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M. I Friswell, S. Adhikari and Y. Lei, “Vibration Analysis of Beams with Non-Local Foundations Using the Finite Element Method,” International Journal of Numerical Methods in Engineering, Vol. 71, No. 11, 2007, pp. 1365-1386. doi:10.1002/nme.2003

has been cited by the following article:

• TITLE: On the Damped Beams with Hysteresis

  AUTHORS: Mihaela Poienariu, Marius-Florinel Ionescu, Iulian Girip, Ligia Munteanu, Veturia Chiroiu

  KEYWORDS: Hysteresis, Euler-Bernoulli Beam, Nonlocal Theory, Auxetic Material

  JOURNAL NAME: World Journal of Mechanics, Vol.1 No.1, January 30, 2011

  ABSTRACT: This paper discusses the hysteretic behavior of beams with external elements made from auxetic materials. The damping force is modeled by using the nonlocal theory. Unlike the local models, the damping force is modeled as a weighted average of the velocity field over the temporal and spatial domains, determined by a kernel function based on distance measures. The hysteresis operator is continuous and it is defined in con-nection with the Euler-Bernoulli equation. The problem is solved by reducing it to a system of differential inclusions.