Stochastic analysis of lattice, nonlocal continuous beams in vibration

Authors

  • Yuchen Li Université Bretagne Sud, UMR CNRS 6027, IRDL, F-56100 Lorient, France
  • Noël Challamel Université Bretagne Sud, UMR CNRS 6027, IRDL, F-56100 Lorient, France
  • Isaac Elishakoff Department of Ocean and Mechanical Engineering, Florida Atlantic University, 777 Glades Road – EG 36/Rm 106, Boca Raton, FL 33431, United States

DOI:

https://doi.org/10.15625/0866-7136/15671

Keywords:

Vibration, Lattice elasticity, Discrete beams, multibody system dynamics, Nonlocal beams

Abstract

In this paper, we study the stochastic behavior of some lattice beams, called Hencky bar-chain model and their non-local continuous beam approximations. Hencky bar-chain model is a beam lattice composed of rigid segments, connected by some homogeneous rotational elastic links. In the present stochastic analysis, the stiffness of these elastic links is treated as a continuous random variable, with given probability density function. The fundamental eigenfrequency of the linear difference eigenvalue problem is also a random variable in this context. The reliability is defined as the probability that this fundamental frequency is less than an excitation frequency. This reliability function is exactly calculated for the lattice beam in conjunction with various boundary conditions. An exponential distribution is considered for the random stiffness of the elastic links. The stochastic lattice model is then compared to a stochastic nonlocal beam model, based on the continualization of the difference equation of the lattice model. The efficiency of the nonlocal beam model to approximate the lattice beam model is shown in presence of rotational elastic link randomness. We also compare such stochastic function with the one of a continuous local Euler-Bernoulli beam, with a special emphasis on scale effect in presence of randomness. Scale effect is captured both in deterministic and non-deterministic frameworks.

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Published

28-06-2021

How to Cite

Li, Y., Challamel, N., & Elishakoff, I. (2021). Stochastic analysis of lattice, nonlocal continuous beams in vibration. Vietnam Journal of Mechanics, 43(2), 139–170. https://doi.org/10.15625/0866-7136/15671

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Research Paper