Addressing Harmonic Excitation in Complex Aeronautical Test Cases Using Stochastic Modal Appropriation

The present study extends previous developments by the authors on the Stochastic Modal Appropriation (SMA) technique, enhancing its robustness against harmonic excitations. The proposed approach, denoted as SVD-SMA, integrates Singular Value Decomposition within the SMA framework to improve the estimation accuracy of modal parameters, particularly in systems exhibiting closely spaced modes. A statistical post-processing stage employing Support Vector Machines (SVM) is used to map the performance boundaries of SVD-SMA. Experimental results indicate that the method can reliably identify modal parameters and reject harmonic contamination when the excitation frequency is separated by at least 1.6 Hz from the system natural frequencies. This critical threshold exhibits a measurable dependence on forcing amplitude. Several test cases are considered. Initially, a cantilever beam with well-separated natural frequencies is analyzed to establish a performance baseline relative to the standard SMA formulation. Subsequently, experiments on a free plate with closely spaced modes, excited by a controlled harmonic input at the Structural Dynamics Laboratory (DIMA), "La Sapienza" University of Rome, are conducted. Results demonstrate that SVD-SMA retains the inherent robustness of SMA to harmonic disturbances while significantly improving modal parameter estimation in systems with closely spaced poles. The investigation ends with the PAZY wing benchmark, a high-aspect ratio wind tunnel model exhibiting geometric nonlinearity and mode coupling at increasing flow speeds. Wind tunnel tests at "La Sapienza" University assess the method performance under controlled conditions, first focusing on the ability to deal with closely spaced system and subsequently assessing robustness to harmonic contamination. The excitation frequency and amplitude are systematically varied to delineate the method operational limits. The validated SVD-SMA framework provides a robust solution for operational modal analysis of aerospace structures subjected to combined stochastic aerodynamic loading and harmonic mechanical excitation, conditions representative of both wind tunnel and in-flight environments. By maintaining identification accuracy in the presence of harmonic disturbances and closely spaced modes, the proposed method addresses a key limitation of conventional Operational Modal Analysis identification techniques.