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Stochastic Perturbation-Based Finite Element for Free Vibration of Functionally Graded Beams with an Uncertain Elastic Modulus

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Mechanics of Composite Materials Aims and scope

The stochastic eigenvalue problem for free vibrations of functionally graded beams with a random elastic modulus is investigated. The effective material properties and beam cross section are assumed to vary continuously in different directions according to the exponential law. The governing equations for the natural frequency of the functionally graded beams are derived from Hamilton’s principle. In the stochastic finite-element method, the random process was discretized by averaging random variables in each element to increase the accuracy of the natural frequency found. A solution of the stochastic eigenvalue problem formulated was obtained using the perturbation technique in conjunction with the finite-element method. The spectral representation was used to generate a random process to employ the Monte Carlo simulation. A good agreement was obtained between the results of the first-order perturbation technique and the Monte Carlo simulation.

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Acknowledgments

The authors would like to acknowledge the support from the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 107.01-2017.314.

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Correspondence to N. V. Thuan.

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Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 56, No. 4, pp. 715-730, July-August, 2020.

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Thuan, N.V., Hien, T.D. Stochastic Perturbation-Based Finite Element for Free Vibration of Functionally Graded Beams with an Uncertain Elastic Modulus. Mech Compos Mater 56, 485–496 (2020). https://doi.org/10.1007/s11029-020-09897-z

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  • DOI: https://doi.org/10.1007/s11029-020-09897-z

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