Damping function estimation based on modal receptance models and neural nets

 A method for the estimation of an isotropic material damping based on the isotropic, augmented Hooke's law (AHL) and the concept of isotropic, modal and material damping functions is proposed. The method is a straightforward application of standard neural net (NN) back propagation techniques combined with back propagation of simulation errors using “response-to-damping parameter” mapping based on an analytical, modal receptance model incorporating AHL damping. Damping parameters are estimated by fitting the receptance model iteratively, using NN technique, to measured receptance data. Owing to the response model used, the proposed estimation technique provides new possibilities to completely separate pure damping properties from geometry, elastic (static) data and undamped modal data. The method is applicable to homogeneous materials and cases where cross coupling, due to damping, between the modes can be neglected. Even though in this sense restricted, the technique may be applied to a wide class of cases, including cases with very high damping and highly overlapping damped modes. Necessary background theory, including a suitable NN structure, for application of the method is presented. The estimation procedure is demonstrated for a plexiglas (PMMA) plate (modal loss factors ≈ 0.1 at room temperature) used as experimental test case. Very good agreement between measured receptances and responses predicted using the estimated damping function parameters is obtained. Validation was done using both modal and direct finite element (FE) computations.