems, the reduction is based on Lyapunov Subcenter Manifold (LSM) theory, whereas for damped-forced systems, we use Spectral Submanifold (SSM) theory. To evaluate our explicit formulas for the reduced model, no coordinate changes are required beyond an initial linear one. The reduced-order models we derive are simple and depend only on physical and modal parameters, allowing us to extract fundamental characteristics, such as backbone curves and forcedresponse curves, of multi-degree-of-freedom mechanical systems. To numerically verify the accuracy of the reduced models, we test the reduction formulas on several mechanical systems, including a higher-dimensional nonlinear Timoshenko beam.

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Section: Setupmentioning

confidence: 99%

Explicit third-order model reduction formulas for general nonlinear mechanical systems

Veraszto

Ponsioen

Haller

2020

Journal of Sound and Vibration

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“…In these works, electrodynamic shakers were rigidly connected to the test structures to provide the burst excitation required by the method. More recently, Londono et al [7] applied a modified version of the method to a single-degree-of-freedom system represented by a base-excited mass mounted on bearings sliding with low friction along steel shafts. The mass was also connected to two preloaded transversal springs which produced nonlinear stiffness.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Modal Testing Performed by Pulsed-Air Jet Excitation System

Piraccini

Maio

Sante

2016

Nonlinear Dynamics, Volume 1

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. ABSTRACTThis paper presents a novel approach for testing structural component to nonlinear vibrations. Nowadays, nonlinear testing is mainly carried out by using electromagnetic shakers. These are efficient and powerful excitation systems which transmit the force by a rigid stinger and can be driven by different excitation signals. The rigid connection contributes to create mechanical impedance mismatch between the shaker and the test structure thus reducing the efficiency of the driving force. An alternative solution to shakers is represented by use of a pulsed air jet excitation method, which drives the force by a pulsed air-jets and therefore contactless. This condition eliminates the mechanical impedance mismatch with the test structure and the excitation can be more efficient than the one created by shakers. The pulsed air-jet excitation system is used to study nonlinear vibrations of composites components. These were designed to be mock-ups of fan blades the layup of which was varied for the three types of components used in this work. Tests were carried out by performing forced response and free decay measurements. The free decay type of test revealed interesting results and the novelty of using such an exciter for nonlinear testing. The major novelty consists of interrupting the air flow from a steady state condition and let happen the free decay, all these without experiencing undesired dynamics as experienced by contact excitation.

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“…The whole structure is suspended on soft springs such that rigid-body-like modes are restrained below 5 Hz. The reader is referred to Londoño et al [4] for further details about the experimental setup. The peaks corresponding to the first two modes shift towards higher frequencies and the whole FRF is altered by nonlinear stochastic distortions.…”

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confidence: 99%

Nonlinear Phase Separation Testing of an Experimental Wing-Engine Structure

Renson

Noël

Barton

et al. 2017

Rotating Machinery, Hybrid Test Methods, Vibro-Acoustics &Amp; Laser Vibrometry, Volume 8

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Modal testing of nonlinear engineering structures is currently a research area that attracts substantial attention. Recently, a nonlinear generalisation of phase separation testing has been proposed for identifying nonlinear normal modes (NNMs) based on input and output measurements. The nonlinear phase separation (NPS) method integrates identification and continuation tools to calculate multiple NNMs from broadband data. The present contribution reports the first experimental application of the NPS method. The structure of interest is a model inspired by a wing with two engines connected by means of nonlinear pylons with softening-hardening stiffness characteristics. The frequency-energy dependences of four NNMs in the 0-100 Hz range are estimated, including modal interactions. NNMs identified using the NPS method are also compared to free-decay testing results.Keywords: nonlinear normal modes, experimental identification, broadband excitation, experimental model, discretetime continuation.Experimental linear modal analysis (EMA) is routinely practiced in industry and plays an important role in the development and certification of aerospace structures. For instance, the resonance frequencies, vibration modes and damping ratios identified from experimental tests are used to update and validate mathematical models that can be used for flutter predictions. However, the increasing presence of nonlinearity arising, for example, from large displacements, joints or complex material properties, poses a number of issues leading to erroneous identification results [1] .Nonlinear normal modes (NNMs) offer a theoretical framework to extend the concept of modal analysis to nonlinear systems. NNMs can explain important nonlinear phenomena such as mode bifurcations and interactions between modes with wellseparated, non-commensurate natural frequencies. The most popular definition defines NNMs as periodic solutions of the unforced, undamped equations of motion of the system in question. The experimental identification of such periodic motions can be performed by applying an excitation, multi-harmonic and distributed across the structure as appropriate, in phase quadrature with the response of the structure. At quadrature, the applied excitation counterbalances exactly the damping forces present in the system and the dynamics of the unforced, undamped system is recovered [2] . Such an approach follows the philosophy of linear phase resonance (force appropriation) techniques to extract each NNM individually.A nonlinear phase separation (NPS) technique where multiple NNMs are extracted from broadband data collected during a single experiment was proposed and demonstrated on a nonlinear beam using simulated data [3] . The present paper improves this NPS methodology and reports its first experimental demonstration.The structure of interest for this study is shown in Figure 1(a). It consists of a continuous 1m-long, 5mm-thick aluminum plate (the wing) to which two masses of 1.38 kg (the engines) are suspended. The suspension...

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Identification of backbone curves of nonlinear systems from resonance decay responses

Cited by 128 publications

References 17 publications

Explicit third-order model reduction formulas for general nonlinear mechanical systems

Explicit third-order model reduction formulas for general nonlinear mechanical systems

Nonlinear Modal Testing Performed by Pulsed-Air Jet Excitation System

Nonlinear Phase Separation Testing of an Experimental Wing-Engine Structure

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