Related papers: Platonic Localisation: One Ring to Bind Them
This work investigates the effect of nonlinearities on topologically protected edge states in one and two-dimensional phononic lattices. We first show that localized modes arise at the interface between two spring-mass chains that are…
We propose a new method to characterize the spatial distribution of particles' vibrations in solids with much lower computational costs compared to the usual normal mode analysis. We excite the specific vibrational mode in a two dimensional…
We consider non-stationary localized oscillations of an infinite Bernoulli-Euler beam. The beam lies on the Winkler foundation with a point inhomogeneity (a concentrated spring with negative time-varying stiffness). In such a system with…
We investigate a family of quasiperiodic continuous elastic beams, the topological properties of their vibrational spectra, and their relation to the existence of localized modes. We specifically consider beams featuring arrays of ground…
Phonon localization is a phenomenon that influences numerous material properties in condensed matter physics. Anderson localization brings rise to localized atomic-scale phonon interferences in disordered lattices with an influence limited…
Vibro-tactile feedback is, by far the most common haptic interface in wearable or touchable devices. This feedback can be amplified by controlling the wave propagation characteristics in devices, by utilizing phenomena such as structural…
We study the localization of vibrational modes of frictionless granular media. We introduce a new method, motivated by earlier work on non-Hermitian quantum problems, which works well both in the localized regime where the localization…
In this paper we develop a method capable of modeling the space-time focusing of nondiffracting pulses. The new pulses can possess arbitrary peak velocities and, in addition to being resistant to diffraction, can have their peak intensities…
We derive a closed-form expression that accurately predicts the peak frequency-shift and broadening induced by tiny perturbations of plasmonic nanoresonators without critically relying on repeated electrodynamic simulations of the spectral…
Limit-periodic structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. We study a ball and spring model with a limit-periodic pattern of spring stiffnesses and identify a set of extended modes with…
We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derived and their ground state structures are…
A simplified model of periodic chiral beam-lattices containing local resonators has been formulated to obtain a better understanding of the influence of the chirality and of the dynamic characteristics of the local resonators on the…
This paper presents a rigorous proof that arbitrarily weak perturbations produce localized vibrational (phonon) modes in one- and two-dimensional discrete lattices, inspired by analogous results for the Schr{\"o}dinger and Maxwell…
In this paper, the axial vibration of cracked beams, the free flexural vibrations of nanobeams and plates based on Timoshenko beam theory and first-order shear deformable plate theory, respectively, using Eringen's nonlocal elasticity…
A mathematical model of a simply supported Euler-Bernoulli beam with attached spring-mass system is considered. The model is controlled by distributed piezo actuators and lumped force. We address the issue of asymptotic behavior of…
The non-evanescent vibration, evanescent vibration and forced vibration of an oscillator attached to the massless spring are always discussed in general mechanics courses. In this article, we focus on the heavy-spring conditions. We first…
In this paper, we experimentally demonstrate how discrete resonances can be used to image acoustic sources and mechanical changes in thin plates with different boundary shapes. The proposed method uses coupled numerical and experimental…
The terms "acoustic/elastic meta-materials" describe a class of periodic structures with unit cells exhibiting local resonance. This localized resonant structure has been shown to result in negative effective stiffness and/or mass at…
It is recent that the emergence of topological insulators in condensed matter physics has inspired analogous wave phenomena in mechanical systems, mostly in the setting of discrete lattice models. Here we report a numerical and experimental…
We give an example of a relation between local and effective properties for elastic structures, up to geometric constants. The model considered is a periodic structure with isotropic and homogeneous local elasticity tensor in planar linear…