Odd periodic oscillations in Comb-drive finger actuators

A dual principle for symmetric periodic solutions Bi-stability in noninterdigitated Comb-drive MEMS

“…We observe that φ m,N coincides with the odd (m, p)-periodic solution ϕ m,p (t) defined in [2] for the corresponding autonomous equation, i.e., φ m,N (t) ≡ ϕ m,p (t) where ϕ m,p (t) is an odd mT -periodic solution of the autonomous equation with exactly 2p zeros on [0, mT [. Additionally, by following the arguments in the discussion of the Section 2.3 in [2] it is not difficult to conclude that (15) implies that the solution φ m,N is both parabolic unstable and Lyapunov unstable.…”

“…Furthermore, since (15) holds and ϕ m,p (t) is a nontrivial solution of the null Dirichlet problem associated with equation ( 17), we obtain as a direct consequence of Theorem 3.1 in [2] that there exist δ m,p > 0 and a unique smooth function ∆ m,p (δ) defined on [0, δ m,p [ such that ∆ m,p (0) = v N and Φ m,p (t, δ) := x(t, ∆ m,p (δ), δ) for δ ∈ [0, δ m,p [ is a nontrivial solution of the corresponding null Dirichlet problem associated with (16) that emanates from ϕ m,p (t). Here x(t, v, δ) denotes the general solution of (16),i.e., x(0, v, δ) = 0, ẋ(0, v, δ) = v. Moreover, because of the uniqueness of the branch given above by the Implicit Function Theorem, we have that for δ > 0 small enough Φ m,p (t, δ) ≡ x m,N (t), where x m,N (t) ≡ x(t, ωm,N , δ) is the solution of (16) given by Proposition 2.8 in the former section.…”

“…Recently, works like [14,15,16] have considered the ideas in [17] to introduce some extensions and generalizations of the Ortega's principle in different contexts. In fact, the author in [14] obtained an extension of the variational principle to study the existence of even periodic solutions for the generalized Sitnikov problem.…”

“…In fact, the author in [14] obtained an extension of the variational principle to study the existence of even periodic solutions for the generalized Sitnikov problem. Then, the authors in [15] provided an extension of the principle for equations with finite domain and also studied the existence of odd periodic responses for a Comb-drive finger MEMS model with a linear stiffness term and interdigitated fingers, and the case with a cubic nonlinear stiffness was considered in [11]. Later, a generalization of the Ortega's principle was obtained in [16] by means of the truncation technique and a priori bounds of period solutions.…”

Abundant chaos in a mixer model with a hysteretic iron core inductance

“…Electromechanical devices are frequently used in a number of industrial and household applications such as shaking, sieving, mixing,… to name just some few examples [Núñez et al, 2021;Nana et al, 2018;Kouam Tagne et al, 2021;Tsapla Fotsa & Woafo, 2016;Minnemann Kuhnert et al, 2020;Marcelo Tusset et al, 2015]. These systems offer several advantages due to the mechanical power they provide for the accomplishment of several specific tasks.…”