Nonlinear Model Updating of Aerospace Structures via Taylor-Series Reduced-Order Models
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| Format: | Preprint |
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2026
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| _version_ | 1866908947270598656 |
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| author | Tantaroudas, Nikolaos D. Hollins, Jake Agathos, Konstantinos Papatheou, Evangelos |
| author_facet | Tantaroudas, Nikolaos D. Hollins, Jake Agathos, Konstantinos Papatheou, Evangelos |
| contents | Finite element model updating is a mature discipline for linear structures, yet its extension to nonlinear regimes remains an open challenge. This paper presents a methodology that combines nonlinear model order reduction (NMOR) based on Taylor-series expansion of the equations of motion with the projection-basis adaptation scheme recently proposed by Hollins et al. [2026] for linear model updating. The structural equations of motion, augmented with proportional (Rayleigh) damping and polynomial stiffness nonlinearity, are recast as a first-order autonomous system whose Jacobian possesses complex eigenvectors forming a biorthogonal basis. Taylor operators of second and third order are derived for the nonlinear internal forces and projected onto the reduced eigenvector basis, yielding a low-dimensional nonlinear reduced-order model (ROM). The Cayley transform, generalised from the real orthogonal to the complex unitary group, parametrises the adaptation of the projection basis so that the ROM mode shapes optimally correlate with experimental measurements. The resulting nonlinear model-updating framework is applied to a representative wingbox panel model. Numerical studies demonstrate that the proposed approach captures amplitude-dependent natural frequencies and modal assurance criterion(MAC) values that a purely linear updating scheme cannot reproduce, while recovering the underlying stiffness parameters with improved accuracy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_03788 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonlinear Model Updating of Aerospace Structures via Taylor-Series Reduced-Order Models Tantaroudas, Nikolaos D. Hollins, Jake Agathos, Konstantinos Papatheou, Evangelos Computational Engineering, Finance, and Science Numerical Analysis Systems and Control Mathematical Physics Finite element model updating is a mature discipline for linear structures, yet its extension to nonlinear regimes remains an open challenge. This paper presents a methodology that combines nonlinear model order reduction (NMOR) based on Taylor-series expansion of the equations of motion with the projection-basis adaptation scheme recently proposed by Hollins et al. [2026] for linear model updating. The structural equations of motion, augmented with proportional (Rayleigh) damping and polynomial stiffness nonlinearity, are recast as a first-order autonomous system whose Jacobian possesses complex eigenvectors forming a biorthogonal basis. Taylor operators of second and third order are derived for the nonlinear internal forces and projected onto the reduced eigenvector basis, yielding a low-dimensional nonlinear reduced-order model (ROM). The Cayley transform, generalised from the real orthogonal to the complex unitary group, parametrises the adaptation of the projection basis so that the ROM mode shapes optimally correlate with experimental measurements. The resulting nonlinear model-updating framework is applied to a representative wingbox panel model. Numerical studies demonstrate that the proposed approach captures amplitude-dependent natural frequencies and modal assurance criterion(MAC) values that a purely linear updating scheme cannot reproduce, while recovering the underlying stiffness parameters with improved accuracy. |
| title | Nonlinear Model Updating of Aerospace Structures via Taylor-Series Reduced-Order Models |
| topic | Computational Engineering, Finance, and Science Numerical Analysis Systems and Control Mathematical Physics |
| url | https://arxiv.org/abs/2604.03788 |