{"id":"https://openalex.org/W2012227629","doi":"https://doi.org/10.1063/1.4897367","title":"Size effects on electromechanical coupling fields of a bending piezoelectric nanoplate due to surface effects and flexoelectricity","display_name":"Size effects on electromechanical coupling fields of a bending piezoelectric nanoplate due to surface effects and flexoelectricity","publication_year":2014,"publication_date":"2014-10-06","ids":{"openalex":"https://openalex.org/W2012227629","doi":"https://doi.org/10.1063/1.4897367","mag":"2012227629"},"language":"en","primary_location":{"id":"doi:10.1063/1.4897367","doi":"https://doi.org/10.1063/1.4897367","is_oa":false,"landing_page_url":"https://doi.org/10.1063/1.4897367","pdf_url":null,"source":{"id":"https://openalex.org/S187991544","display_name":"Journal of Applied Physics","issn_l":"0021-8979","issn":["0021-8979","1089-7550","1520-8850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Physics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101474834","display_name":"Zhengrong Zhang","orcid":"https://orcid.org/0000-0002-0099-686X","observed_orcids":["https://orcid.org/0000-0002-0099-686X"]},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Zhengrong Zhang","raw_affiliation_strings":["The University of Western Ontario Department of Mechanical and Materials Engineering, , London, Ontario N6A 5B9, Canada","Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, N6A 5B9, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Western Ontario Department of Mechanical and Materials Engineering, , London, Ontario N6A 5B9, Canada","institution_ids":["https://openalex.org/I125749732"]},{"raw_affiliation_string":"Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, N6A 5B9, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101529445","display_name":"Liying Jiang","orcid":"https://orcid.org/0000-0002-4902-7154","observed_orcids":["https://orcid.org/0000-0002-4902-7154"]},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Liying Jiang","raw_affiliation_strings":["The University of Western Ontario Department of Mechanical and Materials Engineering, , London, Ontario N6A 5B9, Canada","Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, N6A 5B9, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Western Ontario Department of Mechanical and Materials Engineering, , London, Ontario N6A 5B9, Canada","institution_ids":["https://openalex.org/I125749732"]},{"raw_affiliation_string":"Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, N6A 5B9, Canada","institution_ids":["https://openalex.org/I125749732"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I125749732"],"apc_list":{"value":3500,"currency":"USD","value_usd":3500},"apc_paid":null,"fwci":7.7816,"has_fulltext":false,"cited_by_count":105,"citation_normalized_percentile":{"value":0.9830212,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":100},"biblio":{"volume":"116","issue":"13","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10107","display_name":"Ferroelectric and Piezoelectric Materials","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/size-effect","display_name":"size effect","score":0.7450000047683716},{"id":"https://openalex.org/keywords/surface-effects","display_name":"surface effects","score":0.8180000185966492},{"id":"https://openalex.org/keywords/flexoelectricity","display_name":"flexoelectricity","score":0.9950000047683716},{"id":"https://openalex.org/keywords/electromechanical-coupling","display_name":"electromechanical coupling","score":0.9259999990463257},{"id":"https://openalex.org/keywords/surface-residual-stress","display_name":"surface residual stress","score":0.8880000114440918},{"id":"https://openalex.org/keywords/surface-elasticity","display_name":"surface elasticity","score":0.9890000224113464},{"id":"https://openalex.org/keywords/surface-piezoelectricity","display_name":"surface piezoelectricity","score":0.9990000128746033},{"id":"https://openalex.org/keywords/static-bending","display_name":"static bending","score":0.6779999732971191},{"id":"https://openalex.org/keywords/free-vibration","display_name":"free vibration","score":0.996999979019165},{"id":"https://openalex.org/keywords/nanoresonators","display_name":"nanoresonators","score":0.8939999938011169},{"id":"https://openalex.org/keywords/frequency-tuning","display_name":"frequency tuning","score":0.9259999990463257},{"id":"https://openalex.org/keywords/rayleigh-ritz-method","display_name":"Rayleigh-Ritz method","score":0.6169999837875366}],"concepts":[{"id":"https://openalex.org/C2778070859","wikidata":"https://www.wikidata.org/wiki/Q5459026","display_name":"Flexoelectricity","level":3,"score":0.9911009669303894},{"id":"https://openalex.org/C100082104","wikidata":"https://www.wikidata.org/wiki/Q183759","display_name":"Piezoelectricity","level":2,"score":0.7663975954055786},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.6745562553405762},{"id":"https://openalex.org/C87210426","wikidata":"https://www.wikidata.org/wiki/Q1072476","display_name":"Bending","level":2,"score":0.5727547407150269},{"id":"https://openalex.org/C16826683","wikidata":"https://www.wikidata.org/wiki/Q2098720","display_name":"Plate theory","level":3,"score":0.4127291738986969},{"id":"https://openalex.org/C198394728","wikidata":"https://www.wikidata.org/wiki/Q3695508","display_name":"Vibration","level":2,"score":0.4033809304237366},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.3698596954345703},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.3208664357662201},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15424257516860962},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.10453668236732483}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1063/1.4897367","doi":"https://doi.org/10.1063/1.4897367","is_oa":false,"landing_page_url":"https://doi.org/10.1063/1.4897367","pdf_url":null,"source":{"id":"https://openalex.org/S187991544","display_name":"Journal of Applied Physics","issn_l":"0021-8979","issn":["0021-8979","1089-7550","1520-8850"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Physics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321487","display_name":"Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W1515137979","https://openalex.org/W1971074347","https://openalex.org/W1972652282","https://openalex.org/W1977497643","https://openalex.org/W1982243627","https://openalex.org/W1984705808","https://openalex.org/W1987504686","https://openalex.org/W1989443647","https://openalex.org/W1993012428","https://openalex.org/W1993576917","https://openalex.org/W1998189944","https://openalex.org/W1998764191","https://openalex.org/W2000644205","https://openalex.org/W2003530927","https://openalex.org/W2008908173","https://openalex.org/W2014931743","https://openalex.org/W2018069496","https://openalex.org/W2018218674","https://openalex.org/W2018381348","https://openalex.org/W2023433979","https://openalex.org/W2027285490","https://openalex.org/W2027620823","https://openalex.org/W2032861207","https://openalex.org/W2033524260","https://openalex.org/W2041035116","https://openalex.org/W2042583435","https://openalex.org/W2043161171","https://openalex.org/W2044302851","https://openalex.org/W2045260724","https://openalex.org/W2045322888","https://openalex.org/W2051617107","https://openalex.org/W2056709126","https://openalex.org/W2060233858","https://openalex.org/W2061877720","https://openalex.org/W2065426923","https://openalex.org/W2068487172","https://openalex.org/W2070540066","https://openalex.org/W2071714898","https://openalex.org/W2071999545","https://openalex.org/W2072214942","https://openalex.org/W2073725438","https://openalex.org/W2078248053","https://openalex.org/W2080653131","https://openalex.org/W2081224892","https://openalex.org/W2081385637","https://openalex.org/W2082949672","https://openalex.org/W2086477600","https://openalex.org/W2088913910","https://openalex.org/W2091458120","https://openalex.org/W2096902685","https://openalex.org/W2121809600","https://openalex.org/W2123892296","https://openalex.org/W2130045457","https://openalex.org/W2137246723","https://openalex.org/W2154575954","https://openalex.org/W2154705361","https://openalex.org/W2156701147","https://openalex.org/W2162584730","https://openalex.org/W2165221791","https://openalex.org/W4211209218"],"related_works":["https://openalex.org/W2084431292","https://openalex.org/W2619981761","https://openalex.org/W2524501213","https://openalex.org/W1911922098","https://openalex.org/W229402755","https://openalex.org/W4388069867","https://openalex.org/W1982243627","https://openalex.org/W7160615700","https://openalex.org/W7117564414","https://openalex.org/W2550852425"],"abstract_inverted_index":{"Due":[0],"to":[1,4,18,62,189],"large":[2],"surface":[3,21,52,54,56,88,137,182],"volume":[5],"ratio":[6],"and":[7,23,58,67,79,90,106,135,152,180,200],"manifest":[8],"strain":[9],"gradients":[10],"typically":[11],"present":[12],"in":[13,25],"nanostructures,":[14],"it":[15,157],"is":[16,60,158,187],"essential":[17],"incorporate":[19],"both":[20,86,177],"effects":[22,89,138],"flexoelectricity":[24,59,92,134,179],"studying":[26],"the":[27,36,39,48,64,80,87,91,96,103,107,130,133,136,140,144,148,153,162,178,181,194,198],"size-dependent":[28],"electromechanical":[29],"coupling":[30],"behaviors":[31,69,142],"of":[32,50,70,102,132,143,165,202],"piezoelectric":[33,73],"materials":[34],"at":[35],"nano-scale.":[37],"In":[38],"current":[40,185],"work,":[41],"a":[42,71],"modified":[43,175],"Kirchhoff":[44],"plate":[45,154],"model":[46],"with":[47,121],"consideration":[49],"residual":[51],"stress,":[53],"elasticity,":[55],"piezoelectricity,":[57],"developed":[61],"investigate":[63],"electroelastic":[65],"responses":[66],"vibrational":[68],"bending":[72,105,141],"nanoplate":[74],"(PNP).":[75],"The":[76,124,184],"governing":[77],"equations":[78],"corresponding":[81],"boundary":[82],"conditions":[83],"accounting":[84],"for":[85,118,197],"are":[93,115],"derived":[94],"by":[95,168,176],"variational":[97],"principle.":[98],"Ritz":[99],"approximate":[100],"solutions":[101],"static":[104],"free":[108],"vibration":[109],"indicate":[110],"that":[111,129,161],"these":[112],"nano-scale":[113],"features":[114],"more":[116],"prominent":[117],"thinner":[119],"plates":[120],"smaller":[122],"thickness.":[123],"simulation":[125],"results":[126],"also":[127,159],"reveal":[128],"influence":[131],"upon":[139],"PNP":[145],"depends":[146],"on":[147,193],"applied":[149,170],"electrical":[150,171],"loading":[151],"dimensions.":[155],"Moreover,":[156],"observed":[160],"frequency":[163],"tuning":[164],"PNP-based":[166,203],"nanoresonators":[167],"adjusting":[169],"load":[172],"can":[173],"be":[174],"effects.":[183],"work":[186],"expected":[188],"provide":[190],"increased":[191],"understanding":[192],"theoretical":[195],"basis":[196],"design":[199],"applications":[201],"nanodevices.":[204]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":1}],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2016-06-24T00:00:00"}
