On nonconservativeness of Eringen's nonlocal elasticity in beam mechanics: correction from a discrete-based approach

N Challamel, Z Zhang, CM Wang, JN Reddy… - Archive of Applied …, 2014 - Springer
In this paper, the self-adjointness of Eringen's nonlocal elasticity is investigated based on
simple one-dimensional beam models. It is shown that Eringen's model may be nonself …

[BOOK][B] Fractional dynamics on networks and lattices

T Michelitsch, AP Riascos, B Collet, A Nowakowski… - 2019 - books.google.com
This book analyzes stochastic processes on networks and regular structures such as lattices
by employing the Markovian random walk approach. Part 1 is devoted to the study of local …

Dispersive propagation of localized waves in a mass-in-mass metamaterial lattice

AV Porubov, AM Krivtsov - Continuum Mechanics and Thermodynamics, 2022 - Springer
Linear localized waves evolution in a discrete mass-in-mass lattice is studied. The presence
of the attached mass in the model contributes to dispersion giving rise to appearance of both …

Random walks with long-range steps generated by functions of Laplacian matrices

AP Riascos, TM Michelitsch, BA Collet… - Journal of Statistical …, 2018 - iopscience.iop.org
In this paper, we explore different Markovian random walk strategies on networks with
transition probabilities between nodes defined in terms of functions of the Laplacian matrix …

Fractional random walk lattice dynamics

TM Michelitsch, BA Collet, AP Riascos… - Journal of Physics A …, 2017 - iopscience.iop.org
We analyze time-discrete and time-continuous' fractional'random walks on undirected
regular networks with special focus on cubic periodic lattices in n= 1, 2, 3,.. dimensions. The …

Continuum model of acoustic metamaterials with diatomic crystal lattice

Y Zhou, P Wei, Y Li, Q Tang - Mechanics of Advanced Materials …, 2017 - Taylor & Francis
The continuum model of one-dimensional acoustic metamaterial with diatomic crystal lattice
is studied in this article. First, the dispersive relation of lattice wave in one-dimensional …

On the fundamental solution of the heat transfer problem in one-dimensional harmonic crystals

OS Loboda, EA Podolskaya, DV Tsvetkov… - Continuum Mechanics …, 2021 - Springer
The work is devoted to the description of unsteady thermal processes in low-dimensional
structures. To obtain the relationship between the microscopic and macroscopic descriptions …

Two-dimensional waves in extended square lattice

AV Porubov, AM Krivtsov, AE Osokina - International Journal of Non-Linear …, 2018 - Elsevier
We consider a two-dimensional square lattice model extended by additional not closed
neighboring interactions. We assume the elastic forces between the masses in the lattice to …

Non-linear plane waves in materials having hexagonal internal structure

AV Porubov, IE Berinskii - International Journal of Non-Linear Mechanics, 2014 - Elsevier
Three different continuum limits for modeling non-linear plane waves in two-dimensional
hexagonal lattice are obtained. New coupled non-linear continuum equations are obtained …

Analysis of dynamic failure of the discrete chain structure with non‐local interactions

N Gorbushin, G Mishuris - Mathematical Methods in the …, 2017 - Wiley Online Library
In the present work, the steady‐state crack propagation in a chain of oscillators with non‐
local interactions is considered. The interactions are modelled as linear springs, while the …