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Formulating The Stochastic Finite Elements For Free Vibration Analysis Of Plates With Variable Elastic Modulus

Authors: Esfahani, Mojtaba Aghamiri; Karkon, Mohammad; Nezhad, Seyed Majid Hosseini; Hosseini-Ara, Reza;

Formulating The Stochastic Finite Elements For Free Vibration Analysis Of Plates With Variable Elastic Modulus

Abstract

{"references": ["B. S. de Lima and N. F. Ebecken, \"A comparison of models for uncertainty analysis by the finite element method,\" Finite Elements in Analysis and Design, vol. 34, pp. 211-232, 2000.", "H.-C. Noh and T. Park, \"Monte Carlo simulation-compatible stochastic field for application to expansion-based stochastic finite element method,\" Computers & structures, vol. 84, pp. 2363-2372, 2006.", "K. Sepahvand, S. Marburg, and H.-J. Hardtke, \"Stochastic free vibration of orthotropic plates using generalized polynomial chaos expansion,\" Journal of Sound and Vibration, vol. 331, pp. 167-179, 2012.", "S. Dey, T. Mukhopadhyay, and S. Adhikari, \"Stochastic free vibration analysis of angle-ply composite plates\u2013a RS-HDMR approach,\" Composite Structures, vol. 122, pp. 526-536, 2015.", "M. Talha and B. Singh, \"Stochastic vibration characteristics of finite element modelled functionally gradient plates,\" Composite Structures, vol. 130, pp. 95-106, 2015.", "S. Chakraborty, B. Mandal, R. Chowdhury, and A. Chakrabarti, \"Stochastic free vibration analysis of laminated composite plates using polynomial correlated function expansion,\" Composite Structures, vol. 135, pp. 236-249, 2016.M. Young, The Techincal Writers Handbook. Mill Valley, CA: University Science, 1989.", "I. Ramu and S. Mohanty, \"Modal Analysis of Functionally Graded Material Plates Using Finite Element Method,\" Procedia Materials Science, vol. 6, pp. 460-467, 2014."]}

In this study, the effect of uncertainty in elastic modulus of a plate on free vibration response is investigated. For this purpose, the elastic modulus of the plate is modeled as stochastic variable with normal distribution. Moreover, the distance autocorrelation function is used for stochastic field. Then, by applying the finite element method and Monte Carlo simulation, stochastic finite element relations are extracted. Finally, with a numerical test, the effect of uncertainty in the elastic modulus on free vibration response of a plate is studied. The results show that the effect of uncertainty in elastic modulus of the plate cannot play an important role on the free vibration response.

Keywords

free vibration, Neumann expansion method., plate bending, Stochastic finite elements, Monte Carlo

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