An FRF-based perturbation approach for stochastic updating of mass, stiffness and damping matrices

Abstract

Most of the current approaches and studies in stochastic FE model updating are based on experimental modal data considering updating of uncertain parameters related to stiffness and mass matrices. In many instances, it is desired that the stochastic FE model is able to predict the variability of dynamic response. This calls for identifying the variability of damping matrix also along with variabilities of mass and stiffness matrices. In the present paper, a new stochastic approach to FE model updating is developed based on variability of measured Frequency Response Functions (FRFs) using a perturbation-based framework. The objective of the method is to identify mean and coefficient of variation of uncertain parameters related to mass, stiffness and damping matrices. Three numerical studies related to, a discrete three degree of freedom spring-mass-damper system, a damped cantilever beam and an airplane model (DLR-AIRMOD structure) are presented to validate the method. The experimental FRFs are simulated using Perturbation and Monte-Carlo approaches. The effect of number of samples of test-structures, effect of modelling error and the effect of noise and incompleteness of the simulated data on the performance of the method are studied. Experimental validation of the method is carried out using different samples of geometrically similar free-free beams to identify mean and variability of coefficient of elasticity and damping.