Operator-norm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast

Kirill Cherednichenko; Igor Velčić; Josip Žubrinić

doi:10.1007/s00526-023-02478-7

Operator-norm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast

Kirill Cherednichenko, Igor Velčić, Josip Žubrinić

University of Zagreb

Research output: Contribution to journal › Article › peer-review

Abstract

We provide resolvent asymptotics as well as various operator-norm estimates for the system of linear partial differential equations describing thin infinite elastic rods with material coefficients that rapidly oscillate along the rod. The resolvent asymptotics is derived simultaneously with respect to the rod thickness and the period of material oscillations, which are taken to be of the same order. The analysis is carried out separately on two invariant subspaces pertaining to the out-of-line and in-line displacements, under the assumption on material symmetries as well as in the general case when these two types of displacements are intertwined.

Original language	English
Article number	147
Number of pages	72
Journal	Calculus of Variations and Partial Differential Equations
Volume	62
Issue number	5
Early online date	12 May 2023
DOIs	https://doi.org/10.1007/s00526-023-02478-7
Publication status	Published - 1 Jun 2023

Bibliographical note

Funding:
KC is grateful for the support of the Engineering and Physical Sciences Research Council (EPSRC): Grant EP/L018802/2 “Mathematical foundations of metamaterials: homogenisation, dissipation and operator theory”. IV and JˇZ have been supported by the Croatian Science Foundation under Grant agreement No. 9477 (MAMPITCoStruFl) and Grant agreement No. IP-2018-01-8904 (Homdirestroptcm). JˇZ is also supported by the Ministry of Science and Higher Education of the Russian Federation, agreement 075-15-2019-1620 date 08/11/2019.

Data availability:
Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.

Keywords

math.AP
35P15, 35C20, 74B05, 74Q05, 74K10

Access to Document

10.1007/s00526-023-02478-7Licence: CC BY

https://arxiv.org/abs/2112.06265?context=math

Cite this

@article{ba09f32f9b7742faa1b87083baec5431,

title = "Operator-norm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast",

abstract = "We provide resolvent asymptotics as well as various operator-norm estimates for the system of linear partial differential equations describing thin infinite elastic rods with material coefficients that rapidly oscillate along the rod. The resolvent asymptotics is derived simultaneously with respect to the rod thickness and the period of material oscillations, which are taken to be of the same order. The analysis is carried out separately on two invariant subspaces pertaining to the out-of-line and in-line displacements, under the assumption on material symmetries as well as in the general case when these two types of displacements are intertwined.",

keywords = "math.AP, 35P15, 35C20, 74B05, 74Q05, 74K10",

author = "Kirill Cherednichenko and Igor Vel{\v c}i{\'c} and Josip {\v Z}ubrini{\'c}",

note = "Funding: KC is grateful for the support of the Engineering and Physical Sciences Research Council (EPSRC): Grant EP/L018802/2 “Mathematical foundations of metamaterials: homogenisation, dissipation and operator theory”. IV and JˇZ have been supported by the Croatian Science Foundation under Grant agreement No. 9477 (MAMPITCoStruFl) and Grant agreement No. IP-2018-01-8904 (Homdirestroptcm). JˇZ is also supported by the Ministry of Science and Higher Education of the Russian Federation, agreement 075-15-2019-1620 date 08/11/2019. Data availability: Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.",

year = "2023",

month = jun,

day = "1",

doi = "10.1007/s00526-023-02478-7",

language = "English",

volume = "62",

journal = "Calculus of Variations and Partial Differential Equations",

issn = "0944-2669",

publisher = "Springer New York",

number = "5",

}

TY - JOUR

T1 - Operator-norm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast

AU - Cherednichenko, Kirill

AU - Velčić, Igor

AU - Žubrinić, Josip

N1 - Funding: KC is grateful for the support of the Engineering and Physical Sciences Research Council (EPSRC): Grant EP/L018802/2 “Mathematical foundations of metamaterials: homogenisation, dissipation and operator theory”. IV and JˇZ have been supported by the Croatian Science Foundation under Grant agreement No. 9477 (MAMPITCoStruFl) and Grant agreement No. IP-2018-01-8904 (Homdirestroptcm). JˇZ is also supported by the Ministry of Science and Higher Education of the Russian Federation, agreement 075-15-2019-1620 date 08/11/2019. Data availability: Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.

PY - 2023/6/1

Y1 - 2023/6/1

N2 - We provide resolvent asymptotics as well as various operator-norm estimates for the system of linear partial differential equations describing thin infinite elastic rods with material coefficients that rapidly oscillate along the rod. The resolvent asymptotics is derived simultaneously with respect to the rod thickness and the period of material oscillations, which are taken to be of the same order. The analysis is carried out separately on two invariant subspaces pertaining to the out-of-line and in-line displacements, under the assumption on material symmetries as well as in the general case when these two types of displacements are intertwined.

AB - We provide resolvent asymptotics as well as various operator-norm estimates for the system of linear partial differential equations describing thin infinite elastic rods with material coefficients that rapidly oscillate along the rod. The resolvent asymptotics is derived simultaneously with respect to the rod thickness and the period of material oscillations, which are taken to be of the same order. The analysis is carried out separately on two invariant subspaces pertaining to the out-of-line and in-line displacements, under the assumption on material symmetries as well as in the general case when these two types of displacements are intertwined.

KW - math.AP

KW - 35P15, 35C20, 74B05, 74Q05, 74K10

UR - http://www.scopus.com/inward/record.url?scp=85159946399&partnerID=8YFLogxK

U2 - 10.1007/s00526-023-02478-7

DO - 10.1007/s00526-023-02478-7

M3 - Article

SN - 0944-2669

VL - 62

JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 5

M1 - 147

ER -

Operator-norm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Collaborative research visit by Josip Žubrinic (University of Zagreb)

Support of collaborative research with Dr I Velcic (University of Zagreb) Croatia

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

Cite this

Operator-norm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Collaborative research visit by Josip Žubrinic (University of Zagreb)

Support of collaborative research with Dr I Velcic (University of Zagreb) Croatia

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

Cite this