Force appropriation of nonlinear structures

Renson, Ludovic; Hill, Thomas L.; Ehrhardt, David A.; Barton, David A. W.; Neild, Simon A

doi:10.1098/rspa.2017.0880

Cited by 14 publications

(21 citation statements)

References 45 publications

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“…They can also be represented by their initial modal conditions at extrema -non-zero displacements with zero velocities. These synchronous cases can be seen in a variety of nonlinear systems -see references [13][14][15][16][17][18][19].…”

Section: Nonlinear Normal Modes Of a Two-mode System With 1 : 1 Internal Resonancementioning

confidence: 99%

“…ω r1 = ω r2 = Ω, which accounts for 1 : 1 internal resonance. Following the procedure described in [16] -with the substitution of expressions (3.2) into the equations of motion (3.1), and the non-resonant terms removed, one can obtain the time-independent solutions from…”

Section: Analytical Analysis Of the Asynchronous Backbone Curvesmentioning

confidence: 99%

“…Such synchronous NNMs include single-mode, in-phase and anti-phase responses, which have been observed in a variety of nonlinear systems, e.g. the two-mass oscillators [13][14][15], beam structures [16,17], rotor systems [18], and cable structures [19].…”

Section: Introductionmentioning

confidence: 99%

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Identifying phase-varying periodic behaviour in conservative nonlinear systems

et al. 2020

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Nonlinear normal modes (NNMs) are a widely used tool for studying nonlinear mechanical systems. The most commonly observed NNMs are synchronous (i.e. single-mode, in-phase and anti-phase NNMs). Additionally, asynchronous NNMs in the form of out-of-unison motion, where the underlying linear modes have a phase difference of 90°, have also been observed. This paper extends these concepts to consider general asynchronous NNMs , where the modes exhibit a phase difference that is not necessarily equal to 90°. A single-mass, 2 d.f. model is firstly used to demonstrate that the out-of-unison NNMs evolve to general asynchronous NNMs with the breaking of the geometrically orthogonal structure of the system. Analytical analysis further reveals that, along with the breaking of the orthogonality, the out-of-unison NNM branches evolve into branches which exhibit amplitude-dependent phase relationships. These NNM branches are introduced here and termed phase-varying backbone curves . To explore this further, a model of a cable, with a support near one end, is used to demonstrate the existence of phase-varying backbone curves (and corresponding general asynchronous NNMs) in a common engineering structure.

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Section: Nonlinear Normal Modes Of a Two-mode System With 1 : 1 Internal Resonancementioning

confidence: 99%

Section: Analytical Analysis Of the Asynchronous Backbone Curvesmentioning

confidence: 99%

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Identifying phase-varying periodic behaviour in conservative nonlinear systems

et al. 2020

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“…These studies show that, for most cases, even a single excitation is sufficient to accurately locate the NNM branches. However, numerical and experimental studies also show limitations and significant errors, arising from the insufficient compensation between the single-location forcing and distributed damping of the structure [28]. Alternative approaches, e.g.…”

Section: Introductionmentioning

confidence: 99%

“…The energy balancing method has also been used to predict the presence of isolas [19,9,5] -i.e. regions of forced responses that are separated from the primary branches of the response; to quantify the relative importance of NNMs by predicting the forcing amplitude required to reach them at resonance [20]; and to identify an appropriate number of excitations and their locations in conducting force appropriation tests [28]. This energy balancing method was originally derived based on systems with conservative nonlinearity and, recently it was extended to account for non-conservative nonlinearity with applications in full-scale structures [35].…”

Section: Introductionmentioning

confidence: 99%

Efficient Energy Balancing Across Multiple Harmonics of Nonlinear Normal Modes

Hong¹,

Hill²,

Neild³

2021

Preprint

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Predicting the forced responses of nonlinear systems is a topic that attracts extensive studies. The energy balancing method considers the net energy transfer in and out of the system over one period, and establishes connections between forced responses and nonlinear normal modes (NNMs). In this paper, we consider the energy balancing across multiple harmonics of NNMs for predicting forced resonances. This technique is constructed by combining the energy balancing mechanism with restrictions (established via excitation scenarios) on external forcing and harmonic phase-shifts; a semi-analytical framework is derived to achieve both accurate/robust results and efficient computations. With known inputs from NNM solutions, the required forcing amplitudes to reach NNMs at resonances, along with their discrepancy, i.e. the harmonic phase-shifts, are computed via a one-step scheme. Several examples are presented for different excitation scenarios to demonstrate the applicability of this method, and to show its capability in accurately predicting the existence of an isola where multiple harmonics play a significant part in the response.

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Topological Optimisation of Friction Dampers for Nonlinear Resonances Mitigation

Denimal

Renson

Salles

2021

NODYCON Conference Proceedings Series

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Friction dampers are commonly used to reduce the vibration amplitude of aircraft turbine blades. However, the shape of such friction dampers can affect significantly damping characteristics and the overall nonlinear dynamic behaviour of the structure. The present work exploits topological optimization to identify damper geometries that minimize response amplitude. The (near-)maximum responses are efficiently computed by solving the harmonic balance equations and a phase quadrature condition. Moving Morphable Components (MMC) are used to describe the damper geometry and an Efficient Global Optimization (EGO) algorithm is used for the optimization.

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Force appropriation of nonlinear structures

Cited by 14 publications

References 45 publications

Identifying phase-varying periodic behaviour in conservative nonlinear systems

Identifying phase-varying periodic behaviour in conservative nonlinear systems

Efficient Energy Balancing Across Multiple Harmonics of Nonlinear Normal Modes

Topological Optimisation of Friction Dampers for Nonlinear Resonances Mitigation

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