A multi-harmonic approach to updating locally nonlinear structures

Improving the fidelity of numerical simulations using available test data is an important activity in the overall process of model verification and validation. While model updating or calibration of linear elastodynamic behaviors has been extensively studied for both academic and industrial applications over the past three decades, methodologies capable of treating nonlinear dynamics remain relatively immature. The authors propose a novel strategy for updating an important subclass of nonlinear models characterized by globally linear stiffness and damping terms in the presence of local nonlinear effects. The approach combines two well-known methods for structural dynamic analysis. The first is the Multi-harmonic Balance (MHB) method for solving the nonlinear equations of motion of a mechanical system under periodic excitation. This approach has the advantage of being much faster than time domain integration procedures while allowing a wide range of nonlinear effects to be taken into account. The second method is the Extended Constitutive Relation Error (ECRE) that has been used in the past for error localization and updating of linear elastodynamic models. The proposed updating strategy will be illustrated using academic examples.