Structural vibration and sensitivity reanalyses via polynomial-type extrapolation

This study proposes a new approach based on polynomial-type extrapolation concepts— namely, minimal polynomial extrapolation and reduced rank extrapolation—for the structural vibration and sensitivity reanalyses. The proposed approach utilises raw modal vector sequences obtained from the Neumann series expansion and constructs polynomial-type extrapolation-based formulations to predict approximate mode shapes, eigenvalues, and their sensitivities for modified structures. This approach involves solving a set of overdetermined linear systems with significantly reduced dimensions. The performance of the proposed approach is evaluated through two vibration reanalysis examples involving high-rank design changes: a tower undergoing size modifications and a cantilever beam subjected to material density variations. Numerical results confirm that the polynomial-type extrapolation approach achieves accurate reanalysis and sensitivity predictions with negligible additional computational effort compared to the Neumann series.