Distributed Parameter Estimation for NASA Mini-Mast Truss using Timoshenko Beam Model

The excessively large number of modal parameters of finite element structural models is an obstacle to parameter estimation. For truss structures, distributed parameter models are particularly well suited for parameter estimation. In the authors´ previous work, the Bernoulli-Euler beam equation was used to represent bending of the NASA Mini-Mast truss. But a deficiency at higher frequencies was apparent. Because the shear deformation of the beam is neglected, the Bernoulli-Euler beam model produces excessively high estimates of frequency for the higher modes. In this paper, a more accurate Timoshenko beam model is used to characterize the bending behavior of the truss. A maximum likelihood estimator for the Timoshenko beam model has been formulated. A closedform solution of the Timoshenko beam equation, for a uniform cantilevered beam with two concentrated masses, is derived so that the procedure for the estimation of modal characteristics is much improved. The updated model to the NASA Mini-Mast test data is demonstrated.