A model updating method for plate elements using particle swarm optimization (PSO), modeling the boundary flexibility, including uncertainties on material and dimensional properties

Abstract

It is a well-known fact that, in a real engineering situation, fixtures are not ideally stiff, so numerical simulations using them are unlikely to present results that are consistent with the experimental ones. The present paper intends to describe a model updating methodology inserting translational and rotational springs in order to better represent the real clamping. For that purpose, the PSO stochastic optimization method will be used to determine the spring stiffness in an iterative way. In addition, uncertainties regarding the material properties, such as density and Young’s Modulus, as well as workpiece dimensions, will also be taken into account in the optimization algorithm. Once the experimental natural frequencies and the geometry of the studied parts are known, the algorithm automatically updates the model, approximating the natural frequencies obtained from the numerical model to the experimentally obtained ones as closely as possible. In addition, the modal shapes of the updated simulation will be compared to the experimental data and to a rigid boundary simulation. Results will demonstrate that the proposed methodology efficiently represents the fixturing flexibility: both natural frequencies and mode shapes found were close to the real dynamic system.