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Keywords: response surface approximation, design of experiments, natural frequency, critical speed, supersonic flow, axial force.

Summary

Light weight structures have been extensively used in many industrial fields such as in mechanical, aerospace and rocket engineering, and therefore vibration and stability problems of plates have become of increasing importance.

Leissa [1,2] has reviewed the comprehensive literature dealing with the vibration and stability of plates. Bolotin has extensively studied the non-conservative problems of elastic stability, detailed explanations for which are provided in his book [3]. Birman and Librescu [4] have analyzed the supersonic flutter of laminated composite flat panel. Shiau [5] has studied the flutter of composite laminated beam plates with delamination. Young and Chen [6] analyzed the stability of skew plates subjected to aerodynamic and in-plane forces. On the other side, there are some papers on the identification of non-conservative problems of plates. Takahashi [7] 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 [8].

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 the response and design variables. The empirical model is called a response surface model or curve fit. The basic idea of the 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 polynominal 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 resopnse surface methodology, which consists of a design of experiments, for estimating the critical speed of the plate is studied. An analysis is presented for the vibration and stability of a tapered orthotropic rectangular plate in a supersonic flow by use of the transfer matrix approach. The method is applied to plates with linearly varying cross-sections, and the natural frequencies and critical speeds are calculated numerically, to provide information about the effect on them of varying cross-section, the rigidity, the axial force 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 speed 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 is sufficient for estimating the critical speeds.

References

1: Leissa A.W., "Vibration of plates", NASA SP-160 1969.
2: Leissa A.W., "Recent research in plate vibrations: 1973-1976: complicating effects", The Shock and Vibration Digest , 10, pp.21-35, 1978. doi:10.1177/058310247801001204
3: Bolotin V.V., "Nonconservative Problems of Theory of Elastic Stability", Pergamon Press, Oxford, 1963.
4: Birman V. and Librescu L., "Supersonic flutter of shear deformable laminated composite flat panel", J. Sound Vibr. 139, pp.265-275, 1990. doi:10.1016/0022-460X(90)90887-6
5: Shiau L.C., "Flutter of composite laminated beam plates with delamination", AIAA J. 30, pp.2504-2511,1992. doi:10.2514/3.11253
6: Young T.H. and Chen F.Y., "Stability of skew plates subjected to aerodynamic and in-plane force", J. Sound Vibr. 171, pp.603-615, 1994. doi:10.1006/jsvi.1994.1144
7: Takahashi I., "Identification for critical speeds of an orthotropic rectangular plate in a supersonic flow using neural networks", Proceedings of CIVIL-COMP 1999, Artificial Intelligence Applications in Civil and Structural Engineering, Civil-Comp Press, UK, pp.131-138, 1999. doi:10.4203/ccp.62.5.4
8: Takahashi I. and Yoshioka T., "Neural identification for critical flutter load of a polar-orthotropic annular plate", Proceedings of CIVIL-COMP 2001, Artificial Intelligence Applications in Civil and Structural Engineering, Civil-Comp Press, UK, CD-ROM, 2001. doi:10.4203/ccp.74.17
9: Mysers R.H. and Montgomery D.C., "Response surface methodology; Process and product optimization using design experiment", John Wiley & Sons. Inc., New York,1995.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 83 PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro Paper 156 Estimation of Critical Speed of an Orthotropic Rectangular Plate in Supersonic Flow I. Takahashi Department of Mechanical Engineering, Kanagawa Institute of Technology, Japan doi:10.4203/ccp.83.156 purchase the full-text of this paper Full Bibliographic Reference for this paper I. Takahashi, "Estimation of Critical Speed of an Orthotropic Rectangular Plate in Supersonic Flow", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 156, 2006. doi:10.4203/ccp.83.156 Keywords: response surface approximation, design of experiments, natural frequency, critical speed, supersonic flow, axial force. Summary Light weight structures have been extensively used in many industrial fields such as in mechanical, aerospace and rocket engineering, and therefore vibration and stability problems of plates have become of increasing importance. Leissa [1,2] has reviewed the comprehensive literature dealing with the vibration and stability of plates. Bolotin has extensively studied the non-conservative problems of elastic stability, detailed explanations for which are provided in his book [3]. Birman and Librescu [4] have analyzed the supersonic flutter of laminated composite flat panel. Shiau [5] has studied the flutter of composite laminated beam plates with delamination. Young and Chen [6] analyzed the stability of skew plates subjected to aerodynamic and in-plane forces. On the other side, there are some papers on the identification of non-conservative problems of plates. Takahashi [7] 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 [8]. 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 the response and design variables. The empirical model is called a response surface model or curve fit. The basic idea of the 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 polynominal 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 resopnse surface methodology, which consists of a design of experiments, for estimating the critical speed of the plate is studied. An analysis is presented for the vibration and stability of a tapered orthotropic rectangular plate in a supersonic flow by use of the transfer matrix approach. The method is applied to plates with linearly varying cross-sections, and the natural frequencies and critical speeds are calculated numerically, to provide information about the effect on them of varying cross-section, the rigidity, the axial force 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 speed 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 is sufficient for estimating the critical speeds. References 1 Leissa A.W., "Vibration of plates", NASA SP-160 1969. 2 Leissa A.W., "Recent research in plate vibrations: 1973-1976: complicating effects", The Shock and Vibration Digest , 10, pp.21-35, 1978. doi:10.1177/058310247801001204 3 Bolotin V.V., "Nonconservative Problems of Theory of Elastic Stability", Pergamon Press, Oxford, 1963. 4 Birman V. and Librescu L., "Supersonic flutter of shear deformable laminated composite flat panel", J. Sound Vibr. 139, pp.265-275, 1990. doi:10.1016/0022-460X(90)90887-6 5 Shiau L.C., "Flutter of composite laminated beam plates with delamination", AIAA J. 30, pp.2504-2511,1992. doi:10.2514/3.11253 6 Young T.H. and Chen F.Y., "Stability of skew plates subjected to aerodynamic and in-plane force", J. Sound Vibr. 171, pp.603-615, 1994. doi:10.1006/jsvi.1994.1144 7 Takahashi I., "Identification for critical speeds of an orthotropic rectangular plate in a supersonic flow using neural networks", Proceedings of CIVIL-COMP 1999, Artificial Intelligence Applications in Civil and Structural Engineering, Civil-Comp Press, UK, pp.131-138, 1999. doi:10.4203/ccp.62.5.4 8 Takahashi I. and Yoshioka T., "Neural identification for critical flutter load of a polar-orthotropic annular plate", Proceedings of CIVIL-COMP 2001, Artificial Intelligence Applications in Civil and Structural Engineering, Civil-Comp Press, UK, CD-ROM, 2001. doi:10.4203/ccp.74.17 9 Mysers R.H. and Montgomery D.C., "Response surface methodology; Process and product optimization using design experiment", John Wiley & Sons. Inc., New York,1995. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £140 +P&P)
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