[12] Elia A, Postiglione A,

Monteleone M. CATALOGA: a software for semantic-based terminological data mining. In: 1st International Conference on Data Compression, Communication and Processing, IEEE, Palinuro (SA), June 21–24. IEEE Computer Society; 2011. p. 153–156. Available from: http:// www.computer.org/csdl/proceedings/ ccp/2011/4528/00/index.html.

[13] Postiglione A, Monteleone M. Semantic-based bilingual text-mining. In: Second International Conference on

**Chapter 2**

Properties

**Abstract**

**1. Introduction**

**13**

*Lionel Merveil Anague Tabejieu,*

Vibrations of an Elastic Beam

Foundation having Fractional

*Blaise Roméo Nana Nbendjo and Giovanni Filatrella*

The present chapter investigates both the effects of moving loads and of stochastic wind on the steady-state vibration of a first mode Rayleigh elastic beam. The

fractional-order viscoelastic material. The viscoelastic property of the foundation is modeled using the constitutive equation of Kelvin-Voigt type, which contain fractional derivatives of real order. Based to the stochastic averaging method, an analytical explanation on the effects of the viscoelastic physical properties and number of the bearings, additive and parametric wind turbulence on the beam oscillations is provided. In particular, it is found that as the number of bearings increase, the resonant amplitude of the beam decreases and shifts towards larger frequency values. The results also indicate that as the order of the fractional derivative increases, the amplitude response decreases. We are also demonstrated that a moderate increase of the additive and parametric wind turbulence contributes to decrease the chance for the beam to reach the resonance. The remarkable agreement between the analytical and numerical results is also presented in this chapter.

**Keywords:** elastic structure, moving loads, viscoelastic bearings, fractional-order,

There is a large amount of vehicles passing through in-service bridges every day, while sizable wind blows on the bridge decks. Vibrations caused by the service loads is of great theoretical and practical significance in civil engineering. In this chapter, it follows a list, by no means exhaustive, of research related to this kind engineer problem. To start with, Xu *et al.* [1] have explored the basic dynamics interaction between suspension bridges and the combined effects of intense wind and a single

stochastic averaging method, Fokker-Planck-Kolmogorov equation

beam is assumed to lay on foundations (bearings) that are characterized by

Moving Loads and Positioned on a

Subjected by Two Kinds of

Order Viscoelastic Physical

Data Compression, Communication, Processing and Security (CCPS 2016), September 22–23, Cetara (SA); 2016. p. 1–4.

[14] Postiglione A, Monteleone M. A Linguistic Semantic Text-Mining for Multiword Units. In: Roni R, editor. MANTUA HUMANISTIC STUDIES. vol. XII. Mantua Humanistic Studies, Mantova:Mantova: Universitas Studiorum; 2020. p. 445–459.

[15] Cormen TH, Leiserson CE, Rivest RL, Stein C. Introduction to Algorithms, Third Edition. 3rd ed. The MIT Press; 2009.
