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Keywords: neural network, natural frequency, shaft, flutter load, cracks, axial force.

Summary

Light weight structure have been extensively used in many industrial fields such as in mechanical, aerospace and rocket engineering, and therefore vibration and stability problems of shafts have become of increasing importance. Especially, the majority of the structural parts of machines are operated in the range of limited fatigue strength, which occures the cracks in overstressed zone. The analysis of the dynamic characteristics of cracked structural elements is an important problem in technology. In particular, the inverse problems of cracked continuous bodies are becoming important in design practice.

The artificial neural network is now one of the most rapidly expanding area of research across many disciplines [1,2]. In mathematical fields the neural network is an effective mapping tool-mapping an input vector to an output vector. On the other hand, the identification technique for support conditions of continuous bodies is becoming important, with the increasing size and complexity of machines and vessels. Yasuda and Goto [3] and Kamiya, et al. [4] proposed the experimental identification technique for boundary conditions of the beam. Saito, et al. [5] and Yasuda, et al. [6] presented the identification of non-linear support systems by using transient response. Takahashi [7,8] proposed the identification method for the axial force (or critical force) and boundary conditions of a beam using the neural networks.

In this paper the possibility of using a Multilayer Perceptron Network trained with the Backpropagation Algorithm for identifying the critical flutter load and support conditions (or shape parameters) of the cracked shaft is studied. The natural frequecies which are the most fundamental and simplest in the modal parameters are adopted here to estimate the flutter load and support conditions (or shape parameters).

The basic idea is to train a neural network with simulated patterns of the relative changes of natural frequencies and corresponding support condition (or shape parameters) and critical flutter load of shafts in order to recognize the behaviour of the shaft. Subjecting this neural network to un-learning natural frequencies should imply information about the support condition (or shape parameters) and critical flutter load of shafts. The training data are obtaining by the values using the transfer matrix method. By a trial-and-error approach, with a view of simplify the network structure and speed up the convergence of the algorithm, we defined the network of three layers. The neural networks were trained with numerical values of the relative changes of the lowest four frequency parameters of shafts.

From the results of the numerical examples we can draw the following conclusions. The support condition (or shape parameters) and critical flutter load of shafts can be predicted by the change in frequency parameters.

References

1: Master, T., "Neural, Novel & Hybrid Algorithms for Time Series Prediction", John Wiley & Sons, Inc.1995.
2: Haykin, S., "Neural Networks", Macmillan Publishing Company, Inc. 1994.
3: Yasuda ,K. and Goto, Y., "Experimental identification technique for boundary conditions of a beam", Bulletin of JSME , 570, C, pp.118-125, 1994.
4: Kamiya ,K., Yasuda, K.and Miya, H., "Experimental identification of a nonlinear beam(when boundary conditions are linear)", Bulletin of JSME , 587, C, pp.212-219, 1995.
5: Sato, H., Iwata, Y. and Sugimoto, S., "Identification of nonlinear support systems by using transient respose", Bulletin of JSME , 585, C, pp.152-156, 1995.
6: Yasuda, K. , Goto, Y. and Hirose, Y ., "Experimental identification technique for boundary conditions of a beam(when boundary conditions are non-linear)", Bulletin of JSME , 599, C, pp.2599-2605, 1996.
7: Takahashi, I., "Identification for axial force and boundary conditions of a beam using neural networks", Proceedings of the 1997 International Conference on Engineering Applications of Neural Networks, Neural Networks in Engineering Systems, pp.253-256, 1997.
8: Takahashi, I., "Identification for critical force and boundary conditions of a beam using neural networks ", J. Sound Vibr, 228, pp.857-870, 1999. doi:10.1006/jsvi.1999.2451

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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: 76 PROCEEDINGS OF THE THIRD INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: B.H.V. Topping and Z. Bittnar Paper 80 Neural Identification for Critical Flutter Load of a Cracked Shaft Simultaneously Subjected to a Follower Force with an Axial Force I. Takahashi Department of Mechanical Engineering, Kanagawa Institute of Technology, Japan doi:10.4203/ccp.76.80 purchase the full-text of this paper Full Bibliographic Reference for this paper I. Takahashi, "Neural Identification for Critical Flutter Load of a Cracked Shaft Simultaneously Subjected to a Follower Force with an Axial Force", in B.H.V. Topping, Z. Bittnar, (Editors), "Proceedings of the Third International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 80, 2002. doi:10.4203/ccp.76.80 Keywords: neural network, natural frequency, shaft, flutter load, cracks, axial force. Summary Light weight structure have been extensively used in many industrial fields such as in mechanical, aerospace and rocket engineering, and therefore vibration and stability problems of shafts have become of increasing importance. Especially, the majority of the structural parts of machines are operated in the range of limited fatigue strength, which occures the cracks in overstressed zone. The analysis of the dynamic characteristics of cracked structural elements is an important problem in technology. In particular, the inverse problems of cracked continuous bodies are becoming important in design practice. The artificial neural network is now one of the most rapidly expanding area of research across many disciplines [1,2]. In mathematical fields the neural network is an effective mapping tool-mapping an input vector to an output vector. On the other hand, the identification technique for support conditions of continuous bodies is becoming important, with the increasing size and complexity of machines and vessels. Yasuda and Goto [3] and Kamiya, et al. [4] proposed the experimental identification technique for boundary conditions of the beam. Saito, et al. [5] and Yasuda, et al. [6] presented the identification of non-linear support systems by using transient response. Takahashi [7,8] proposed the identification method for the axial force (or critical force) and boundary conditions of a beam using the neural networks. In this paper the possibility of using a Multilayer Perceptron Network trained with the Backpropagation Algorithm for identifying the critical flutter load and support conditions (or shape parameters) of the cracked shaft is studied. The natural frequecies which are the most fundamental and simplest in the modal parameters are adopted here to estimate the flutter load and support conditions (or shape parameters). The basic idea is to train a neural network with simulated patterns of the relative changes of natural frequencies and corresponding support condition (or shape parameters) and critical flutter load of shafts in order to recognize the behaviour of the shaft. Subjecting this neural network to un-learning natural frequencies should imply information about the support condition (or shape parameters) and critical flutter load of shafts. The training data are obtaining by the values using the transfer matrix method. By a trial-and-error approach, with a view of simplify the network structure and speed up the convergence of the algorithm, we defined the network of three layers. The neural networks were trained with numerical values of the relative changes of the lowest four frequency parameters of shafts. From the results of the numerical examples we can draw the following conclusions. The support condition (or shape parameters) and critical flutter load of shafts can be predicted by the change in frequency parameters. References 1 Master, T., "Neural, Novel & Hybrid Algorithms for Time Series Prediction", John Wiley & Sons, Inc.1995. 2 Haykin, S., "Neural Networks", Macmillan Publishing Company, Inc. 1994. 3 Yasuda ,K. and Goto, Y., "Experimental identification technique for boundary conditions of a beam", Bulletin of JSME , 570, C, pp.118-125, 1994. 4 Kamiya ,K., Yasuda, K.and Miya, H., "Experimental identification of a nonlinear beam(when boundary conditions are linear)", Bulletin of JSME , 587, C, pp.212-219, 1995. 5 Sato, H., Iwata, Y. and Sugimoto, S., "Identification of nonlinear support systems by using transient respose", Bulletin of JSME , 585, C, pp.152-156, 1995. 6 Yasuda, K. , Goto, Y. and Hirose, Y ., "Experimental identification technique for boundary conditions of a beam(when boundary conditions are non-linear)", Bulletin of JSME , 599, C, pp.2599-2605, 1996. 7 Takahashi, I., "Identification for axial force and boundary conditions of a beam using neural networks", Proceedings of the 1997 International Conference on Engineering Applications of Neural Networks, Neural Networks in Engineering Systems, pp.253-256, 1997. 8 Takahashi, I., "Identification for critical force and boundary conditions of a beam using neural networks ", J. Sound Vibr, 228, pp.857-870, 1999. doi:10.1006/jsvi.1999.2451 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 £85 +P&P)
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