A model reduction method to analyze the dynamic behavior of vibrating structures with uncertain parameters

Duc-Thinh Kieu (1) , Marie-Laure Gobert (1) , Sébastien Berger (1) , Jean-Mathieu Mencik (1)

1 LaMé - Laboratoire de Mécanique Gabriel Lamé

Assessing the dynamic response of vibrating structures which are described by means of finite element (FE) models with many degrees of freedom (DOFs) is usually computationally cumbersome. The fact that the man-ufacturing process and the material properties of structures are usually subject to variability means a dispersionof the physical parameters which can be important. The parameters are therefore considered as uncertain DOFs, which makes FE models more complex. The Monte Carlo (MC) method is commonly used to analyze the propagation of uncertainties through FE modeling. However, it requires a large number of simulations which aretherefore very cumbersome in terms of CPU times. This work aims at developing a low cost computational strategy to compute the harmonic response of vibrating structures having uncertain parameters. The strategy works by considering the Craig-Bampton method to reduce the physical DOFs of a FE model. Also, a sparse Polynomial Chaos (sPC) expansion is considered to describe the propagation of uncertainties and estimate theQuantities of Interest (QoIs), e.g., the displacement at some measurement points, or an energy quantity. In thiswork, the sPC expansion is applied through a non-intrusive method, which requires a non-negligible numberof simulations of the FE model to be performed to estimate the sPC coefficients, and further the statistics (i.e.,mean and variance) of the QoIs. The probability law of the QoIs can be obtained by considering the sPC expan-sions along with the MC method with 10000 trials. The strategy is here applied to model an academic structure composed of three rectangular Kirchhoff-Love plates made up of various materials and connected togetheracross one of their edges by means of a lineic density of springs with an uncertain stiffness. Comparisons withthe results obtained from a reference MC solution involving 10000 simulations of the FE model show goodagreement and substantial reduction of the computational effort. The influence of the Craig-Bampton reductionmethod on the estimation of the QoIs of the FE model is discussed through numerical comparisons.

Mots clés: Intrusive and non-intrusive generalized Polynomial Chaos; Uncertainty propagation; Craig-Bampton method

Domaines: Sciences de l'ingénieur [physics]; Acoustique [physics.class-ph]; Mécanique [physics.med-ph]; Vibrations [physics.class-ph]; Traitement du signal et de l'image [eess.SP]

Duc-Thinh Kieu, Marie-Laure Gobert, Sébastien Berger, Jean-Mathieu Mencik. A model reduction method to analyze the dynamic behavior of vibrating structures with uncertain parameters. Surveillance, Vishno and AVE conferences, INSA-Lyon, Université de Lyon, Jul 2019, Lyon, France. ⟨hal-02190163⟩