Keywords: response surface approximation, design of experiments, natural frequency, critical flutter load, follower force.

This paper has been confined to the study of non-conservative instability of plates based upon the classical theory. Takahashi [1] proposed the identification method for critical speeds of an orthotropic plate in a supersonic flow using neural networks. The neural identification for critical flutter load of a polar-orthotropic annular plates was also studied by Takahashi and Yoshioka [2].

The problem of experimental design or design of experiments (DOE) is encountered in many fields. A common situation for using DOE is when the designer does not know the exact underlying relationship between responses and design variables. The basic idea of response surface methodology is to create explicit approximation functions to the objective and constraints, and then use these when performing the optimization. The approximation functions are typically in the form of low-order polynominals fit by least squares regression analysis. In order to construct the approximation function, it is necessary to have some results for a minimum number of points in the design space. The proper selection of points could drastically improve the quality of a response surface model. The response at the most suitable points, which are selected by the design of experiments (DOE) could have been obtained either by some analysis program or through physical experiments.

In this paper, the possibility of using a response surface methodology with DOE, for estimating the critical flutter load of the plate subjected to a follower force is studied. An analysis is presented for the vibration and stability of a tapered polar-orthotropic annular plate by use of the transfer matrix approach. The method is applied to plates with linearly varying cross-sections, and the natural frequencies and critical flutter loads are calculated numerically, to provide information about the effect on them of varying cross-section, the rigidity and the span and stiffness of intermediate supports.

Some numerical examples were presented to demonstrate the possibility of the response surface approximation. From the results of the numerical examples we can draw the following conclusions. First, the critical flutter load can be predicted by using the response surface approximation with three-level orthogonal Latin squares. Second, the generalization capability of the response surface with three-level orthogonal Latin squares L₂₇(3¹³) is sufficient for estimating the critical flutter loads.

1

Takahashi I., "Identification for critical speeds of an orthotropic rectangular plate in a supersonic flow using neural networks", in Artificial Intelligence Applications in Civil and Structural Engineering, B.H.V. Topping and B. Kumar, (Editors), Civil-Comp Press, Edinburgh, United Kingdom, pp. 131-138, 1999. doi:10.4203/ccp.62.5.4

2

I. Takahashi, "Neural Identification for Critical Flutter Load of A Polar-Orthotropic Annular Plate", in Proceedings of the Sixth International Conference on the Application of Artificial Intelligence to Civil and Structural Engineering, B.H.V. Topping and B. Kumar, (Editors), Civil-Comp Press, Stirling, United Kingdom, paper 17, 2001. doi:10.4203/ccp.74.17

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