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Forced nonlinear vibration of shallow shell and application to technical diagnosis

This paper presents direct and inverse problems of forced nonlinear vibration of shallow shell. From that the method of establishment and solution of technical diagnosis for shallow shell under the vibrated load is proposed. | Vietnam Journal of Mechanics, VAST, Vol. 28, No. 3 (2006), pp. 189- 196 FORCED NONLINEAR V IBRATION OF SHALLOW SHELL AND APPLICATION TO TECHNICAL DIAGNOSIS L E NGOC THACH, TRAN VAN LIEN Hanoi University of Civil Engineering A bstract . This paper presents direct and inverse problems of forced nonlinear vibration of shallow shell. From that the met hod of establishment and solution of technical diagnosis for shallow shell under the vibrated load is proposed. The diagnosis criterion is the minimum of the difference between the square of experimental and theoretical data. The diagnosed parameters are the external loads and the reactions arose at the boundaries. 1. INTRODUCTION We have many different approaches to solve a t echnical di agnosis problem. One of those is employment of experiment determined and theoretical computed frequencies of the forced vibration of structure in order to determine the unknown t echnical parameters. When solving a technical diagnosis problem of structures, the numerical results of a program on structural analysis of the direct problem are oft en employed. However, to the date, t hese numerical results are mostly given for linear problems with small strain assumption. Even, the linear problems have many advantages, but do not completely model the behavior the structures , especially in the case of dynamic problems. In this research direction, in [7] the technical diagnosis problem and its solution for shallow shell are presented , but just for the case of free vibration. In this paper , based on the direct and inverse problems of forced vibration the authors present the method to establish and solve the technical diagnosis problem for shallow shell under the vibrated loads . The diagnosis criterion is t he minimum of the difference between t he square of experimental and theoretical dat a. The diagnosed parameters are the external loads and the reactions arose at the boundaries . 2. MODEL CONSTRUCTION Fig. 1. Shallow shell with .