Dynamics behaviour of an elastic non-ideal (NIS) portal frame, including fractional nonlinearities

Abstract

Abstract. This paper overviews recent developments on some problems related to elastic structures, such as portal frames, taking into account the full interactions of the vibrating systems, with an energy source of limited power supply (small motors, electro-mechanical shakers). We include a discussion on fractional (rational) damping and stiffness effects on the adopted modelling. This was a plenary lecture, delivered in the event titled: Mechanics of Slender Structures, organized in Northampton, England from 21-22, September 2015. IntroductionThis paper shows a series of problems related to nonlinear dynamics and control, correlated to Electromechanical Systems [1] using an elastic support. Here, we analyzed such systems those fall into three groups: the conventional MACRO, MEMS and NEMS electro-mechanical systems, taking into account the existence of a full interaction between mechanical and electrical field quantities. The aim of this paper is to describe a large number of phenomena caused by the action of vibrations on nonlinear electro-mechanical systems and the energy source supply to it. This paper gives a general description of this class of phenomena which has been discussed in recent years.

Stability of a nonideally excited Duffing oscillator

“…On the other hand, a useful lower bound for Φ(t) 2 can be found by choosing an appropriate vector χ as follows: if H = λ i (i ≤ m), then χ = e i ; if H = α j , then χ = e m+2 j (vectors e k represent the standard basis, with the k-th component being 1 and the rest being zero). With such a choice of vector χ , we have that Φ(t) 2 ≥ Φ(t)χ 2 = e 2Ht (102)…”

“…Cveticanin et al [7,8] used averaging techniques to investigate different configurations of nonideally excited systems, including cases of variable mass. The behaviour of elastically supported unbalanced motors with fractional damping was numerically analysed in [2,47]. Bharti et al [3] addressed the appearance of the Sommerfeld effect in the torsional vibrations of a double-Cardan joint driveline.…”

NisI: A Tool for Non-Ideal System Identification

“…In recent years, there has been extensive research into matters regarding non-ideal systems [4,19,18,3,9,2,8]. Dynamic systems often exhibit chaotic behavior, which complicates the task of parametric identification in experimental systems.…”

Efficiency of hysteretic damper in oscillating systems

“…The influence of nonlinear damping effects on the stability of oscillating systems are considered in [14] (see, also the related references). It should also be pointed out the exciting and interesting (generally, from the fundamental point of view) model of generalized viscous damping which is based on the technique of fractional derivatives [2,10,30]. An interest to the generalized viscous damping is connected with the fact that the systems with such a type of nonlinearity demonstrate a chaotic behavior [26].…”