Dynamic Analysis of a High Speed Transport Model by Using a Piecewise Continuous Timoshenko Beam Model

Conventional treatment of structural dynamic analysis and control is based on the finite element structural model. But such a treatment uses a very large number of elements which is usually very expensive and time-consuming, and the control spillover resulting from the modal truncation may lead to degradation of control system performance, or even create instability. In contrast, continuum modeling provides a very practical approach for overall dynamic analysis and control synthesis for the aerospace and aeronautical structures. In the Authors' previous work, a piecewise continuous Timoshenko beam model was developed, and used for the dynamic analysis of tapered beam-like structures. In the analysis, a tapered beam was divided into several segments of uniform beam elements. Instead of the arbitrarily assumed shape functions used in finite element analysis, the closed-form solution of the Timoshenko beam equation was used, along with application of the transfer matrix method. Using corresponding boundary conditions and compatibility conditions a characteristic equation for the global tapered beam was produced, from which natural frequencies were derived. In this paper, the piecewise continuous Timoshenko beam model was applied to the dynamic analysis of a high speed transport (HST) model, which is being developed as a testbed for experimental verification of aircraft structural dynamic analysis and modeling. This test model is a similitude of a high speed transport with M = 4.0 in a 1/20 ratio. Since the structural characteristics of the high speed aircraft emulates those of a long slender body with high flexibility, there is a significant advantage to applying an equivalent distributed parameter beam model to analyze the global dynamic properties of the test model. To evaluate the accuracy of the distributed parameter method, a finite element model using the STAAD III package was also formulated. It should be noted that more than 200 elements with approximately 300 degrees of freedom (DOF) were required even for this rough computational finite element model. While the comparable results to the finite element method are obtained, significant fewer elements were required for the piecewise continuous Timoshenko beam model thus, greatly reducing the computational effort.