Static elastic cloaking, low frequency elastic wave transparency and neutral inclusions

Andrew N. Norris; William J. Parnell

doi:10.1098/rspa.2019.0725

Home/Archive/arXiv

arXiv · 1910.12866

Static elastic cloaking, low frequency elastic wave transparency and neutral inclusions

Andrew N. Norris·William J. Parnell

View original source ↗Read source document ↗Export metadata ↓

Abstract

New connections between static elastic cloaking, low frequency elastic wave scattering and neutral inclusions are established in the context of two dimensional elasticity. A cylindrical core surrounded by a cylindrical shell is embedded in a uniform elastic matrix. Given the core and matrix properties, we answer the questions of how to select the shell material such that (i) it acts as a static elastic cloak, and (ii) it eliminates low frequency scattering of incident elastic waves. It is shown that static cloaking (i) requires an anisotropic shell, whereas scattering reduction (ii) can be satisfied more simply with isotropic materials. Implicit solutions for the shell material are obtained by considering the core-shell composite cylinder as a neutral elastic inclusion. Two types of neutral inclusion are distinguished, \textit{weak} and \textit{strong} with the former equivalent to low frequency transparency {and the classical Christensen and Lo generalised self-consistent result for in-plane shear from 1979. Our introduction of the \textit{strong neutral inclusion} is an important extension of this result in that we show that standard anisotropic shells can act as perfect static cloaks, contrasting previous work that has employed "unphysical" materials.} The relationships between low frequency transparency, static cloaking and neutral inclusions provide the material designer with options for achieving elastic cloaking in the quasi-static limit.

Explore related subjects

physics.class-ph cond-mat.mtrl-sci

Keep this discovery

BibTeX RIS

Andrew N. Norris, William J. Parnell. 2019-10-28. Static elastic cloaking, low frequency elastic wave transparency and neutral inclusions. https://doi.org/10.1098/rspa.2019.0725

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Projection Angles of Projectiles in Sports: Qualitative Assessment of the Effects of Aerodynamic Forces or Run-Up

We examine two major factors that influence the optimum projection angle: aerodynamic forces and the effect of run-up. With respect to aerodynamics, we consider not only the drag but also the lift generated by spin during flight. By linearizing the equations of motion that include these forces, we derive perturbation solutions with respect to drag and lift coefficients and clarify their qualitative effects. The results show that both drag and lift reduce the optimum projection angle, with the latter exerting a stronger influence. To investigate the effect of run-up, we use an extended projection model in which the initial speed depends on the initial angle. Analysis of this model reveals that a stronger run-up increases the relative projection angle but decreases the launch angle observed from the ground. These findings provide a mechanical explanation for the release angle in shot put and the takeoff angle in long jump. The present study establishes a simple theoretical framework for clarifying the respective roles of aerodynamic and run-up effects in determining the optimum projection angles in sports.

physics.class-ph↗

arXiv2026

Dunkl-Based Modeling of Vibrational Modes in Lightweight Elastic Beams

Optimizing slender elastic structures for renewable energy applications requires non-classical continuum formulations capable of accounting for spatial micro-interactions without sacrificing analytical tractability. Here, we extend beam vibration mechanics by replacing standard spatial derivatives with the Dunkl differential operator. This modification introduces a reflection-coupled mathematical structure that accounts for spatial parity effects across the beam domain. We formulate the governing dynamic equations into a generalized eigenvalue problem and derive exact analytical expressions for modal characteristics under standard boundary conditions. The classical limit confirms exact convergence to classical Euler-Bernoulli formulations. Parametric analyses reveal that the Dunkl parameter acts as a reflection-induced modulation parameter, significantly shifting natural frequencies and altering the modal characteristics of higher modes. These results provide an analytical baseline for dynamic optimization in lightweight structural components.

physics.class-ph↗

arXiv2026

A purely mechanical system realizing a Coulomb-like interaction

We solve in closed form a one-dimensional relativistic system: two masses interacting only through elastic collisions with a massless mediator bouncing between them. Momenta, times, and positions are hyperbolic functions of the collision index. The mediator energy, interpreted as the pair's effective potential, obeys an exact discrete Coulomb law, $V\propto 1/r$, with a Lorentz-invariant action as coupling. A massive Newtonian mediator instead transmits a $1/r^{3}$ force; one adiabatic invariant traces both laws to the mediator's dispersion relation. Continued to negative mediator energy, the closed forms turn trigonometric, binding a one-dimensional mechanical analog of the Coulomb atom.

physics.class-ph↗