Related papers: Asymptotic self-restabilization of a continuous el…
A mechanical system consisting of an elastic beam under harmonic excitation and an attached sliding body is investigated. Recent experimental observations suggest that the system passively (self-)adapts the axial location of the slider to…
One of the most challenging and basic problems in elastic rod dynamics is a description of rods in contact that prevents any unphysical self-intersections. Most previous works addressed this issue through the introduction of short-range…
This paper deals with the classical problem of exploring a ring by a cohort of synchronous robots. We focus on the perpetual version of this problem in which it is required that each node of the ring is visited by a robot infinitely often.…
This paper is devoted to describe the asymptotic behavior of a structure made by a thin plate and a thin rod in the framework of nonlinear elasticity. We scale the applied forces in such a way that the level of the total elastic energy…
We introduce a system where an elastic lattice of particles is moved slowly at a constant velocity under the influence of a local external potential, construct a rigid-body model through simplification processes, and show that the two…
We study the dynamics of an elastic body whose shape and position evolve due to the gravitational forces exerted by a pointlike planet. We work in the quadrupole approximation. We consider the solution in which the center of mass of the…
Stability is a fundamental concept that refers to a system's ability to return close to its original state after disturbances. The minimal conditions for stability when system parameters vary in time, though common in physics, have been…
In this paper, we are interested in the relation between the solutions of the control system $\dot x=f(x,u)$ and the solutions of its (potentially unknown) perturbation $\dot x=f(x,u)+w(x,t).$ Under the assumption that the linear part of…
Quasicrystals whose building blocks are of mesoscopic rather than atomic scale have recently been discovered in several soft-matter systems. Contrary to metallurgic quasicrystals whose source of stability remains a question of great debate…
Small oscillations of an elastic system of point masses (particles) with a nonlocal interaction are considered. We study the asymptotic behavior of the system, when number of particles tends to infinity, and the distances between them and…
The design of compliant mechanisms is crucial in several technologies and relies on the availability of solutions for nonlinear structural problems. One of these solutions is given and experimentally validated in the present article for a…
This paper aims to study existence condition of possible bursting oscillations generated by low frequency excitation of a nonlinear vibratory system in the presence of parametric excitation. Slow-fast dissection technique and numerical…
Spatio-temporal patterns emerging from an initial quiescent, uniform state is a phenomenon observed in many dynamical systems sustained far from thermodynamic equilibrium, the practical application of which has only recently begun to be…
Elastohydrodynamic lubrication, or simply soft lubrication, refers to the motion of deformable objects near a boundary lubricated by a fluid, and is one of the key physical mechanisms to minimise friction and wear in natural and engineered…
This paper addresses the problem of stabilizing a part of variables for control systems described by stochastic differential equations of the Ito type. The considered problem is related to the asymptotic stability property of invariant sets…
This paper consists of two parts. In the first part we prove the unique solvability for the abstract variational-hemivariational inequality with history-dependent operator. The proof is based on the existing result for the static…
Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple…
An exact transformation method is introduced that reduces the governing equations of a continuum structure coupled to strong nonlinearities to a low dimensional equation with memory. The method is general and well suited to problems with…
In this second part we prove that the full nonlinear fluid-solid system introduced in Part I is stabilizable by deformations of the solid that have to satisfy nonlinear constraints. Some of these constraints are physical and guarantee the…
We present a method for determining optimal modes of operation for autonomously oscillating systems with uncertain parameters. In a typical application of the method, a nonlinear dynamical system is optimized with respect to an economic…