Identification of non-local continua for lattice-like materials
نویسندگان
چکیده
The paper is focused on the dynamic homogenization of lattice-like materials with lumped mass at nodes to obtain energetically consistent models providing accurate descriptions acoustic behavior discrete system. equation motion Lagrangian one-dimensional lattice transformed according a unitary approach aimed identify equivalent non-local continuum integral-differential and gradient type, latter obtained through standard or enhanced continualization. bilateral Z-transform difference lattice, mapped unit circle, matched governing in Fourier space, which has same frequency band structure as one. Firstly, it shown that approximation kernels via Taylor polynomials leads differential field equations higher order continua endowed constitutive terms. derived from such corresponds ones so called However, problem turns out be ill-posed because non-positive definiteness potential energy density continuum. Energetically have been identified proper mapping correlating macro-displacements space new auxiliary regularizing macro-displacement space. Specifically, here introduced zeros edge first Brillouin zone. corresponding one reformulated an continualization, characterized by inertial non-localities. Here, exhibit polar singularities proposed generalized way two-dimensional lattices using multidimensional Z- transforms, procedure may easily extended three-dimensional lattices. Finally, two examples systems consisting periodic pre-stressed cable-nets point are analyzed. resulting provide dispersion curves who excellent agreement those systems.
منابع مشابه
A dynamic lattice model for heterogeneous materials
In this paper, the mechanical behavior of three-phase inhomogeneous materials is modeled using the meso-scale model with lattice beams for static and dynamic analyses. The Timoshenko beam theory is applied instead of the classical Euler-Bernoulli beam theory and the mechanical properties of lattice beam connection are derived based on the continuum medium using the non-local continuum theory. T...
متن کاملa dynamic lattice model for heterogeneous materials
in this paper, the mechanical behavior of three-phase inhomogeneous materials is modeled using the meso-scale model with lattice beams for static and dynamic analyses. the timoshenko beam theory is applied instead of the classical euler-bernoulli beam theory and the mechanical properties of lattice beam connection are derived based on the continuum medium using the non-local continuum theory. t...
متن کاملThe fixed point property for arc component preserving mappings of non-metric tree-like continua
The main purpose of this paper is to study the fixed point property of non-metric tree-like continua. Using the inverse systems method, it is proved that if X is a non-metric tree-like continuum and if f : X → X is a mapping which sends each arc component into itself, then f has the fixed point property.
متن کاملNon Local Interaction in the Kondo Lattice
A Kondo lattice has been obtained applying the Schrieffer-Wolff transformation [I] on an Anderson lattice, keeping the term corresponding to non-local Kondo interaction. Using the Integral Functional method, proposed by Lacroix and Cyrot [2], we study the influence of that interaction on the phase diagram of the Kondo lattice, restricted to the nearest neighbour case. Introduction H* = Jl C ( f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Engineering Science
سال: 2021
ISSN: ['1879-2197', '0020-7225']
DOI: https://doi.org/10.1016/j.ijengsci.2020.103430