Related papers: Platonic Localisation: One Ring to Bind Them
We consider an elastic system containing a small region where the density is very much higher then elsewhere. Such system possesses two types of eigenvibrations, which are local and global vibrations. Complete asymptotic expansions of…
The non-localized cluster model provides a new perspective on nuclear cluster effects and has been applied successfully to study cluster structures in various bound states and quasi-bound states (i.e., long-lived resonant states). In this…
The paper investigates localized deformation patterns resulting from the onset of instabilities in lattice structures. The study is motivated by previous observations on discrete hexagonal lattices, where the onset of non-uniform,…
The paper focuses on the enhanced stiffness modeling of robotic manipulators by taking into account influence of the external force/torque acting upon the end point. It implements the virtual joint technique that describes the compliance of…
Implant placement under soft tissues operation is described. In this operation tissues can reach such deformations that nonlinear properties are appeared. A mass-spring model modification for modeling nonlinear tissue operation is…
Amongst the various fascinating types of material behavior featured by magnetic gels and elastomers are magnetostrictive effects. That is, deformations in shape or changes in volume are induced from outside by external magnetic fields.…
We use a transfer-matrix method to study the localization properties of vibrations in a `mass and spring' model with simple cubic lattice structure. Disorder is applied as a box-distribution to the force-constants $k$ of the springs. We…
We show that the natural resonant frequency of a suspended flexible string is significantly modified (by one order of magnitude) by adding a freely pivoting attached mass at its lower end. This articulated system then exhibits complex…
In pattern-forming systems, localized patterns are readily found when stable patterns exist at the same parameter values as the stable unpatterned state. Oscillons are spatially localized, time-periodic structures, which have been found…
The phase--space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, sudden reductions in the phase-space volume or gaps…
This paper is concerned with the theoretical study of plasmonic resonances for linear elasticity governed by the Lam\'e system in $\mathbb{R}^3$, and their application for cloaking due to anomalous localized resonances. We derive a very…
We study the Langevin dynamics of a two-dimensional discrete oscillator chain absorbed on a periodic substrate and subjected to an external localized point force. Going beyond the commonly used harmonic bead-spring model, we consider a…
Flapping-wing insects, birds, and robots are thought to offset the high power cost of oscillatory wing motion by using elastic elements for energy storage and return. Insects possess highly resilient elastic regions in their flight anatomy…
We present direct observation of the ring-down dynamics in the rotating frame of a resonantly driven single-mode nonlinear nanomechanical resonator. An additional close to resonance harmonic force excites nonlinear oscillations about the…
The paper gives a description of wave propagation in discrete-periodic one-dimensional media with block structure. For one-dimensional problems mathematical models are proposed that describe block structures in the form of a mass chain or…
We develop a new closed-form model for the dynamics of an elastic and isotropic sphere and use it to derive new closed-form resonant frequencies.
Linearised relativistic elasticity equations of motion are considered for a rod and a spinning ring encountering a gravitational wave. In the case of the rod, the equations reduce to a wave equation with appropriate boundary conditions.…
Mitigating low-frequency vibration or noise is of vital importance to both human health and mechanical engineering. Two-dimensional phononic crystal (PC) structures were proposed by attaching rubber and metallic cylinders on one or both…
In this paper, a method of local perturbations, previously successfully applied to decompose the problem of elasticity in the system of connected thin rods and beams [Kolpakov and Andrianov, 2013], is used to study the asymptotic behaviour…
The paper includes novel results for the scattering and localisation of a time-harmonic flexural wave by a semi-infinite herringbone waveguide of rigid pins embedded within an elastic Kirchhoff plate. The analytical model takes into account…