IDENTIFICATION OF DYNAMIC PROPERTIES OF PLATE-LIKE STRUCTURES BY USING A CONTINUUM MODEL

The common approach currently used in the aircraft structural analysis is the finite element method. NASA's research in computational structures technology (CST) is helping to develop the finite element analysis to a new stage, although the significant limitations still exist. The elements used in the finite dement method are usually void of dynamics. The consequence is that hundreds and thousands of elements are needed to represent large flexible aircraft structures in order to acquire analytical accuracy. To avoid the large dimensionality the current practice is to reduce the order of the model for structural system identification and control synthesis. This approximation, however, can lead to system instability due to the dynamics which are ignored. In contrast, distributed parameter modeling seems to offer a viable alternative to the finite dement approach for modeling large flexible aerospace structures. Distributed parameter models have the advantage of improved accuracy, reduced number of modal parameters, and the avoidance of modal order reduction. Most of the effort on the continuum modeling so far is contributed to the beam-like structures which are composed of beams, tethers and rigid bodies. For the aircraft structural analysis, however, another important type of structural elements is plate. The principle of the monocoque or semi-monocoque type of aircraft construction is fundamentally the use of a thin-walled tube to carry compression, tension, shear, and bending. It is necessary, therefore, to expand the continuum modeling methodology to the plate-like structures to satisfy the requirement in the aircraft structural analysis, especially for the monocoque structures. This paper has developed a continuum modeling algorithm for the identification of dynamic properties of plate-like structures. A closed-form solution of the Timoshenko plate equation consistent with the maximum likelihood estimator has been derived. The closed-form expressions of the gradient functions have thereby been resulted from the solution of the partial differential equation. The proposed distributed parameter model involves far fewer unknown parameters than independent modal characteristics for finite element models. Illustration of this approach is given by a computer simulation which shows that the estimated results by using continuum model are reasonably accurate compared with the theoretical results.