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Stochastic response of an axially moving viscoelastic beam with fractional order constitutive relation and random excitations

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Abstract

A convenient and universal residue calculus method is proposed to study the stochastic response behaviors of an axially moving viscoelastic beam with random noise excitations and fractional order constitutive relationship, where the random excitation can be decomposed as a nonstationary stochastic process, Mittag-Leffler internal noise, and external stationary noise excitation. Then, based on the Laplace transform approach, we derived the mean value function, variance function and covariance function through the Green’s function technique and the residue calculus method, and obtained theoretical results. In some special case of fractional order derivative α, the Monte Carlo approach and error function results were applied to check the effectiveness of the analytical results, and good agreement was found. Finally in a general-purpose case, we also confirmed the analytical conclusion via the direct Monte Carlo simulation.

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Authors and Affiliations

  1. Department of Applied Mathematics, Northwestern Polytechnical University, 710072, Xi’an, China

    Di Liu, Wei Xu & Yong Xu

Authors
  1. Di Liu
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  2. Wei Xu
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  3. Yong Xu
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Correspondence to Di Liu.

Additional information

The project was supported by the National Natural Science Foundation of China (11172233, 10932009 and 10972181), Program for New Century Excellent Talents in University, the Shaanxi Project for Young New Star in Science & Technology, NPU Foundation for Fundamental Research and New Faculties and Research Area Project.

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Liu, D., Xu, W. & Xu, Y. Stochastic response of an axially moving viscoelastic beam with fractional order constitutive relation and random excitations. Acta Mech Sin 29, 443–451 (2013). https://doi.org/10.1007/s10409-013-0029-y

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  • DOI: https://doi.org/10.1007/s10409-013-0029-y

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