Finite Element Model Updating for Nozzles Based on an Equivalent Homogenized Model

Accurate structural dynamic models are essential in aerospace engineering. Modeling a liquid rocket engine nozzle with a regenerative-cooling sandwich structure is particularly challenging. While a detailed three-dimensional (3D) finite element (FE) model provides high-fidelity structural representation, it is computationally expensive and often impractical for dynamic analysis. To address this issue, this paper proposes a two-dimensional (2D) homogenized FE model as an efficient alternative. The homogenization process is based on Classical Laminated Plate Theory (CLPT) and the deformation energy equivalence method to determine the equivalent stiffness properties. Additionally, the neutral plane is offset to account for the unequal inner and outer wall thicknesses. The accuracy of the method is verified by comparing the results with those of the 3D detailed FE model. In practical applications, a modal test is performed using a 3D Scanning Laser Doppler Vibrometer (3D-SLDV) technique to obtain natural frequencies and accurate full-field mode shapes under free-free boundary conditions. The homogenized FE model is manually adjusted to obtain a suitable initial model, followed by automatic model updating based on the test data to fine-tune uncertain equivalent parameters. After updating, the first 12 natural frequencies of the model agree with experimental results within a maximum error of 3.47%, and the Modal Assurance Criterion (MAC) values indicate full mode-shape consistency. These results confirm that the proposed 2D homogenized FE model, consisting of a single layer of shell elements, can accurately capture the essential dynamic characteristics of complex sandwich nozzles while greatly reducing computational cost, offering a practical tool for engineering applications.