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An asymptotically exact first-order shear deformation theory for functionally graded elastic plates is derived using the variational-asymptotic method. As an application, an analytical solution to the problem of wave propagation in a…

Soft Condensed Matter · Physics 2023-05-09 Khanh Chau Le

We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic…

Analysis of PDEs · Mathematics 2018-02-06 Yi-Hsuan Lin , Shixu Meng

A non-local dynamic homogenization technique for the analysis of a viscoelastic heterogeneous material which displays a periodic microstructure is herein proposed. The asymptotic expansion of the micro-displacement field in the transformed…

Applied Physics · Physics 2018-11-26 Rosaria Del Toro , Andrea Bacigalupo , Marco Paggi

In this paper an asymptotic homogenization method for the analysis of composite materials with periodic microstructure in presence of thermodiffusion is described. Appropriate down-scaling relations correlating the microscopic fields to the…

Mathematical Physics · Physics 2015-12-31 A. Bacigalupo , L. Morini , A. Piccolroaz

We investigate the effective elastic properties of periodic dilute two-phase composites consisting of an homogeneous isotropic matrix and a periodic array of rigid inclusions. We assume the rigid inclusion in a unit cell is a simply…

Analysis of PDEs · Mathematics 2024-03-26 Daehee Cho , Doosung Choi , Mikyoung Lim

A complete methodology, based on a two-scale asymptotic approach, that enables the homogenisation of elastic lattices at non-zero frequencies is developed. Elastic lattices are distinguished from scalar lattices in that two or more types of…

Classical Physics · Physics 2014-07-09 D. J. Colquitt , R. V. Craster , M. Makwana

The periodic solutions of a type of nonlinear hyperbolic partial differential equations with a localized nonlinearity are investigated. For instance, these equations are known to describe several acoustical systems with fluid-structure…

Dynamical Systems · Mathematics 2013-06-20 Benjamin Ricaud

We consider a singularly perturbed second order elliptic system in the whole space. The coefficients of the systems fast oscillate and depend both of slow and fast variables. We obtain the homogenized operator and in the uniform norm sense…

Mathematical Physics · Physics 2007-05-23 Denis Borisov

This paper focuses on the simultaneous homogenization and dimension reduction of periodic composite plates within the framework of non-linear elasticity. The composite plate in its reference (undeformed) configuration consists of a periodic…

Analysis of PDEs · Mathematics 2026-02-03 Amartya Chakrabortty , Georges Griso , Julia Orlik

We quantize the elastic modes in a plate. For this, we find a complete, orthogonal set of eigenfunctions of the elastic equations and we normalize them. These are the phonon modes in the plate and their specific forms and dispersion…

Materials Science · Physics 2007-10-03 T. Kühn , D. V. Anghel

In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…

Analysis of PDEs · Mathematics 2019-09-04 Fabian Christowiak , Carolin Kreisbeck

Asymptotic homogenisation is used to systematically derive reduced-order macroscopic models of conductive behaviour in spirally-wound layered materials in which the layers have very different conductivities. The problem is motivated by the…

Applied Physics · Physics 2020-11-10 Steven Psaltis , Robert Timms , Colin Please , S. Jonathan Chapman

We study the dynamical regime of wave turbulence of a vibrated thin elastic plate based on experimental and numerical observations. We focus our study to the strongly non linear regime described in a previous letter by N. Yokoyama & M.…

Chaotic Dynamics · Physics 2015-06-16 Benjamin Miquel , Alexandros Alexakis , Christophe Josserand , Nicolas Mordant

We study homogenization problem for the stationary Maxwell system. It is supposed that the magnetic permeability and the dielectric permittivity locally close to fast-oscillating (with respect to some small parameter) periodic functions…

Mathematical Physics · Physics 2011-01-28 Alexey A. Pozharskii

Recent applications (e.g. active gels and self-assembly of elastic sheets) motivate the need to efficiently simulate the dynamics of thin elastic sheets. We present semi-implicit time stepping algorithms to improve the time step constraints…

Computational Physics · Physics 2019-10-23 Silas Alben , Alex A. Gorodetsky , Donghak Kim , Robert D. Deegan

In this paper we study the homogenization effects on the model of elastic plate in the bending regime, under the assumption that the energy density (material) oscillates in the direction of thickness. We study two different cases. First, we…

Analysis of PDEs · Mathematics 2014-10-09 Maroje Marohnic , Igor Velcic

In this article we present a novel method for studying the asymptotic behaviour, with order-sharp error estimates, of the resolvents of parameter-dependent operator families. The method is applied to the study of differential equations with…

Analysis of PDEs · Mathematics 2017-06-05 Shane Cooper , Marcus Waurick

This contribution presents an asymptotic formulation for the stick-slip behaviour of incomplete contacts under oscillatory variation of normal load, moment, shear load and differential bulk tension. The asymptotic description allows us not…

Soft Condensed Matter · Physics 2021-03-30 Hendrik Andresen , Rodolfo M. N. Fleury , Matthew R. Moore , David A. Hills

We study the asymptotic behaviour, as the small parameter $\varepsilon$ tends to zero, of the resolvents of uniformly elliptic second-order differential operators with locally periodic coefficients depending on the slow variable $x$ and the…

Analysis of PDEs · Mathematics 2020-01-09 Svetlana Pastukhova

We present an operator-asymptotic approach to the problem of homogenization of periodic composite media in the setting of three-dimensional linearized elasticity. This is based on a uniform approximation with respect to the inverse…

Analysis of PDEs · Mathematics 2024-12-11 Yi-Sheng Lim , Josip Žubrinić