An Explanation for Why Natural Frequencies Shifting in Structures with Membrane Stresses, Using Backbone Curve Models

Liu, Xiang; Wagg, DJ; Neild, Simon A

doi:10.1007/978-3-319-54404-5_2

Cited by 3 publications

(4 citation statements)

References 14 publications

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“…For example, numerous methods focus on the extraction of backbone curves for nonlinear systems. The backbone curves can be used to characterise and quantify nonlinearities in the system and to inform reduced order models (Liu et al 2019). A detailed review of the theoretical basis and validity of NNMs for reduced order modelling is given in (Haller and Ponsioen 2016).…”

Section: Usage In Romsmentioning

confidence: 99%

Machine Learning Approach to Model Order Reduction of Nonlinear Systems via Autoencoder and LSTM Networks

Simpson,

Dervilis,

Chatzi

2021

Preprint

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In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer hardware. In certain use cases, however, such as uncertainty quantification or high precision real-time simulation, the computational cost remains a challenge. This necessitates adoption of reduced order modelling methods, which can reduce the computational toll of such nonlinear analyses. In this work, we propose a reduction scheme relying on the exploitation of an Autoencoder, as means to infer a latent space from output-only response data. This latent space, which in essence approximates the systems Nonlinear Normal Modes (NNMs), serves as an invertible reduction basis for the nonlinear system. The proposed machine learning framework is then complemented via use of Long-Short term Memory (LSTM) networks in the reduced space. These are used for creating a nonlinear Reduced Order Model (ROM) of the system, able to recreate the full system's dynamic response under a known driving input.

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Section: Usage In Romsmentioning

confidence: 99%

Machine Learning Approach to Model Order Reduction of Nonlinear Systems via Autoencoder and LSTM Networks

Simpson,

Dervilis,

Chatzi

2021

Preprint

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“…This example has already been studied in detail in [46], and here it is used to consider the application of the reduced-order-direct normal form technique for a system with internal resonance. Following the approach in [46], the nonlinear partial differential equations governing the dynamic behaviour of the plate of large-amplitude responses can be projected onto an orthogonal set of linear eigenmodes, from which a set of ordinary differential equations can be obtained of the formq…”

Section: Example 2: a Continuous Plate Systemmentioning

confidence: 99%

“…(5.1). In this paper, we consider the same plate investigated in [46]. The geometrical and material properties of the plate and the values of the natural frequencies and nonlinear terms coefficients are given in appendix A.…”

Section: Example 2: a Continuous Plate Systemmentioning

confidence: 99%

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Simultaneous normal form transformation and model-order reduction for systems of coupled nonlinear oscillators

Liu

Wagg

2019

Proc. R. Soc. A.

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In this paper, we describe a direct normal form decomposition for systems of coupled nonlinear oscillators. We demonstrate how the order of the system can be reduced during this type of normal form transformation process. Two specific examples are considered to demonstrate particular challenges that can occur in this type of analysis. The first is a 2 d.f. system with both quadratic and cubic nonlinearities, where there is no internal resonance, but the nonlinear terms are not necessarily ε 1 -order small. To obtain an accurate solution, the direct normal form expansion is extended to ε 2 -order to capture the nonlinear dynamic behaviour, while simultaneously reducing the order of the system from 2 to 1 d.f. The second example is a thin plate with nonlinearities that are ε 1 -order small, but with an internal resonance in the set of ordinary differential equations used to model the low-frequency vibration response of the system. In this case, we show how a direct normal form transformation can be applied to further reduce the order of the system while simultaneously obtaining the normal form, which is used as a model for the internal resonance. The results are verified by comparison with numerically computed results using a continuation software.

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Understanding the dynamics of multi-degree-of-freedom nonlinear systems using backbone curves

Wagg

2017

Procedia Engineering

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An Explanation for Why Natural Frequencies Shifting in Structures with Membrane Stresses, Using Backbone Curve Models

Cited by 3 publications

References 14 publications

Machine Learning Approach to Model Order Reduction of Nonlinear Systems via Autoencoder and LSTM Networks

Machine Learning Approach to Model Order Reduction of Nonlinear Systems via Autoencoder and LSTM Networks

Simultaneous normal form transformation and model-order reduction for systems of coupled nonlinear oscillators

Understanding the dynamics of multi-degree-of-freedom nonlinear systems using backbone curves

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