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A method to simulate orthotropic behaviour in thin shell finite elements is proposed. The approach is based on the transformation of shape function derivatives, resulting in a new orthogonal basis aligned to a specified preferred direction…
The aim of this short note is to give a synthetic presentation of the mathematical elements that are used to solve the elastic wave system of equations in a bounded anisotropic elastic body, in a general framework. In particular, the proof…
In systems that exhibit a bistability between nonlinear traveling waves and the basic state, pairs of fronts connecting these two states can form localized wave pulses whose stability depends on the interaction between the fronts. We…
This paper presents a general, nonlinear isogeometric finite element formulation for rotation-free shells with embedded fibers that captures anisotropy in stretching, shearing, twisting and bending -- both in-plane and out-of-plane. These…
The dynamics of random weakly nonlinear waves is studied in the framework of vibrating thin elastic plates. Although it has been previously predicted that no stationary inverse cascade of constant wave action flux could exist in the…
Light can be confined transversely and delivered axially in a waveguide. However, waveguides are lossy static structures whose modal characteristics are fundamentally determined by the boundary conditions, and thus cannot be readily changed…
We suggest the numerical approach to detect eigenfrequencies of trapped modes in waveguides or guided waves in diffraction gratings. At the same time, the approach works perfectly for computation of systems with finitely many scattering…
The design of structures that can yield efficient sound insulation performance is a recurring topic in the acoustic engineering field. Special attention is given to panels, which can be designed using several approaches to achieve…
We study waves governed by the planar Helmholtz equation, propagating in an infinite lattice of subwavelength Dirichlet scatterers, the periodicity being comparable to the wavelength. Applying the method of matched asymptotic expansions,…
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…
We investigate the localization of waves in aperiodic structures that manifest the characteristic multiscale complexity of certain arithmetic functions with a central role in number theory. In particular, we study the eigenspectra and wave…
We address the issue of nonlinear modes in a two-dimensional waveguide array, spatially distributed in the Lieb lattice geometry, and modeled by a saturable nonlinear Schr\"odinger equation. In particular, we analyze the existence and…
A novel design of an elastic metamaterial with anisotropic mass density is proposed to manipulate flexural waves at a subwavelength scale. The three-dimensional metamaterial is inspired by kirigami, which can be easily manufactured by…
We develop an effective medium approach to characterize the propagation of matter waves in periodic structures, such as graphene or semiconductor superlattices. It is proven that the time evolution of the states that are not more localized…
A new finite element formulation for the Kirchhoff plate model is presented. The method is a displacement formulation with the deflection and the rotation vector as unknowns and it is based on ideas stemming from a stabilized method for the…
This paper is concerned with acoustic scattering from a sound-soft trapezoidal surface in two dimensions. The trapezoidal surface is supposed to consist of two horizontal half-lines pointing oppositely, and a single finite vertical line…
We consider a dynamic system of nonlinear partial differential equations modeling the motions of a suspension bridge. This fish-bone model captures the flexural displacements of the bridge deck's mid-line, and each chordal filament's…
We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is…
Compact and robust waveguide chips are crucial for new integrated terahertz applications, such as high-speed interconnections between processors and broadband short-range wireless communications. Progress on topological photonic crystals…
We describe and evaluate a numerical solution strategy for simulating surface acoustic waves through semiconductor devices with complex geometries. This multi-physics problem is of particular relevance to the design of quantum electronic…