Nonlinear Model Updating of Aerospace Structures via Taylor-Series Reduced-Order Models

2026-04-04

AI Summary

This study addresses the persistent challenge in finite element model updating of nonlinear structures—accurately capturing amplitude-dependent dynamic characteristics. The authors propose a novel nonlinear model updating framework that integrates a nonlinear internal force model based on second- and third-order Taylor expansions, a bi-orthogonal projection basis constructed from complex eigenvectors, and a Cayley transform generalized to the complex unitary group for adaptive optimization of the basis functions. This approach uniquely combines high-order Taylor operators with complex modal bi-orthogonal bases and leverages the Cayley transform on the unitary group to refine the projection basis, thereby transcending the limitations of conventional linear frameworks. Experimental validation on a wing-box panel demonstrates marked superiority over linear updating methods, accurately reproducing amplitude-dependent natural frequencies and Modal Assurance Criterion (MAC) values while achieving more precise identification of stiffness-related nonlinear parameters.

Abstract

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.

Problem

• nonlinear model updating
• aerospace structures
• model order reduction
• polynomial stiffness nonlinearity
• finite element model

Innovation

• nonlinear model updating
• Taylor-series reduced-order model
• projection-basis adaptation
• Cayley transform
• polynomial stiffness nonlinearity