A meshless collocation method for band structure simulation of nanoscale phononic crystals based on nonlocal elasticity theory

•A meshfree LRBFCM based on the nonlocal elasticity theory is developed for wave propagation analysis in nanoscale phononic crystals.•The band structures of 1D nanoscale phononic crystals obtained by the LRBFCM agree well with the reference results.•The band structures and transmission coefficients...

Full description

Saved in:

Bibliographic Details
Published in:	Journal of computational physics Vol. 408; p. 109268
Main Authors:	Zheng, Hui, Zhou, Chuanbing, Yan, Dong-Jia, Wang, Yue-Sheng, Zhang, Chuanzeng
Format:	Journal Article
Language:	English
Published:	Cambridge Elsevier Inc 01.05.2020 Elsevier Science Ltd
Subjects:	Band structure of solids Band structures Collocation methods Computational physics Crystal structure Elastic waves First principles Mathematical analysis Meshless methods Nanoscale phononic crystals Nonlocal elasticity Nonlocal elasticity theory Periodic structures Radial basis function Radial basis functions Transfer matrices Band structures Nanoscale phononic crystals Radial basis functions Elastic waves Nonlocal elasticity theory
ISSN:	0021-9991, 1090-2716
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	•A meshfree LRBFCM based on the nonlocal elasticity theory is developed for wave propagation analysis in nanoscale phononic crystals.•The band structures of 1D nanoscale phononic crystals obtained by the LRBFCM agree well with the reference results.•The band structures and transmission coefficients of elastic waves in 2D nanoscale phononic crystals are computed and analyzed by the LRBFCM. In this paper, the band structures of nanoscale phononic crystals based on the nonlocal elasticity theory are calculated by using a meshfree local radial basis function collocation method (LRBFCM). The direct method is applied to enhance the stability of the derivative calculations in the LRBFCM. A simple summation in the LRBFCM is proposed to deal with the integration related to the nonlocal stresses or tractions. The LRBFCM for the band structure calculations is validated by the results obtained with the first-principle and the transfer matrix (TM) method for one-dimensional (1D) phononic crystals, as well as the comparison of the frequency responses of the two-dimensional (2D) periodic structures.
AbstractList	In this paper, the band structures of nanoscale phononic crystals based on the nonlocal elasticity theory are calculated by using a meshfree local radial basis function collocation method (LRBFCM). The direct method is applied to enhance the stability of the derivative calculations in the LRBFCM. A simple summation in the LRBFCM is proposed to deal with the integration related to the nonlocal stresses or tractions. The LRBFCM for the band structure calculations is validated by the results obtained with the first-principle and the transfer matrix (TM) method for one-dimensional (1D) phononic crystals, as well as the comparison of the frequency responses of the two-dimensional (2D) periodic structures. •A meshfree LRBFCM based on the nonlocal elasticity theory is developed for wave propagation analysis in nanoscale phononic crystals.•The band structures of 1D nanoscale phononic crystals obtained by the LRBFCM agree well with the reference results.•The band structures and transmission coefficients of elastic waves in 2D nanoscale phononic crystals are computed and analyzed by the LRBFCM. In this paper, the band structures of nanoscale phononic crystals based on the nonlocal elasticity theory are calculated by using a meshfree local radial basis function collocation method (LRBFCM). The direct method is applied to enhance the stability of the derivative calculations in the LRBFCM. A simple summation in the LRBFCM is proposed to deal with the integration related to the nonlocal stresses or tractions. The LRBFCM for the band structure calculations is validated by the results obtained with the first-principle and the transfer matrix (TM) method for one-dimensional (1D) phononic crystals, as well as the comparison of the frequency responses of the two-dimensional (2D) periodic structures.
ArticleNumber	109268
Author	Zhang, Chuanzeng Zheng, Hui Yan, Dong-Jia Zhou, Chuanbing Wang, Yue-Sheng
Author_xml	– sequence: 1 givenname: Hui orcidid: 0000-0003-4644-2907 surname: Zheng fullname: Zheng, Hui organization: School of Civil Engineering and Architecture, Nanchang University, Nanchang 330000, China – sequence: 2 givenname: Chuanbing surname: Zhou fullname: Zhou, Chuanbing organization: School of Civil Engineering and Architecture, Nanchang University, Nanchang 330000, China – sequence: 3 givenname: Dong-Jia orcidid: 0000-0003-3053-0013 surname: Yan fullname: Yan, Dong-Jia email: yandongjia@tsinghua.edu.cn organization: Center for Mechanics and Materials, AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China – sequence: 4 givenname: Yue-Sheng surname: Wang fullname: Wang, Yue-Sheng organization: Department of Mechanics, Tianjin University, Tianjin 300350, China – sequence: 5 givenname: Chuanzeng surname: Zhang fullname: Zhang, Chuanzeng organization: Department of Civil Engineering, University of Siegen, Siegen D-57068, Germany
BookMark	eNp9kE1v4yAQhlHVSk3a_oDekPbsLNjGYO0pqvZLirSX9ozIeFCwiEkBr5TL_vYl9Z72kBMwep8Z5lmT2ylMSMgzZxvOePd53Ixw2tSsvrz7ulM3ZFUurKol727JirGaV33f83uyTmlkjCnRqhX5s6VHTAePKVEI3gcw2YWpFPMhDNSGSPdmGmjKcYY8R6TJHWe_hIKlk5lCAuORng6h_MkBhXhO2fhUwIQDLblSvzT2FL1J2YHLZ5oPGOL5kdzZEsWnf-cDefv29fXlR7X79f3ny3ZXQdPzXLWGKb63AkBIaS3IjvOByQbEnilj98Ji03StaYVSqKzqBauVGASXtutEjc0D-bT0PcXwPmPKegxznMpIXbctV0r2si0pvqQghpQiWn2K7mjiWXOmL5r1qItmfdGsF82Fkf8xZb0PPTka56-SXxYSy-K_HUadwOEEOLiIkPUQ3BX6L1Iqm9E
CitedBy_id	crossref_primary_10_1016_j_apm_2025_116325 crossref_primary_10_1088_1402_4896_ae00a7 crossref_primary_10_1063_5_0142534 crossref_primary_10_1016_j_apm_2025_115971 crossref_primary_10_1016_j_enganabound_2024_02_008 crossref_primary_10_1038_s41598_024_75049_1 crossref_primary_10_1016_j_aml_2022_108458 crossref_primary_10_1016_j_enganabound_2024_01_034 crossref_primary_10_1016_j_ijmecsci_2021_106711 crossref_primary_10_12693_APhysPolA_147_172 crossref_primary_10_1016_j_enganabound_2023_06_016 crossref_primary_10_1016_j_tws_2023_111316 crossref_primary_10_1016_j_cam_2025_117074 crossref_primary_10_1177_10812865221098352 crossref_primary_10_1063_5_0180143 crossref_primary_10_1016_j_jcmds_2022_100038 crossref_primary_10_1016_j_jcp_2025_114013 crossref_primary_10_1142_S0217984924501689 crossref_primary_10_3390_nano12071080 crossref_primary_10_1016_j_jcp_2023_112556 crossref_primary_10_1155_2021_6694369 crossref_primary_10_1016_j_fuel_2022_125908 crossref_primary_10_1016_j_ijmecsci_2022_107100 crossref_primary_10_1016_j_aml_2025_109463 crossref_primary_10_1108_EC_09_2020_0516 crossref_primary_10_1155_2020_8832197 crossref_primary_10_1007_s10483_023_2945_6 crossref_primary_10_1140_epjs_s11734_025_01559_2 crossref_primary_10_1007_s00366_021_01379_7 crossref_primary_10_1016_j_apm_2023_09_002 crossref_primary_10_1016_j_tws_2022_109982 crossref_primary_10_1016_j_enganabound_2022_01_003 crossref_primary_10_3390_math10050773 crossref_primary_10_3390_cryst11121457 crossref_primary_10_32604_cmes_2022_019715 crossref_primary_10_1016_j_advengsoft_2020_102888 crossref_primary_10_1016_j_camwa_2022_11_007
Cites_doi	10.1103/PhysRevB.69.094301 10.1103/PhysRevB.76.104304 10.1016/j.jsv.2009.06.009 10.4208/nmtma.2017-OA-0100 10.1016/j.physleta.2004.05.030 10.1016/j.cam.2017.06.011 10.1108/09615530610669148 10.1016/j.jcp.2015.10.020 10.1002/nme.5366 10.1016/j.enganabound.2019.03.042 10.1002/mma.3294 10.1016/j.ijmecsci.2018.04.054 10.1016/0898-1221(90)90270-T 10.1063/1.110940 10.1016/j.enganabound.2010.03.003 10.1103/PhysRevB.60.11993 10.1063/1.2043242 10.1103/PhysRevLett.71.2022 10.1016/j.jcp.2011.03.010 10.1007/s10483-013-1732-6 10.1016/j.ultras.2015.10.006 10.1016/0020-7225(72)90039-0 10.1016/j.jcp.2016.12.008 10.1016/j.jcp.2019.03.017 10.1016/j.jcp.2017.01.065 10.4208/cicp.OA-2018-0182 10.1063/1.332803 10.1016/j.physe.2011.08.032 10.1002/nme.5351 10.1016/j.enganabound.2016.01.012 10.1007/s10409-012-0092-9 10.1016/j.jcp.2005.05.030 10.1016/j.camwa.2006.04.013 10.1016/j.apm.2018.03.023 10.7498/aps.52.1943 10.1016/j.wavemoti.2012.12.001 10.1007/s11433-007-0056-4
ContentType	Journal Article
Copyright	2020 Elsevier Inc. Copyright Elsevier Science Ltd. May 1, 2020
Copyright_xml	– notice: 2020 Elsevier Inc. – notice: Copyright Elsevier Science Ltd. May 1, 2020
DBID	AAYXX CITATION 7SC 7SP 7U5 8FD JQ2 L7M L~C L~D
DOI	10.1016/j.jcp.2020.109268
DatabaseName	CrossRef Computer and Information Systems Abstracts Electronics & Communications Abstracts Solid State and Superconductivity Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional
DatabaseTitle	CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Solid State and Superconductivity Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional
DatabaseTitleList	Technology Research Database
DeliveryMethod	fulltext_linktorsrc
Discipline	Applied Sciences
EISSN	1090-2716
ExternalDocumentID	10_1016_j_jcp_2020_109268 S0021999120300425
GroupedDBID	--K --M -~X .~1 0R~ 1B1 1RT 1~. 1~5 4.4 457 4G. 5GY 5VS 6OB 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAXUO AAYFN ABBOA ABFRF ABJNI ABMAC ABNEU ABYKQ ACBEA ACDAQ ACFVG ACGFO ACGFS ACNCT ACRLP ACZNC ADBBV ADEZE AEBSH AEFWE AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHZHX AIALX AIEXJ AIKHN AITUG AIVDX AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD AXJTR BKOJK BLXMC CS3 DM4 DU5 EBS EFBJH EFLBG EO8 EO9 EP2 EP3 F5P FDB FEDTE FIRID FNPLU FYGXN G-Q GBLVA GBOLZ HLZ HVGLF IHE J1W K-O KOM LG5 LX9 LZ4 M37 M41 MO0 N9A O-L O9- OAUVE OGIMB OZT P-8 P-9 P2P PC. Q38 RNS ROL RPZ SDF SDG SDP SES SPC SPCBC SPD SSQ SSV SSZ T5K TN5 UPT YQT ZMT ZU3 ~02 ~G- 29K 6TJ 8WZ 9DU A6W AAQXK AATTM AAXKI AAYWO AAYXX ABFNM ABWVN ABXDB ACLOT ACNNM ACRPL ACVFH ADCNI ADFGL ADIYS ADJOM ADMUD ADNMO AEIPS AEUPX AFFNX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP ASPBG AVWKF AZFZN BBWZM CAG CITATION COF D-I EFKBS EJD FGOYB G-2 HME HMV HZ~ NDZJH R2- SBC SEW SHN SPG T9H UQL WUQ ZY4 ~HD 7SC 7SP 7U5 8FD JQ2 L7M L~C L~D
ID	FETCH-LOGICAL-c391t-4a081bf5cc577ffc7611d073c5b08afb5fe3364a4588e8f8950285d517f6652e3
ISICitedReferencesCount	45
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000521731200006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0021-9991
IngestDate	Sun Nov 30 03:58:18 EST 2025 Sat Nov 29 03:10:27 EST 2025 Tue Nov 18 22:06:19 EST 2025 Fri Feb 23 02:48:04 EST 2024
IsPeerReviewed	true
IsScholarly	true
Keywords	Band structures Nanoscale phononic crystals Radial basis functions Elastic waves Nonlocal elasticity theory
Language	English
LinkModel	OpenURL
MergedId	FETCHMERGED-LOGICAL-c391t-4a081bf5cc577ffc7611d073c5b08afb5fe3364a4588e8f8950285d517f6652e3
Notes	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ORCID	0000-0003-3053-0013 0000-0003-4644-2907
PQID	2441887974
PQPubID	2047462
ParticipantIDs	proquest_journals_2441887974 crossref_primary_10_1016_j_jcp_2020_109268 crossref_citationtrail_10_1016_j_jcp_2020_109268 elsevier_sciencedirect_doi_10_1016_j_jcp_2020_109268
PublicationCentury	2000
PublicationDate	2020-05-01 2020-05-00 20200501
PublicationDateYYYYMMDD	2020-05-01
PublicationDate_xml	– month: 05 year: 2020 text: 2020-05-01 day: 01
PublicationDecade	2020
PublicationPlace	Cambridge
PublicationPlace_xml	– name: Cambridge
PublicationTitle	Journal of computational physics
PublicationYear	2020
Publisher	Elsevier Inc Elsevier Science Ltd
Publisher_xml	– name: Elsevier Inc – name: Elsevier Science Ltd
References	Shi, Wang, Zhang (br0210) 2013; 34 Yan, Wang (br0200) 2007; 50 Zhen, Li, Wang, Zhang (br0230) 2012; 28 Zheng, Zhang, Bi, Gao, Du, Chen (br0180) 2017; 110 Li, Wang, Zhang, Yu (br0160) 2013; 50 Zheng, Bi, Zhang, Zhang, Chen (br0170) 2019; 104 Sarler, Vertnik (br0290) 2006; 51 Vertnik, Sarler (br0300) 2006; 16 Assari, Dehghan (br0420) 2018; 11 Kafesaki, Economou (br0150) 1999; 60 Wang, Zheng, Xin, Shi (br0250) 2018; 10 Wu, Huang, Lin (br0120) 2004; 69 Shelvean, Peter (br0240) 2018; 327 Ibach, Luth (br0380) 1995 Wright, Fornberg (br0280) 2006; 212 Martin, Fornberg (br0320) 2017; 335 Tsai, Kolibal, Li (br0390) 2010; 34 Eringen (br0080) 1998 Hart, Cox, Djidjeli (br0330) 2011; 230 Zheng, Yang, Zhang, Mark (br0370) 2018; 60 Kushwaha, Halevi, Dobrzynski, Djafarirouhani (br0010) 1993; 71 Shi, Wang, Zhang (br0220) 2014; 38 Kansa (br0260) 1990; 19 Li, Ling (br0410) 2019; 26 Eringen (br0040) 1983; 54 Zheng, Zhang, Wang, Sladek, Sladek (br0340) 2016; 305 Kushwaha, Halevi (br0020) 1994; 64 Chen, Yan, Wang, Zhang (br0090) 2016; 65 Zheng, Zhang, Wang, Sladek, Sladek (br0350) 2016; 66 Chen, Wang (br0050) 2011; 44 Eringen (br0070) 2002 Sun, Wu (br0140) 2007; 76 Fasshauer (br0270) 2007 Ramprasad, Shi (br0060) 2005; 87 Bayona, Flyer, Fornberg, Barnett (br0310) 2017; 332 Zheng, Zhang, Wang, Chen, Sladek, Sladek (br0360) 2017; 110 Cao, Hou, Liu (br0110) 2004; 327 Yan, Chen, Wang, Zhang, Golub (br0100) 2018; 142–143 Eringen, Edelen (br0030) 1972; 10 Wang, Wen, Han, Zhao (br0130) 2003; 52 Chen, Karageorghis (br0400) 2019; 25 Yan, Zhang, Wang (br0190) 2009; 327 Eringen (10.1016/j.jcp.2020.109268_br0070) 2002 Hart (10.1016/j.jcp.2020.109268_br0330) 2011; 230 Chen (10.1016/j.jcp.2020.109268_br0050) 2011; 44 Eringen (10.1016/j.jcp.2020.109268_br0080) 1998 Shi (10.1016/j.jcp.2020.109268_br0210) 2013; 34 Ramprasad (10.1016/j.jcp.2020.109268_br0060) 2005; 87 Fasshauer (10.1016/j.jcp.2020.109268_br0270) 2007 Chen (10.1016/j.jcp.2020.109268_br0090) 2016; 65 Tsai (10.1016/j.jcp.2020.109268_br0390) 2010; 34 Sarler (10.1016/j.jcp.2020.109268_br0290) 2006; 51 Eringen (10.1016/j.jcp.2020.109268_br0030) 1972; 10 Ibach (10.1016/j.jcp.2020.109268_br0380) 1995 Kansa (10.1016/j.jcp.2020.109268_br0260) 1990; 19 Shelvean (10.1016/j.jcp.2020.109268_br0240) 2018; 327 Wang (10.1016/j.jcp.2020.109268_br0250) 2018; 10 Kushwaha (10.1016/j.jcp.2020.109268_br0020) 1994; 64 Yan (10.1016/j.jcp.2020.109268_br0200) 2007; 50 Kushwaha (10.1016/j.jcp.2020.109268_br0010) 1993; 71 Vertnik (10.1016/j.jcp.2020.109268_br0300) 2006; 16 Zheng (10.1016/j.jcp.2020.109268_br0340) 2016; 305 Eringen (10.1016/j.jcp.2020.109268_br0040) 1983; 54 Yan (10.1016/j.jcp.2020.109268_br0100) 2018; 142–143 Shi (10.1016/j.jcp.2020.109268_br0220) 2014; 38 Zheng (10.1016/j.jcp.2020.109268_br0360) 2017; 110 Cao (10.1016/j.jcp.2020.109268_br0110) 2004; 327 Li (10.1016/j.jcp.2020.109268_br0160) 2013; 50 Wright (10.1016/j.jcp.2020.109268_br0280) 2006; 212 Martin (10.1016/j.jcp.2020.109268_br0320) 2017; 335 Wang (10.1016/j.jcp.2020.109268_br0130) 2003; 52 Assari (10.1016/j.jcp.2020.109268_br0420) 2018; 11 Zheng (10.1016/j.jcp.2020.109268_br0370) 2018; 60 Kafesaki (10.1016/j.jcp.2020.109268_br0150) 1999; 60 Yan (10.1016/j.jcp.2020.109268_br0190) 2009; 327 Li (10.1016/j.jcp.2020.109268_br0410) 2019; 26 Zheng (10.1016/j.jcp.2020.109268_br0180) 2017; 110 Zheng (10.1016/j.jcp.2020.109268_br0350) 2016; 66 Wu (10.1016/j.jcp.2020.109268_br0120) 2004; 69 Sun (10.1016/j.jcp.2020.109268_br0140) 2007; 76 Zhen (10.1016/j.jcp.2020.109268_br0230) 2012; 28 Zheng (10.1016/j.jcp.2020.109268_br0170) 2019; 104 Bayona (10.1016/j.jcp.2020.109268_br0310) 2017; 332 Chen (10.1016/j.jcp.2020.109268_br0400) 2019; 25
References_xml	– volume: 64 start-page: 1085 year: 1994 end-page: 1087 ident: br0020 article-title: Band-gap engineering in periodic elastic composites publication-title: Appl. Phys. Lett. – year: 1998 ident: br0080 article-title: Microcontinuum Field Theories – volume: 69 year: 2004 ident: br0120 article-title: Surface and bulk acoustic waves in two-dimensional phononic crystal consisting of materials with general anisotropy publication-title: Phys. Rev. B – volume: 66 start-page: 77 year: 2016 end-page: 90 ident: br0350 article-title: Band structure computation of in-plane elastic waves in 2D phononic crystals by a meshfree local RBF collocation method publication-title: Eng. Anal. Bound. Elem. – volume: 50 start-page: 525 year: 2013 end-page: 541 ident: br0160 article-title: Bandgap calculations of two-dimensional solid-fluid phononic crystals with the boundary element method publication-title: Wave Motion – year: 1995 ident: br0380 article-title: Solid-State Physics – volume: 332 start-page: 257 year: 2017 end-page: 273 ident: br0310 article-title: On the role of polynomials in RBF-FD approximations, II: numerical solution of elliptic PDEs publication-title: J. Comput. Phys. – volume: 60 start-page: 447 year: 2018 end-page: 459 ident: br0370 article-title: A local radial basis function collocation method for band structure computation of phononic crystals with scatterers of arbitrary geometry publication-title: Appl. Math. Model. – volume: 16 start-page: 617 year: 2006 end-page: 640 ident: br0300 article-title: Meshless local radial basis function collocation method for convective-diffusive solid-liquid phase change problems publication-title: Int. J. Numer. Methods Heat Fluid Flow – volume: 10 start-page: 233 year: 1972 end-page: 248 ident: br0030 article-title: On nonlocal elasticity publication-title: Int. J. Eng. Sci. – volume: 230 start-page: 4910 year: 2011 end-page: 4921 ident: br0330 article-title: Compact RBF meshless methods for photonic crystal modelling publication-title: J. Comput. Phys. – year: 2002 ident: br0070 article-title: Nonlocal Continuum Field Theories – volume: 34 start-page: 1123 year: 2013 end-page: 1144 ident: br0210 article-title: Band structure calculation of scalar waves in two-dimensional phononic crystals based on generalized multipole technique publication-title: Appl. Math. Mech.-Engl. – volume: 327 start-page: 247 year: 2004 end-page: 253 ident: br0110 article-title: Convergence problem of plane-wave expansion method for phononic crystals publication-title: Phys. Lett. A – volume: 76 year: 2007 ident: br0140 article-title: Propagation of acoustic waves in phononic-crystal plates and waveguides using a finite-difference time-domain method publication-title: Phys. Rev. B – volume: 305 start-page: 997 year: 2016 end-page: 1014 ident: br0340 article-title: A meshfree local RBF collocation method for anti-plane transverse elastic wave propagation analysis in 2D phononic crystals publication-title: J. Comput. Phys. – volume: 44 start-page: 317 year: 2011 end-page: 321 ident: br0050 article-title: Size-effect on band structures of nanoscale phononic crystals publication-title: Physica E – volume: 335 start-page: 828 year: 2017 end-page: 845 ident: br0320 article-title: Seismic modeling with radial basis function-generated finite differences (RBF-FD) - a simplified treatment of interfaces publication-title: J. Comput. Phys. – volume: 52 start-page: 1943 year: 2003 end-page: 1947 ident: br0130 article-title: Finite difference time domain method for the study of band gap in two-dimensional phononic crystals publication-title: Acta Phys. Sin. – volume: 60 start-page: 11993 year: 1999 end-page: 12001 ident: br0150 article-title: Multiple-scattering theory for three-dimensional periodic acoustic composites publication-title: Phys. Rev. B – volume: 38 start-page: 3246 year: 2014 end-page: 3263 ident: br0220 article-title: Application of the generalized multipole technique in band structure calculation of two-dimensional solid/fluid phononic crystals publication-title: Math. Methods Appl. Sci. – volume: 10 start-page: 136 year: 2018 end-page: 150 ident: br0250 article-title: A Petrov-Galerkin finite element interface method for interface problems with Bloch-periodic boundary conditions and its application in phononic crystals publication-title: J. Comput. Phys. – volume: 26 start-page: 785 year: 2019 end-page: 808 ident: br0410 article-title: Collocation methods for Cauchy problems of elliptic operators via conditional stabilities publication-title: Commun. Comput. Phys. – volume: 54 start-page: 4703 year: 1983 end-page: 4710 ident: br0040 article-title: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves publication-title: J. Appl. Phys. – volume: 28 start-page: 1143 year: 2012 end-page: 1153 ident: br0230 article-title: Bandgap calculation for mixed in-plane waves in 2D phononic crystals based on Dirichlet-to-Neumann map publication-title: Acta Mech. Sin. - PRC – year: 2007 ident: br0270 article-title: Meshfree Approximations with MATLAB – volume: 51 start-page: 1269 year: 2006 end-page: 1282 ident: br0290 article-title: Meshfree explicit local radial basis function collocation method for diffusion problems publication-title: Comput. Math. Appl. – volume: 11 start-page: 540 year: 2018 end-page: 568 ident: br0420 article-title: A meshless discrete Galerkin method based on the free shape parameter radial basis functions for solving Hammerstein integral equation publication-title: Numer. Math. Theor. Methods Appl. – volume: 104 start-page: 170 year: 2019 end-page: 182 ident: br0170 article-title: Fictitious eigenfrequencies in the BEM for interior acoustic problems publication-title: Eng. Anal. Bound. Elem. – volume: 34 start-page: 738 year: 2010 end-page: 746 ident: br0390 article-title: The golden section search algorithm for finding a good shape parameter for meshless collocation methods publication-title: Eng. Anal. Bound. Elem. – volume: 87 year: 2005 ident: br0060 article-title: Scalability of phononic crystal heterostructures publication-title: Appl. Phys. Lett. – volume: 25 start-page: 41 year: 2019 end-page: 67 ident: br0400 article-title: Local RBF algorithms for elliptic boundary value problems in annular domains publication-title: Commun. Comput. Phys. – volume: 65 start-page: 154 year: 2016 end-page: 164 ident: br0090 article-title: Anti-plane transverse waves propagation in nanoscale periodic layered piezoelectric structures publication-title: Ultrasonics – volume: 19 start-page: 127 year: 1990 end-page: 145 ident: br0260 article-title: Multiquadrics – a scattered data approximation scheme with applications to computational fluid dynamics, I: surface approximations and partial derivative estimates publication-title: Comput. Math. Appl. – volume: 212 start-page: 99 year: 2006 end-page: 123 ident: br0280 article-title: Scattered node compact finite difference-type formulas generated from radial basis functions publication-title: J. Comput. Phys. – volume: 50 start-page: 622 year: 2007 end-page: 630 ident: br0200 article-title: Wavelet-based method for computing elastic band gaps of one-dimensional phononic crystals publication-title: Sci. China Ser. G – volume: 110 start-page: 163 year: 2017 end-page: 185 ident: br0180 article-title: Coupled FE-BE method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain publication-title: Int. J. Numer. Methods Eng. – volume: 142–143 start-page: 276 year: 2018 end-page: 288 ident: br0100 article-title: In-plane elastic wave propagation in nanoscale periodic layered piezoelectric structures publication-title: Int. J. Mech. Sci. – volume: 327 start-page: 109 year: 2009 end-page: 120 ident: br0190 article-title: Wave propagation and localization in randomly disordered layered composites with local resonances publication-title: J. Sound Vib. – volume: 327 start-page: 208 year: 2018 end-page: 225 ident: br0240 article-title: A plane wave discontinuous Galerkin method with a Dirichlet to Neumann boundary condition for the scattering problem in acoustics publication-title: J. Comput. Appl. Math. – volume: 110 start-page: 467 year: 2017 end-page: 500 ident: br0360 article-title: A local RBF collocation method for band structure computations of 2D solid/fluid and fluid/solid phononic crystals publication-title: Int. J. Numer. Methods Eng. – volume: 71 start-page: 2022 year: 1993 end-page: 2025 ident: br0010 article-title: Acoustic band-structure of periodic elastic composites publication-title: Phys. Rev. Lett. – volume: 69 issue: 9 year: 2004 ident: 10.1016/j.jcp.2020.109268_br0120 article-title: Surface and bulk acoustic waves in two-dimensional phononic crystal consisting of materials with general anisotropy publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.69.094301 – volume: 76 issue: 10 year: 2007 ident: 10.1016/j.jcp.2020.109268_br0140 article-title: Propagation of acoustic waves in phononic-crystal plates and waveguides using a finite-difference time-domain method publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.76.104304 – volume: 327 start-page: 109 issue: 1–2 year: 2009 ident: 10.1016/j.jcp.2020.109268_br0190 article-title: Wave propagation and localization in randomly disordered layered composites with local resonances publication-title: J. Sound Vib. doi: 10.1016/j.jsv.2009.06.009 – volume: 11 start-page: 540 year: 2018 ident: 10.1016/j.jcp.2020.109268_br0420 article-title: A meshless discrete Galerkin method based on the free shape parameter radial basis functions for solving Hammerstein integral equation publication-title: Numer. Math. Theor. Methods Appl. doi: 10.4208/nmtma.2017-OA-0100 – volume: 327 start-page: 247 issue: 2–3 year: 2004 ident: 10.1016/j.jcp.2020.109268_br0110 article-title: Convergence problem of plane-wave expansion method for phononic crystals publication-title: Phys. Lett. A doi: 10.1016/j.physleta.2004.05.030 – volume: 327 start-page: 208 year: 2018 ident: 10.1016/j.jcp.2020.109268_br0240 article-title: A plane wave discontinuous Galerkin method with a Dirichlet to Neumann boundary condition for the scattering problem in acoustics publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2017.06.011 – volume: 16 start-page: 617 issue: 5 year: 2006 ident: 10.1016/j.jcp.2020.109268_br0300 article-title: Meshless local radial basis function collocation method for convective-diffusive solid-liquid phase change problems publication-title: Int. J. Numer. Methods Heat Fluid Flow doi: 10.1108/09615530610669148 – year: 2002 ident: 10.1016/j.jcp.2020.109268_br0070 – volume: 305 start-page: 997 year: 2016 ident: 10.1016/j.jcp.2020.109268_br0340 article-title: A meshfree local RBF collocation method for anti-plane transverse elastic wave propagation analysis in 2D phononic crystals publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2015.10.020 – volume: 110 start-page: 467 year: 2017 ident: 10.1016/j.jcp.2020.109268_br0360 article-title: A local RBF collocation method for band structure computations of 2D solid/fluid and fluid/solid phononic crystals publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.5366 – volume: 104 start-page: 170 year: 2019 ident: 10.1016/j.jcp.2020.109268_br0170 article-title: Fictitious eigenfrequencies in the BEM for interior acoustic problems publication-title: Eng. Anal. Bound. Elem. doi: 10.1016/j.enganabound.2019.03.042 – volume: 38 start-page: 3246 issue: 15 year: 2014 ident: 10.1016/j.jcp.2020.109268_br0220 article-title: Application of the generalized multipole technique in band structure calculation of two-dimensional solid/fluid phononic crystals publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.3294 – year: 1995 ident: 10.1016/j.jcp.2020.109268_br0380 – year: 2007 ident: 10.1016/j.jcp.2020.109268_br0270 – volume: 142–143 start-page: 276 year: 2018 ident: 10.1016/j.jcp.2020.109268_br0100 article-title: In-plane elastic wave propagation in nanoscale periodic layered piezoelectric structures publication-title: Int. J. Mech. Sci. doi: 10.1016/j.ijmecsci.2018.04.054 – volume: 10 start-page: 136 issue: 4 year: 2018 ident: 10.1016/j.jcp.2020.109268_br0250 article-title: A Petrov-Galerkin finite element interface method for interface problems with Bloch-periodic boundary conditions and its application in phononic crystals publication-title: J. Comput. Phys. – volume: 19 start-page: 127 issue: 8–9 year: 1990 ident: 10.1016/j.jcp.2020.109268_br0260 article-title: Multiquadrics – a scattered data approximation scheme with applications to computational fluid dynamics, I: surface approximations and partial derivative estimates publication-title: Comput. Math. Appl. doi: 10.1016/0898-1221(90)90270-T – volume: 64 start-page: 1085 issue: 9 year: 1994 ident: 10.1016/j.jcp.2020.109268_br0020 article-title: Band-gap engineering in periodic elastic composites publication-title: Appl. Phys. Lett. doi: 10.1063/1.110940 – volume: 34 start-page: 738 year: 2010 ident: 10.1016/j.jcp.2020.109268_br0390 article-title: The golden section search algorithm for finding a good shape parameter for meshless collocation methods publication-title: Eng. Anal. Bound. Elem. doi: 10.1016/j.enganabound.2010.03.003 – volume: 60 start-page: 11993 year: 1999 ident: 10.1016/j.jcp.2020.109268_br0150 article-title: Multiple-scattering theory for three-dimensional periodic acoustic composites publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.60.11993 – volume: 87 year: 2005 ident: 10.1016/j.jcp.2020.109268_br0060 article-title: Scalability of phononic crystal heterostructures publication-title: Appl. Phys. Lett. doi: 10.1063/1.2043242 – volume: 71 start-page: 2022 issue: 13 year: 1993 ident: 10.1016/j.jcp.2020.109268_br0010 article-title: Acoustic band-structure of periodic elastic composites publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.71.2022 – volume: 230 start-page: 4910 issue: 12 year: 2011 ident: 10.1016/j.jcp.2020.109268_br0330 article-title: Compact RBF meshless methods for photonic crystal modelling publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2011.03.010 – volume: 34 start-page: 1123 issue: 9 year: 2013 ident: 10.1016/j.jcp.2020.109268_br0210 article-title: Band structure calculation of scalar waves in two-dimensional phononic crystals based on generalized multipole technique publication-title: Appl. Math. Mech.-Engl. doi: 10.1007/s10483-013-1732-6 – volume: 65 start-page: 154 year: 2016 ident: 10.1016/j.jcp.2020.109268_br0090 article-title: Anti-plane transverse waves propagation in nanoscale periodic layered piezoelectric structures publication-title: Ultrasonics doi: 10.1016/j.ultras.2015.10.006 – volume: 10 start-page: 233 year: 1972 ident: 10.1016/j.jcp.2020.109268_br0030 article-title: On nonlocal elasticity publication-title: Int. J. Eng. Sci. doi: 10.1016/0020-7225(72)90039-0 – volume: 332 start-page: 257 year: 2017 ident: 10.1016/j.jcp.2020.109268_br0310 article-title: On the role of polynomials in RBF-FD approximations, II: numerical solution of elliptic PDEs publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2016.12.008 – volume: 25 start-page: 41 year: 2019 ident: 10.1016/j.jcp.2020.109268_br0400 article-title: Local RBF algorithms for elliptic boundary value problems in annular domains publication-title: Commun. Comput. Phys. doi: 10.1016/j.jcp.2019.03.017 – volume: 335 start-page: 828 year: 2017 ident: 10.1016/j.jcp.2020.109268_br0320 article-title: Seismic modeling with radial basis function-generated finite differences (RBF-FD) - a simplified treatment of interfaces publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2017.01.065 – volume: 26 start-page: 785 year: 2019 ident: 10.1016/j.jcp.2020.109268_br0410 article-title: Collocation methods for Cauchy problems of elliptic operators via conditional stabilities publication-title: Commun. Comput. Phys. doi: 10.4208/cicp.OA-2018-0182 – volume: 54 start-page: 4703 year: 1983 ident: 10.1016/j.jcp.2020.109268_br0040 article-title: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves publication-title: J. Appl. Phys. doi: 10.1063/1.332803 – volume: 44 start-page: 317 year: 2011 ident: 10.1016/j.jcp.2020.109268_br0050 article-title: Size-effect on band structures of nanoscale phononic crystals publication-title: Physica E doi: 10.1016/j.physe.2011.08.032 – volume: 110 start-page: 163 year: 2017 ident: 10.1016/j.jcp.2020.109268_br0180 article-title: Coupled FE-BE method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.5351 – volume: 66 start-page: 77 year: 2016 ident: 10.1016/j.jcp.2020.109268_br0350 article-title: Band structure computation of in-plane elastic waves in 2D phononic crystals by a meshfree local RBF collocation method publication-title: Eng. Anal. Bound. Elem. doi: 10.1016/j.enganabound.2016.01.012 – volume: 28 start-page: 1143 issue: 4 year: 2012 ident: 10.1016/j.jcp.2020.109268_br0230 article-title: Bandgap calculation for mixed in-plane waves in 2D phononic crystals based on Dirichlet-to-Neumann map publication-title: Acta Mech. Sin. - PRC doi: 10.1007/s10409-012-0092-9 – volume: 212 start-page: 99 year: 2006 ident: 10.1016/j.jcp.2020.109268_br0280 article-title: Scattered node compact finite difference-type formulas generated from radial basis functions publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2005.05.030 – volume: 51 start-page: 1269 issue: 8 year: 2006 ident: 10.1016/j.jcp.2020.109268_br0290 article-title: Meshfree explicit local radial basis function collocation method for diffusion problems publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2006.04.013 – volume: 60 start-page: 447 year: 2018 ident: 10.1016/j.jcp.2020.109268_br0370 article-title: A local radial basis function collocation method for band structure computation of phononic crystals with scatterers of arbitrary geometry publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2018.03.023 – year: 1998 ident: 10.1016/j.jcp.2020.109268_br0080 – volume: 52 start-page: 1943 issue: 8 year: 2003 ident: 10.1016/j.jcp.2020.109268_br0130 article-title: Finite difference time domain method for the study of band gap in two-dimensional phononic crystals publication-title: Acta Phys. Sin. doi: 10.7498/aps.52.1943 – volume: 50 start-page: 525 issue: 3 year: 2013 ident: 10.1016/j.jcp.2020.109268_br0160 article-title: Bandgap calculations of two-dimensional solid-fluid phononic crystals with the boundary element method publication-title: Wave Motion doi: 10.1016/j.wavemoti.2012.12.001 – volume: 50 start-page: 622 issue: 5 year: 2007 ident: 10.1016/j.jcp.2020.109268_br0200 article-title: Wavelet-based method for computing elastic band gaps of one-dimensional phononic crystals publication-title: Sci. China Ser. G doi: 10.1007/s11433-007-0056-4
SSID	ssj0008548
Score	2.5080602
Snippet	•A meshfree LRBFCM based on the nonlocal elasticity theory is developed for wave propagation analysis in nanoscale phononic crystals.•The band structures of 1D... In this paper, the band structures of nanoscale phononic crystals based on the nonlocal elasticity theory are calculated by using a meshfree local radial basis...
SourceID	proquest crossref elsevier
SourceType	Aggregation Database Enrichment Source Index Database Publisher
StartPage	109268
SubjectTerms	Band structure of solids Band structures Collocation methods Computational physics Crystal structure Elastic waves First principles Mathematical analysis Meshless methods Nanoscale phononic crystals Nonlocal elasticity Nonlocal elasticity theory Periodic structures Radial basis function Radial basis functions Transfer matrices
Title	A meshless collocation method for band structure simulation of nanoscale phononic crystals based on nonlocal elasticity theory
URI	https://dx.doi.org/10.1016/j.jcp.2020.109268 https://www.proquest.com/docview/2441887974
Volume	408
WOSCitedRecordID	wos000521731200006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1090-2716 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0008548 issn: 0021-9991 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3Pb9MwFLbKxoELvxGDgXxAHKiMEidO4mMFncZUFSQ6qXCxEsfeWnVpWdppXPjH-Od4ju2kTGOCA5eocvNL-b689-X5PT-EXsVccprTBN5vWpCYBSUpdBKRJNe55nEuVdmsrj9Kx-NsOuWfer2fvhbmYpFWVXZ5yVf_FWoYA7BN6ew_wN2eFAbgN4AOW4Adtn8F_KB_purThbFgBuSljcm5VtE2O7MJljcLx5rpg3p25np4NVkdebWsATjVN1nrTX8cef4dNOSi7huXV5rpBRhvnGBfgfg2edkg5de-yv86sSub5hE-8GjDKa2a_3qqrMU53My6seXGpgNs8qrw_tWYJxuxfb-sTsjRrHMqLu79ZaPIZ3O-7XAGDbrkQRtj83U23rR1yU229iAkRtJa72VNdsADQlNbseltehxkW1Y5vNZX2LDF_O1cmnVLabOyFrU9fn5fl3v8URwcj0ZiMpxOXq--EdOyzEztu_4tt9AuTRkHk7o7-DCcHrVCIGOxFQLupv2kepNeeOWqf5JFVwRCo3om99FdhyAeWJo9QD1VPUT33KcLdk-vfoR-DLBnHd5iHbasw8A6bFiHW9bhjnV4qXHLOuxZhz3rcMM6DPt51uGOddiy7jE6PhhO3h0S19qDyIiHaxLnIEULzaRkaaq1TJMwLMHbSFYEWa4LplUUJXFu6qhVpjPOQAezkoWpThJGVfQE7cBF1VOEpda0SNIoZzGP41JxXphycKoVL_OwVHso8E9WSLfuvWm_shA-wXEuAAxhwBAWjD30pj1kZRd9uWnn2MMlnGq1alQA0W46bN9DK5z1qAVo7RC8PnzjP7v57-foTvfy7KMdAE-9QLflxXpWn790RPwFf1rHhA
linkProvider	Elsevier
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+meshless+collocation+method+for+band+structure+simulation+of+nanoscale+phononic+crystals+based+on+nonlocal+elasticity+theory&rft.jtitle=Journal+of+computational+physics&rft.au=Zheng%2C+Hui&rft.au=Zhou%2C+Chuanbing&rft.au=Yan%2C+Dong-Jia&rft.au=Wang%2C+Yue-Sheng&rft.date=2020-05-01&rft.pub=Elsevier+Science+Ltd&rft.issn=0021-9991&rft.eissn=1090-2716&rft.volume=408&rft.spage=1&rft_id=info:doi/10.1016%2Fj.jcp.2020.109268&rft.externalDBID=NO_FULL_TEXT
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0021-9991&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0021-9991&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0021-9991&client=summon