Experimental non-linear system : application of the Proper Orthogonal Decomposition method

This study deals with an application of the proper orthogonal decomposition (POD) method to a simplified structural dynamic system with local known non-linearities. The POD method is applied to experimental and simulated time-series data, in order to extract modes that efficiently represent the system. The ability of these modes to detect and identify structural non-linear behaviours is then investigated. The results obtained are compared to results issued from the standard linear process used in aircraft Ground Vibration Testing (GVT), with the aim of developing new or complementary GVT methods able to characterize non-linear structural behaviour, in particular within a high-density modal technical context. Nomenclature B, α non-linear coefficient and non-linear exponent of the non-linear internal force o C covariance matrix error truncature error during the data reconstruction process j f , j f0 modal frequency and reference modal frequency of mode number j (Hz) F objective function Fi excitation force levels with i = 1, 2, ... nl excit F F , excitation force, non-linear internal force Φ matrix containing the modal vectors of a system l number of POMs used in the data reconstruction process Lin Fi, NL Fi referenced names for the different measurement series m number of spatial data n number of snapshots (time-domain data) C K M , , mass, stiffness and damping matrices β γ μ , , modal mass, modal stiffness and modal damping matrices t time (s) Σ V U , , matrices of the singular value decomposition (SVD) Σ V U ∆ ∆ ∆ , , matrices containing the differences between experimental and simulated Σ V U , , matrices z , z , z & & & displacement (m), velocity (m/s), acceleration (m/s) z z y , , time-varying part of the system responses, time-domain responses and their mean values Y observation matrix k ψ , k λ k eigenvector and corresponding eigenvalue solution of the eigenvalue problem