Dynamics of functionally graded micro-cantilevers
The nonlinear size-dependent dynamics of a functionally graded micro-cantilever is investigated when subject to a base excitation resulting in large-amplitude oscillations. A geometric nonlinearities due to large changes in the curvature is taken into account. Employing the Mori–Tanaka homogenisatio...
Saved in:
| Published in | International journal of engineering science Vol. 115; pp. 117 - 130 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford
Elsevier Ltd
01.06.2017
Elsevier BV |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | The nonlinear size-dependent dynamics of a functionally graded micro-cantilever is investigated when subject to a base excitation resulting in large-amplitude oscillations. A geometric nonlinearities due to large changes in the curvature is taken into account. Employing the Mori–Tanaka homogenisation technique (for the material properties), the modified couple stress theory (MCST) is used to formulate the potential and kinetic energies of the system in terms of the transverse and axial motions. A dynamic energy balance is performed between the energy terms, yielding the continuous models for the axial and transverse displacements. The inextensibility condition results in the size-dependent model of the functionally graded micro-cantilever involving inertial and stiffness nonlinear terms. The resultant model is discretised based on a weighted-residual technique yielding a high-dimensional truncated model (required for accurate simulations). A parameter-continuation scheme together with a time integration method is introduced to the truncated model so as to determine the resonances with stable and unstable solution branches with special consideration to the effect of different system parameters, such as material gradient index and the length-scale effect on the nonlinear dynamics of the functionally graded micro-cantilever. |
|---|---|
| AbstractList | The nonlinear size-dependent dynamics of a functionally graded micro-cantilever is investigated when subject to a base excitation resulting in large-amplitude oscillations. A geometric nonlinearities due to large changes in the curvature is taken into account. Employing the Mori-Tanaka homogenisation technique (for the material properties), the modified couple stress theory (MCST) is used to formulate the potential and kinetic energies of the system in terms of the transverse and axial motions. A dynamic energy balance is performed between the energy terms, yielding the continuous models for the axial and transverse displacements. The inextensibility condition results in the size-dependent model of the functionally graded micro-cantilever involving inertial and stiffness nonlinear terms. The resultant model is discretised based on a weighted-residual technique yielding a high-dimensional truncated model (required for accurate simulations). A parameter-continuation scheme together with a time integration method is introduced to the truncated model so as to determine the resonances with stable and unstable solution branches with special consideration to the effect of different system parameters, such as material gradient index and the length-scale effect on the nonlinear dynamics of the functionally graded micro-cantilever. |
| Author | Gholipour, Alireza Ghayesh, Mergen H. Farokhi, Hamed |
| Author_xml | – sequence: 1 givenname: Hamed surname: Farokhi fullname: Farokhi, Hamed organization: Department of Mechanical Engineering, McGill University, Montreal, Quebec H3A 0C3, Canada – sequence: 2 givenname: Mergen H. surname: Ghayesh fullname: Ghayesh, Mergen H. email: mergen.ghayesh@adelaide.edu.au organization: School of Mechanical Engineering, University of Adelaide, South Australia 5005, Australia – sequence: 3 givenname: Alireza surname: Gholipour fullname: Gholipour, Alireza organization: School of Mechanical Engineering, University of Adelaide, South Australia 5005, Australia |
| BookMark | eNqFkE9LAzEUxINUsFW_ghQ875qX7G424EGpf6HgRc8hm30pWbbZmmwL_famVC9eenqHNzPM_GZk4gePhNwAzYFCddflrkO_isbljILIKeSUFmdkCrWQGQMpJmRKKaOZYKy8ILMYO0ppyaWcEnjae712Js4HO7dbb0Y3eN33-_kq6BbbefqFITPaj67HHYZ4Rc6t7iNe_95L8vXy_Ll4y5Yfr--Lx2VmWFmOmZES6qYqGFgsRFtr3iDlxmoNpq6NYbpq2gabAkRluSm5qbVtRWqra4kC-CW5PeZuwvC9xTiqbtiG1C0qkDzN4lKUSVUdValljAGt2gS31mGvgKoDHtWpPzzqgEdRUAlPMt7_Mxo36sP6MWjXn7Y_HO2YEOwcBpUU6A22LqAZVTu4UxE_ib6IJA |
| CitedBy_id | crossref_primary_10_1080_15397734_2025_2454347 crossref_primary_10_1007_s40996_021_00707_7 crossref_primary_10_1002_msd2_12137 crossref_primary_10_1177_1077546319869139 crossref_primary_10_1016_j_ijengsci_2018_08_009 crossref_primary_10_1016_j_ijengsci_2022_103625 crossref_primary_10_1007_s40435_024_01565_7 crossref_primary_10_1016_j_ijengsci_2021_103549 crossref_primary_10_1007_s00542_020_04757_1 crossref_primary_10_1080_07391102_2020_1751297 crossref_primary_10_1007_s40435_025_01614_9 crossref_primary_10_1007_s00366_020_01152_2 crossref_primary_10_3390_vibration2020013 crossref_primary_10_1016_j_ijengsci_2019_103139 crossref_primary_10_1007_s00707_021_03028_y crossref_primary_10_1080_07391102_2020_1760939 crossref_primary_10_3390_mi8090263 crossref_primary_10_1016_j_ijengsci_2018_02_010 crossref_primary_10_1080_17455030_2021_2000675 crossref_primary_10_1016_j_enganabound_2022_10_030 crossref_primary_10_1007_s00366_020_01242_1 crossref_primary_10_1016_j_compositesb_2019_107006 crossref_primary_10_1016_j_ijengsci_2019_06_013 crossref_primary_10_1016_j_ijengsci_2017_06_015 crossref_primary_10_1016_j_ijengsci_2020_103413 crossref_primary_10_1016_j_compstruct_2018_07_045 crossref_primary_10_1016_j_ijengsci_2017_08_016 crossref_primary_10_1016_j_enganabound_2019_08_014 crossref_primary_10_1038_s41598_019_56726_y crossref_primary_10_1007_s00542_018_4181_y crossref_primary_10_3390_vibration3010002 crossref_primary_10_1016_j_ijengsci_2018_05_009 crossref_primary_10_1016_j_ijengsci_2020_103450 crossref_primary_10_1016_j_ijengsci_2024_104174 crossref_primary_10_1016_j_ijengsci_2018_02_005 crossref_primary_10_1142_S0219455424500135 crossref_primary_10_1016_j_ijengsci_2018_02_009 crossref_primary_10_1016_j_ijengsci_2018_10_005 crossref_primary_10_1016_j_ijheatmasstransfer_2018_01_056 crossref_primary_10_1016_j_ijengsci_2017_11_004 crossref_primary_10_1007_s00542_019_04530_z crossref_primary_10_1016_j_ijnonlinmec_2025_105067 crossref_primary_10_1016_j_compstruct_2020_113146 crossref_primary_10_1016_j_engstruct_2020_110711 crossref_primary_10_1016_j_ijengsci_2018_02_003 crossref_primary_10_1016_j_compstruct_2020_113150 crossref_primary_10_1016_j_ijengsci_2022_103727 crossref_primary_10_1016_j_tws_2024_112422 crossref_primary_10_1177_1077546320971379 crossref_primary_10_1515_zna_2017_0249 crossref_primary_10_1016_j_camwa_2018_09_001 crossref_primary_10_1016_j_ijengsci_2018_11_003 crossref_primary_10_1016_j_compstruct_2020_113152 crossref_primary_10_1016_j_ijengsci_2018_11_005 crossref_primary_10_1080_15397734_2024_2363497 crossref_primary_10_1016_j_ijengsci_2017_12_001 crossref_primary_10_1016_j_ijengsci_2019_103141 crossref_primary_10_1080_15397734_2024_2390666 crossref_primary_10_1002_msd2_70003 crossref_primary_10_1016_j_ijengsci_2018_12_001 crossref_primary_10_1002_msd2_70001 crossref_primary_10_1016_j_ijengsci_2019_03_003 crossref_primary_10_1007_s00419_021_01900_w crossref_primary_10_3390_math8071128 crossref_primary_10_1007_s11071_018_4705_0 crossref_primary_10_1016_j_compstruct_2019_110896 crossref_primary_10_1016_j_ijengsci_2021_103455 crossref_primary_10_1016_j_ijengsci_2018_09_006 |
| Cites_doi | 10.1016/j.ijengsci.2010.09.025 10.1016/j.ijengsci.2010.12.009 10.1016/j.ijengsci.2015.05.007 10.1016/j.ijengsci.2011.11.010 10.1016/j.ijengsci.2015.07.008 10.1016/j.ijmecsci.2014.11.002 10.1016/j.ijnonlinmec.2012.12.008 10.1016/j.ijengsci.2016.03.002 10.1016/j.compstruct.2013.03.001 10.1016/j.ijengsci.2015.11.007 10.1016/j.ijsolstr.2008.10.012 10.1016/j.ijengsci.2015.12.010 10.1016/j.ijengsci.2015.08.009 10.1016/j.ijengsci.2014.07.008 10.1016/j.ijengsci.2016.02.007 10.1016/j.ijengsci.2015.12.012 10.1016/j.ijengsci.2013.05.006 10.1016/j.ijengsci.2015.02.005 10.1016/j.ijengsci.2014.10.004 10.1016/j.ijsolstr.2007.08.006 10.1016/j.ijengsci.2015.12.008 10.1016/j.euromechsol.2014.01.002 10.1016/j.compositesb.2013.12.074 10.1016/j.ijengsci.2014.08.011 10.1007/s00339-013-7787-z 10.1016/j.compstruct.2012.11.020 10.1016/j.compositesb.2013.12.030 10.1016/j.ijengsci.2015.01.004 10.1007/s00339-013-7894-x 10.1016/j.ijengsci.2016.09.007 10.4028/www.scientific.net/MSF.492-493.255 10.1016/j.ijengsci.2016.09.004 10.1016/j.ijengsci.2012.12.001 10.1016/j.ijengsci.2013.04.004 10.1016/j.ijengsci.2012.01.001 10.1016/j.matdes.2009.12.006 10.1016/j.ijengsci.2015.12.009 10.1016/j.compstruct.2012.10.003 10.1016/j.ijengsci.2015.07.004 10.1007/s11071-014-1773-7 10.1016/j.ijengsci.2007.10.002 10.1016/j.ijengsci.2010.09.027 10.1016/j.compstruc.2012.09.005 10.1007/s00419-012-0630-8 10.1109/TCST.2008.2008638 10.1016/j.ijnonlinmec.2012.08.003 10.1016/j.ijengsci.2013.03.001 10.1016/j.ijengsci.2014.06.007 10.1109/JSEN.2006.890158 |
| ContentType | Journal Article |
| Copyright | 2017 Elsevier Ltd Copyright Elsevier BV Jun 2017 |
| Copyright_xml | – notice: 2017 Elsevier Ltd – notice: Copyright Elsevier BV Jun 2017 |
| DBID | AAYXX CITATION 7TB 8FD FR3 KR7 |
| DOI | 10.1016/j.ijengsci.2017.01.004 |
| DatabaseName | CrossRef Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database Civil Engineering Abstracts |
| DatabaseTitle | CrossRef Civil Engineering Abstracts Engineering Research Database Technology Research Database Mechanical & Transportation Engineering Abstracts |
| DatabaseTitleList | Civil Engineering Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1879-2197 |
| EndPage | 130 |
| ExternalDocumentID | 10_1016_j_ijengsci_2017_01_004 S0020722517301568 |
| GroupedDBID | --K --M -~X .~1 0R~ 1B1 1~. 1~5 29J 4.4 457 4G. 5GY 5VS 6TJ 7-5 71M 8P~ 9JN AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABFNM ABJNI ABMAC ABTAH ABXDB ABYKQ ACDAQ ACGFS ACIWK ACKIV ACNNM ACRLP ADBBV ADEZE ADMUD ADTZH AEBSH AECPX AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AI. AIEXJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q G8K GBLVA HVGLF HZ~ H~9 IHE J1W JJJVA KOM LY7 M41 MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SDF SDG SDP SES SET SEW SPC SPCBC SST SSZ T5K TN5 VH1 VOH WUQ XPP ZMT ZY4 ~02 ~G- AATTM AAXKI AAYWO AAYXX ABDPE ABWVN ACRPL ACVFH ADCNI ADNMO ADVLN AEIPS AEUPX AFJKZ AFPUW AFXIZ AGCQF AGQPQ AGRNS AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP BNPGV CITATION SSH 7TB 8FD EFKBS FR3 KR7 |
| ID | FETCH-LOGICAL-c255t-c9918b6421fe47d8a3be03cfaa1c88cc2a6bdbeb4176f3c53c8afd7197a89e713 |
| IEDL.DBID | .~1 |
| ISSN | 0020-7225 |
| IngestDate | Sun Jul 13 05:32:43 EDT 2025 Thu Apr 24 23:02:22 EDT 2025 Tue Jul 01 03:05:28 EDT 2025 Fri Feb 23 02:33:09 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Functionally graded micro-cantilever MEMS MCST Dynamics |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c255t-c9918b6421fe47d8a3be03cfaa1c88cc2a6bdbeb4176f3c53c8afd7197a89e713 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 1932193975 |
| PQPubID | 2045466 |
| PageCount | 14 |
| ParticipantIDs | proquest_journals_1932193975 crossref_primary_10_1016_j_ijengsci_2017_01_004 crossref_citationtrail_10_1016_j_ijengsci_2017_01_004 elsevier_sciencedirect_doi_10_1016_j_ijengsci_2017_01_004 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | June 2017 2017-06-00 20170601 |
| PublicationDateYYYYMMDD | 2017-06-01 |
| PublicationDate_xml | – month: 06 year: 2017 text: June 2017 |
| PublicationDecade | 2010 |
| PublicationPlace | Oxford |
| PublicationPlace_xml | – name: Oxford |
| PublicationTitle | International journal of engineering science |
| PublicationYear | 2017 |
| Publisher | Elsevier Ltd Elsevier BV |
| Publisher_xml | – name: Elsevier Ltd – name: Elsevier BV |
| References | Karparvarfard, Asghari, Vatankhah (bib0036) 2015; 91 Farokhi, Ghayesh, Gholipour, Hussain (bib0018) 2017; 112 Ghayesh, Farokhi (bib0026) 2015; 86 Arbind, Reddy (bib0006) 2013; 98 Taati (bib0045) 2016; 100 Shafiei, Kazemi, Ghadiri (bib0043) 2016; 101 Ghayesh, Farokhi (bib0027) 2015; 96 Zheng, Dong, Lee, Gao (bib0050) 2009; 17 Akgöz, Civalek (bib0002) 2011; 49 Asghari, Ahmadian, Kahrobaiyan, Rahaeifard (bib0007) 2010; 31 Ghayesh, Farokhi, Hussain (bib0030) 2016; 109 Huang (bib0034) 2008; 45 Tajalli, Rahaeifard, Kahrobaiyan, Movahhedy, Akbari, Ahmadian (bib0046) 2013; 102 Ghayesh, Amabili (bib0022) 2013; 49 Farokhi, Ghayesh, Hussain (bib0019) 2016; 106 Akgöz, Civalek (bib0004) 2013; 70 Baghani (bib0009) 2012; 54 Ghayesh, Farokhi, Amabili (bib0028) 2013; 71 Farokhi, Ghayesh, Amabili (bib0017) 2013; 68 Witvrouw, Mehta (bib0048) 2005; 492 Kazemirad, Ghayesh, Amabili (bib0037) 2013; 83 Asghari, Kahrobaiyan, Ahmadian (bib0008) 2010; 48 Farokhi, Ghayesh (bib0014) 2015; 91 Dehrouyeh-Semnani (bib0011) 2014; 85 Dai, Wang, Wang (bib0010) 2015; 94 Dehrouyeh-Semnani, Dehrouyeh, Torabi-Kafshgari, Nikkhah-Bahrami (bib0013) 2015; 96 Zhang, Meng (bib0049) 2007; 7 Akgöz, Civalek (bib0003) 2013; 98 Li, Pan (bib0039) 2015; 97 Mojahedi, Rahaeifard (bib0041) 2016; 100 Ghayesh, Amabili (bib0021) 2012; 112–113 Ghayesh, Amabili, Farokhi (bib0024) 2013; 51 Şimşek (bib0044) 2010; 48 Ghayesh, Amabili, Farokhi (bib0025) 2013; 63 Dehrouyeh-Semnani, BehboodiJouybari, Dehrouyeh (bib0012) 2016; 101 Tang, Ni, Wang, Luo, Wang (bib0047) 2014; 84 Ghayesh, Farokhi, Amabili (bib0031) 2013; 112 Aghazadeh, Cigeroglu, Dag (bib0001) 2014; 46 Ghayesh, Farokhi, Amabili (bib0029) 2014; 60 Farokhi, Ghayesh, Amabili (bib0020) 2013; 113 Kahrobaiyan, Rahaeifard, Tajalli, Ahmadian (bib0035) 2012; 52 Kong, Zhou, Nie, Wang (bib0038) 2008; 46 Gholipour, Farokhi, Ghayesh (bib0032) 2015; 79 Hosseini, Bahaadini (bib0033) 2016; 101 Lü, Lim, Chen (bib0040) 2009; 46 Farokhi, Ghayesh (bib0015) 2015; 90 Farokhi, Ghayesh (bib0016) 2016 Akgöz, Civalek (bib0005) 2014; 85 Ghayesh, Amabili (bib0023) 2014; 60 Shafiei, Kazemi, Ghadiri (bib0042) 2016; 102 Akgöz (10.1016/j.ijengsci.2017.01.004_bib0004) 2013; 70 Dehrouyeh-Semnani (10.1016/j.ijengsci.2017.01.004_bib0011) 2014; 85 Hosseini (10.1016/j.ijengsci.2017.01.004_bib0033) 2016; 101 Ghayesh (10.1016/j.ijengsci.2017.01.004_bib0024) 2013; 51 Ghayesh (10.1016/j.ijengsci.2017.01.004_bib0027) 2015; 96 Şimşek (10.1016/j.ijengsci.2017.01.004_bib0044) 2010; 48 Lü (10.1016/j.ijengsci.2017.01.004_bib0040) 2009; 46 Akgöz (10.1016/j.ijengsci.2017.01.004_bib0005) 2014; 85 Aghazadeh (10.1016/j.ijengsci.2017.01.004_bib0001) 2014; 46 Huang (10.1016/j.ijengsci.2017.01.004_bib0034) 2008; 45 Akgöz (10.1016/j.ijengsci.2017.01.004_bib0003) 2013; 98 Dai (10.1016/j.ijengsci.2017.01.004_bib0010) 2015; 94 Tang (10.1016/j.ijengsci.2017.01.004_bib0047) 2014; 84 Arbind (10.1016/j.ijengsci.2017.01.004_bib0006) 2013; 98 Ghayesh (10.1016/j.ijengsci.2017.01.004_bib0029) 2014; 60 Kahrobaiyan (10.1016/j.ijengsci.2017.01.004_bib0035) 2012; 52 Gholipour (10.1016/j.ijengsci.2017.01.004_bib0032) 2015; 79 Farokhi (10.1016/j.ijengsci.2017.01.004_bib0018) 2017; 112 Baghani (10.1016/j.ijengsci.2017.01.004_bib0009) 2012; 54 Li (10.1016/j.ijengsci.2017.01.004_bib0039) 2015; 97 Farokhi (10.1016/j.ijengsci.2017.01.004_bib0016) 2016 Zhang (10.1016/j.ijengsci.2017.01.004_bib0049) 2007; 7 Tajalli (10.1016/j.ijengsci.2017.01.004_bib0046) 2013; 102 Taati (10.1016/j.ijengsci.2017.01.004_bib0045) 2016; 100 Ghayesh (10.1016/j.ijengsci.2017.01.004_bib0023) 2014; 60 Asghari (10.1016/j.ijengsci.2017.01.004_bib0007) 2010; 31 Asghari (10.1016/j.ijengsci.2017.01.004_bib0008) 2010; 48 Kong (10.1016/j.ijengsci.2017.01.004_bib0038) 2008; 46 Dehrouyeh-Semnani (10.1016/j.ijengsci.2017.01.004_bib0012) 2016; 101 Farokhi (10.1016/j.ijengsci.2017.01.004_bib0015) 2015; 90 Ghayesh (10.1016/j.ijengsci.2017.01.004_bib0022) 2013; 49 Ghayesh (10.1016/j.ijengsci.2017.01.004_bib0028) 2013; 71 Witvrouw (10.1016/j.ijengsci.2017.01.004_bib0048) 2005; 492 Farokhi (10.1016/j.ijengsci.2017.01.004_bib0019) 2016; 106 Kazemirad (10.1016/j.ijengsci.2017.01.004_bib0037) 2013; 83 Shafiei (10.1016/j.ijengsci.2017.01.004_bib0043) 2016; 101 Ghayesh (10.1016/j.ijengsci.2017.01.004_bib0031) 2013; 112 Ghayesh (10.1016/j.ijengsci.2017.01.004_bib0030) 2016; 109 Karparvarfard (10.1016/j.ijengsci.2017.01.004_bib0036) 2015; 91 Shafiei (10.1016/j.ijengsci.2017.01.004_bib0042) 2016; 102 Farokhi (10.1016/j.ijengsci.2017.01.004_bib0014) 2015; 91 Mojahedi (10.1016/j.ijengsci.2017.01.004_bib0041) 2016; 100 Zheng (10.1016/j.ijengsci.2017.01.004_bib0050) 2009; 17 Ghayesh (10.1016/j.ijengsci.2017.01.004_bib0021) 2012; 112–113 Farokhi (10.1016/j.ijengsci.2017.01.004_bib0020) 2013; 113 Ghayesh (10.1016/j.ijengsci.2017.01.004_bib0026) 2015; 86 Dehrouyeh-Semnani (10.1016/j.ijengsci.2017.01.004_bib0013) 2015; 96 Farokhi (10.1016/j.ijengsci.2017.01.004_bib0017) 2013; 68 Akgöz (10.1016/j.ijengsci.2017.01.004_bib0002) 2011; 49 Ghayesh (10.1016/j.ijengsci.2017.01.004_bib0025) 2013; 63 |
| References_xml | – volume: 46 start-page: 1176 year: 2009 end-page: 1185 ident: bib0040 article-title: Size-dependent elastic behavior of FGM ultra-thin films based on generalized refined theory publication-title: International Journal of Solids and Structures – volume: 46 start-page: 427 year: 2008 end-page: 437 ident: bib0038 article-title: The size-dependent natural frequency of Bernoulli–Euler micro-beams publication-title: International Journal of Engineering Science – volume: 85 start-page: 90 year: 2014 end-page: 104 ident: bib0005 article-title: Thermo-mechanical buckling behavior of functionally graded microbeams embedded in elastic medium publication-title: International Journal of Engineering Science – start-page: 1 year: 2016 end-page: 16 ident: bib0016 article-title: Viscoelasticity effects on resonant response of a shear deformable extensible microbeam publication-title: Nonlinear Dynamics – volume: 83 start-page: 25 year: 2013 end-page: 42 ident: bib0037 article-title: Thermo-mechanical nonlinear dynamics of a buckled axially moving beam publication-title: Archive of Applied Mechanics – volume: 112 start-page: 1 year: 2017 end-page: 17 ident: bib0018 article-title: Motion characteristics of bilayered extensible Timoshenko microbeams publication-title: International Journal of Engineering Science – volume: 109 start-page: 243 year: 2016 end-page: 255 ident: bib0030 article-title: Viscoelastically coupled size-dependent dynamics of microbeams publication-title: International Journal of Engineering Science – volume: 49 start-page: 40 year: 2013 end-page: 49 ident: bib0022 article-title: Steady-state transverse response of an axially moving beam with time-dependent axial speed publication-title: International Journal of Non-Linear Mechanics – volume: 98 start-page: 272 year: 2013 end-page: 281 ident: bib0006 article-title: Nonlinear analysis of functionally graded microstructure-dependent beams publication-title: Composite Structures – volume: 46 start-page: 1 year: 2014 end-page: 11 ident: bib0001 article-title: Static and free vibration analyses of small-scale functionally graded beams possessing a variable length scale parameter using different beam theories publication-title: European Journal of Mechanics-A/Solids – volume: 113 start-page: 297 year: 2013 end-page: 307 ident: bib0020 article-title: Nonlinear resonant behavior of microbeams over the buckled state publication-title: Applied Physics A – volume: 86 start-page: 60 year: 2015 end-page: 73 ident: bib0026 article-title: Nonlinear dynamics of microplates publication-title: International Journal of Engineering Science – volume: 101 start-page: 29 year: 2016 end-page: 44 ident: bib0043 article-title: On size-dependent vibration of rotary axially functionally graded microbeam publication-title: International Journal of Engineering Science – volume: 94 start-page: 103 year: 2015 end-page: 112 ident: bib0010 article-title: Nonlinear dynamics of cantilevered microbeams based on modified couple stress theory publication-title: International Journal of Engineering Science – volume: 60 start-page: 371 year: 2014 end-page: 377 ident: bib0023 article-title: Coupled longitudinal-transverse behaviour of a geometrically imperfect microbeam publication-title: Composites Part B: Engineering – volume: 45 start-page: 568 year: 2008 end-page: 579 ident: bib0034 article-title: Size-dependent response of ultra-thin films with surface effects publication-title: International Journal of Solids and Structures – volume: 52 start-page: 65 year: 2012 end-page: 76 ident: bib0035 article-title: A strain gradient functionally graded Euler–Bernoulli beam formulation publication-title: International Journal of Engineering Science – volume: 91 start-page: 12 year: 2015 end-page: 33 ident: bib0014 article-title: Thermo-mechanical dynamics of perfect and imperfect Timoshenko microbeams publication-title: International Journal of Engineering Science – volume: 96 start-page: 34 year: 2015 end-page: 45 ident: bib0027 article-title: Chaotic motion of a parametrically excited microbeam publication-title: International Journal of Engineering Science – volume: 49 start-page: 1268 year: 2011 end-page: 1280 ident: bib0002 article-title: Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams publication-title: International Journal of Engineering Science – volume: 100 start-page: 171 year: 2016 end-page: 182 ident: bib0041 article-title: A size-dependent model for coupled 3D deformations of nonlinear microbridges publication-title: International Journal of Engineering Science – volume: 70 start-page: 1 year: 2013 end-page: 14 ident: bib0004 article-title: A size-dependent shear deformation beam model based on the strain gradient elasticity theory publication-title: International Journal of Engineering Science – volume: 101 start-page: 50 year: 2016 end-page: 63 ident: bib0012 article-title: On size-dependent lead-lag vibration of rotating microcantilevers publication-title: International Journal of Engineering Science – volume: 106 start-page: 29 year: 2016 end-page: 41 ident: bib0019 article-title: Large-amplitude dynamical behaviour of microcantilevers publication-title: International Journal of Engineering Science – volume: 31 start-page: 2324 year: 2010 end-page: 2329 ident: bib0007 article-title: On the size-dependent behavior of functionally graded micro-beams publication-title: Materials and Design – volume: 97 start-page: 40 year: 2015 end-page: 59 ident: bib0039 article-title: Static bending and free vibration of a functionally graded piezoelectric microplate based on the modified couple-stress theory publication-title: International Journal of Engineering Science – volume: 91 start-page: 63 year: 2015 end-page: 75 ident: bib0036 article-title: A geometrically nonlinear beam model based on the second strain gradient theory publication-title: International Journal of Engineering Science – volume: 84 start-page: 1 year: 2014 end-page: 10 ident: bib0047 article-title: Nonlinear modeling and size-dependent vibration analysis of curved microtubes conveying fluid based on modified couple stress theory publication-title: International Journal of Engineering Science – volume: 68 start-page: 11 year: 2013 end-page: 23 ident: bib0017 article-title: Nonlinear dynamics of a geometrically imperfect microbeam based on the modified couple stress theory publication-title: International Journal of Engineering Science – volume: 102 start-page: 72 year: 2013 end-page: 80 ident: bib0046 article-title: Mechanical behavior analysis of size-dependent micro-scaled functionally graded Timoshenko beams by strain gradient elasticity theory publication-title: Composite Structure – volume: 112 start-page: 329 year: 2013 end-page: 338 ident: bib0031 article-title: Coupled nonlinear size-dependent behaviour of microbeams publication-title: Applied Physics A – volume: 48 start-page: 1749 year: 2010 end-page: 1761 ident: bib0008 article-title: A nonlinear Timoshenko beam formulation based on the modified couple stress theory publication-title: International Journal of Engineering Science – volume: 100 start-page: 45 year: 2016 end-page: 60 ident: bib0045 article-title: Analytical solutions for the size dependent buckling and postbuckling behavior of functionally graded micro-plates publication-title: International Journal of Engineering Science – volume: 63 start-page: 52 year: 2013 end-page: 60 ident: bib0025 article-title: Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory publication-title: International Journal of Engineering Science – volume: 48 start-page: 1721 year: 2010 end-page: 1732 ident: bib0044 article-title: Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory publication-title: International Journal of Engineering Science – volume: 7 start-page: 370 year: 2007 end-page: 380 ident: bib0049 article-title: Nonlinear dynamic analysis of electrostatically actuated resonant MEMS sensors under parametric excitation publication-title: IEEE Sensors Journal – volume: 17 start-page: 1432 year: 2009 end-page: 1438 ident: bib0050 article-title: Active disturbance rejection control for MEMS gyroscopes publication-title: IEEE Transactions on Control Systems Technology – volume: 60 start-page: 423 year: 2014 end-page: 439 ident: bib0029 article-title: In-plane and out-of-plane motion characteristics of microbeams with modal interactions publication-title: Composites Part B: Engineering – volume: 54 start-page: 99 year: 2012 end-page: 105 ident: bib0009 article-title: Analytical study on size-dependent static pull-in voltage of microcantilevers using the modified couple stress theory publication-title: International Journal of Engineering Science – volume: 79 start-page: 1771 year: 2015 end-page: 1785 ident: bib0032 article-title: In-plane and out-of-plane nonlinear size-dependent dynamics of microplates publication-title: Nonlinear Dynamics – volume: 90 start-page: 133 year: 2015 end-page: 144 ident: bib0015 article-title: Nonlinear dynamical behaviour of geometrically imperfect microplates based on modified couple stress theory publication-title: International Journal of Mechanical Sciences – volume: 492 start-page: 255 year: 2005 end-page: 260 ident: bib0048 article-title: The use of functionally graded poly-SiGe layers for MEMS applications publication-title: Materials Science Forum – volume: 98 start-page: 314 year: 2013 end-page: 322 ident: bib0003 article-title: Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory publication-title: Composite Structures – volume: 102 start-page: 12 year: 2016 end-page: 26 ident: bib0042 article-title: Nonlinear vibration of axially functionally graded tapered microbeams publication-title: International Journal of Engineering Science – volume: 112–113 start-page: 406 year: 2012 end-page: 421 ident: bib0021 article-title: Nonlinear dynamics of axially moving viscoelastic beams over the buckled state publication-title: Computers & Structures – volume: 71 start-page: 137 year: 2013 end-page: 155 ident: bib0028 article-title: Nonlinear behaviour of electrically actuated MEMS resonators publication-title: International Journal of Engineering Science – volume: 96 start-page: 68 year: 2015 end-page: 85 ident: bib0013 article-title: An investigation into size-dependent vibration damping characteristics of functionally graded viscoelastically damped sandwich microbeams publication-title: International Journal of Engineering Science – volume: 85 start-page: 66 year: 2014 end-page: 73 ident: bib0011 article-title: A discussion on different non-classical constitutive models of microbeam publication-title: International Journal of Engineering Science – volume: 51 start-page: 54 year: 2013 end-page: 74 ident: bib0024 article-title: Coupled global dynamics of an axially moving viscoelastic beam publication-title: International Journal of Non-Linear Mechanics – volume: 101 start-page: 1 year: 2016 end-page: 13 ident: bib0033 article-title: Size dependent stability analysis of cantilever micro-pipes conveying fluid based on modified strain gradient theory publication-title: International Journal of Engineering Science – volume: 48 start-page: 1749 year: 2010 ident: 10.1016/j.ijengsci.2017.01.004_bib0008 article-title: A nonlinear Timoshenko beam formulation based on the modified couple stress theory publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2010.09.025 – volume: 49 start-page: 1268 year: 2011 ident: 10.1016/j.ijengsci.2017.01.004_bib0002 article-title: Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2010.12.009 – volume: 94 start-page: 103 year: 2015 ident: 10.1016/j.ijengsci.2017.01.004_bib0010 article-title: Nonlinear dynamics of cantilevered microbeams based on modified couple stress theory publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2015.05.007 – volume: 52 start-page: 65 year: 2012 ident: 10.1016/j.ijengsci.2017.01.004_bib0035 article-title: A strain gradient functionally graded Euler–Bernoulli beam formulation publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2011.11.010 – volume: 96 start-page: 68 year: 2015 ident: 10.1016/j.ijengsci.2017.01.004_bib0013 article-title: An investigation into size-dependent vibration damping characteristics of functionally graded viscoelastically damped sandwich microbeams publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2015.07.008 – volume: 90 start-page: 133 year: 2015 ident: 10.1016/j.ijengsci.2017.01.004_bib0015 article-title: Nonlinear dynamical behaviour of geometrically imperfect microplates based on modified couple stress theory publication-title: International Journal of Mechanical Sciences doi: 10.1016/j.ijmecsci.2014.11.002 – volume: 51 start-page: 54 year: 2013 ident: 10.1016/j.ijengsci.2017.01.004_bib0024 article-title: Coupled global dynamics of an axially moving viscoelastic beam publication-title: International Journal of Non-Linear Mechanics doi: 10.1016/j.ijnonlinmec.2012.12.008 – volume: 106 start-page: 29 year: 2016 ident: 10.1016/j.ijengsci.2017.01.004_bib0019 article-title: Large-amplitude dynamical behaviour of microcantilevers publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2016.03.002 – volume: 102 start-page: 72 year: 2013 ident: 10.1016/j.ijengsci.2017.01.004_bib0046 article-title: Mechanical behavior analysis of size-dependent micro-scaled functionally graded Timoshenko beams by strain gradient elasticity theory publication-title: Composite Structure doi: 10.1016/j.compstruct.2013.03.001 – volume: 100 start-page: 45 year: 2016 ident: 10.1016/j.ijengsci.2017.01.004_bib0045 article-title: Analytical solutions for the size dependent buckling and postbuckling behavior of functionally graded micro-plates publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2015.11.007 – volume: 46 start-page: 1176 year: 2009 ident: 10.1016/j.ijengsci.2017.01.004_bib0040 article-title: Size-dependent elastic behavior of FGM ultra-thin films based on generalized refined theory publication-title: International Journal of Solids and Structures doi: 10.1016/j.ijsolstr.2008.10.012 – volume: 100 start-page: 171 year: 2016 ident: 10.1016/j.ijengsci.2017.01.004_bib0041 article-title: A size-dependent model for coupled 3D deformations of nonlinear microbridges publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2015.12.010 – volume: 97 start-page: 40 year: 2015 ident: 10.1016/j.ijengsci.2017.01.004_bib0039 article-title: Static bending and free vibration of a functionally graded piezoelectric microplate based on the modified couple-stress theory publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2015.08.009 – volume: 85 start-page: 66 year: 2014 ident: 10.1016/j.ijengsci.2017.01.004_bib0011 article-title: A discussion on different non-classical constitutive models of microbeam publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2014.07.008 – volume: 102 start-page: 12 year: 2016 ident: 10.1016/j.ijengsci.2017.01.004_bib0042 article-title: Nonlinear vibration of axially functionally graded tapered microbeams publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2016.02.007 – volume: 101 start-page: 1 year: 2016 ident: 10.1016/j.ijengsci.2017.01.004_bib0033 article-title: Size dependent stability analysis of cantilever micro-pipes conveying fluid based on modified strain gradient theory publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2015.12.012 – volume: 71 start-page: 137 year: 2013 ident: 10.1016/j.ijengsci.2017.01.004_bib0028 article-title: Nonlinear behaviour of electrically actuated MEMS resonators publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2013.05.006 – volume: 91 start-page: 12 year: 2015 ident: 10.1016/j.ijengsci.2017.01.004_bib0014 article-title: Thermo-mechanical dynamics of perfect and imperfect Timoshenko microbeams publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2015.02.005 – volume: 86 start-page: 60 year: 2015 ident: 10.1016/j.ijengsci.2017.01.004_bib0026 article-title: Nonlinear dynamics of microplates publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2014.10.004 – volume: 45 start-page: 568 year: 2008 ident: 10.1016/j.ijengsci.2017.01.004_bib0034 article-title: Size-dependent response of ultra-thin films with surface effects publication-title: International Journal of Solids and Structures doi: 10.1016/j.ijsolstr.2007.08.006 – volume: 101 start-page: 29 year: 2016 ident: 10.1016/j.ijengsci.2017.01.004_bib0043 article-title: On size-dependent vibration of rotary axially functionally graded microbeam publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2015.12.008 – volume: 46 start-page: 1 year: 2014 ident: 10.1016/j.ijengsci.2017.01.004_bib0001 article-title: Static and free vibration analyses of small-scale functionally graded beams possessing a variable length scale parameter using different beam theories publication-title: European Journal of Mechanics-A/Solids doi: 10.1016/j.euromechsol.2014.01.002 – volume: 60 start-page: 423 year: 2014 ident: 10.1016/j.ijengsci.2017.01.004_bib0029 article-title: In-plane and out-of-plane motion characteristics of microbeams with modal interactions publication-title: Composites Part B: Engineering doi: 10.1016/j.compositesb.2013.12.074 – volume: 85 start-page: 90 year: 2014 ident: 10.1016/j.ijengsci.2017.01.004_bib0005 article-title: Thermo-mechanical buckling behavior of functionally graded microbeams embedded in elastic medium publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2014.08.011 – volume: 112 start-page: 329 year: 2013 ident: 10.1016/j.ijengsci.2017.01.004_bib0031 article-title: Coupled nonlinear size-dependent behaviour of microbeams publication-title: Applied Physics A doi: 10.1007/s00339-013-7787-z – volume: 98 start-page: 314 year: 2013 ident: 10.1016/j.ijengsci.2017.01.004_bib0003 article-title: Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory publication-title: Composite Structures doi: 10.1016/j.compstruct.2012.11.020 – volume: 60 start-page: 371 year: 2014 ident: 10.1016/j.ijengsci.2017.01.004_bib0023 article-title: Coupled longitudinal-transverse behaviour of a geometrically imperfect microbeam publication-title: Composites Part B: Engineering doi: 10.1016/j.compositesb.2013.12.030 – volume: 91 start-page: 63 year: 2015 ident: 10.1016/j.ijengsci.2017.01.004_bib0036 article-title: A geometrically nonlinear beam model based on the second strain gradient theory publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2015.01.004 – volume: 113 start-page: 297 year: 2013 ident: 10.1016/j.ijengsci.2017.01.004_bib0020 article-title: Nonlinear resonant behavior of microbeams over the buckled state publication-title: Applied Physics A doi: 10.1007/s00339-013-7894-x – volume: 112 start-page: 1 year: 2017 ident: 10.1016/j.ijengsci.2017.01.004_bib0018 article-title: Motion characteristics of bilayered extensible Timoshenko microbeams publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2016.09.007 – volume: 492 start-page: 255 year: 2005 ident: 10.1016/j.ijengsci.2017.01.004_bib0048 article-title: The use of functionally graded poly-SiGe layers for MEMS applications publication-title: Materials Science Forum doi: 10.4028/www.scientific.net/MSF.492-493.255 – volume: 109 start-page: 243 year: 2016 ident: 10.1016/j.ijengsci.2017.01.004_bib0030 article-title: Viscoelastically coupled size-dependent dynamics of microbeams publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2016.09.004 – volume: 63 start-page: 52 year: 2013 ident: 10.1016/j.ijengsci.2017.01.004_bib0025 article-title: Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2012.12.001 – volume: 70 start-page: 1 year: 2013 ident: 10.1016/j.ijengsci.2017.01.004_bib0004 article-title: A size-dependent shear deformation beam model based on the strain gradient elasticity theory publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2013.04.004 – volume: 54 start-page: 99 year: 2012 ident: 10.1016/j.ijengsci.2017.01.004_bib0009 article-title: Analytical study on size-dependent static pull-in voltage of microcantilevers using the modified couple stress theory publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2012.01.001 – volume: 31 start-page: 2324 year: 2010 ident: 10.1016/j.ijengsci.2017.01.004_bib0007 article-title: On the size-dependent behavior of functionally graded micro-beams publication-title: Materials and Design doi: 10.1016/j.matdes.2009.12.006 – volume: 101 start-page: 50 year: 2016 ident: 10.1016/j.ijengsci.2017.01.004_bib0012 article-title: On size-dependent lead-lag vibration of rotating microcantilevers publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2015.12.009 – volume: 98 start-page: 272 year: 2013 ident: 10.1016/j.ijengsci.2017.01.004_bib0006 article-title: Nonlinear analysis of functionally graded microstructure-dependent beams publication-title: Composite Structures doi: 10.1016/j.compstruct.2012.10.003 – volume: 96 start-page: 34 year: 2015 ident: 10.1016/j.ijengsci.2017.01.004_bib0027 article-title: Chaotic motion of a parametrically excited microbeam publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2015.07.004 – volume: 79 start-page: 1771 year: 2015 ident: 10.1016/j.ijengsci.2017.01.004_bib0032 article-title: In-plane and out-of-plane nonlinear size-dependent dynamics of microplates publication-title: Nonlinear Dynamics doi: 10.1007/s11071-014-1773-7 – volume: 46 start-page: 427 year: 2008 ident: 10.1016/j.ijengsci.2017.01.004_bib0038 article-title: The size-dependent natural frequency of Bernoulli–Euler micro-beams publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2007.10.002 – volume: 48 start-page: 1721 year: 2010 ident: 10.1016/j.ijengsci.2017.01.004_bib0044 article-title: Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2010.09.027 – volume: 112–113 start-page: 406 year: 2012 ident: 10.1016/j.ijengsci.2017.01.004_bib0021 article-title: Nonlinear dynamics of axially moving viscoelastic beams over the buckled state publication-title: Computers & Structures doi: 10.1016/j.compstruc.2012.09.005 – volume: 83 start-page: 25 year: 2013 ident: 10.1016/j.ijengsci.2017.01.004_bib0037 article-title: Thermo-mechanical nonlinear dynamics of a buckled axially moving beam publication-title: Archive of Applied Mechanics doi: 10.1007/s00419-012-0630-8 – volume: 17 start-page: 1432 year: 2009 ident: 10.1016/j.ijengsci.2017.01.004_bib0050 article-title: Active disturbance rejection control for MEMS gyroscopes publication-title: IEEE Transactions on Control Systems Technology doi: 10.1109/TCST.2008.2008638 – volume: 49 start-page: 40 year: 2013 ident: 10.1016/j.ijengsci.2017.01.004_bib0022 article-title: Steady-state transverse response of an axially moving beam with time-dependent axial speed publication-title: International Journal of Non-Linear Mechanics doi: 10.1016/j.ijnonlinmec.2012.08.003 – volume: 68 start-page: 11 year: 2013 ident: 10.1016/j.ijengsci.2017.01.004_bib0017 article-title: Nonlinear dynamics of a geometrically imperfect microbeam based on the modified couple stress theory publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2013.03.001 – start-page: 1 year: 2016 ident: 10.1016/j.ijengsci.2017.01.004_bib0016 article-title: Viscoelasticity effects on resonant response of a shear deformable extensible microbeam publication-title: Nonlinear Dynamics – volume: 84 start-page: 1 year: 2014 ident: 10.1016/j.ijengsci.2017.01.004_bib0047 article-title: Nonlinear modeling and size-dependent vibration analysis of curved microtubes conveying fluid based on modified couple stress theory publication-title: International Journal of Engineering Science doi: 10.1016/j.ijengsci.2014.06.007 – volume: 7 start-page: 370 year: 2007 ident: 10.1016/j.ijengsci.2017.01.004_bib0049 article-title: Nonlinear dynamic analysis of electrostatically actuated resonant MEMS sensors under parametric excitation publication-title: IEEE Sensors Journal doi: 10.1109/JSEN.2006.890158 |
| SSID | ssj0005399 |
| Score | 2.3274148 |
| Snippet | The nonlinear size-dependent dynamics of a functionally graded micro-cantilever is investigated when subject to a base excitation resulting in large-amplitude... |
| SourceID | proquest crossref elsevier |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 117 |
| SubjectTerms | Computer simulation Curvature Dynamical systems Dynamics Functionally graded micro-cantilever Functionally gradient materials Homogenization Kinetics MCST MEMS Nonlinear dynamics Scale effect Stiffness Stress state Time integration |
| Title | Dynamics of functionally graded micro-cantilevers |
| URI | https://dx.doi.org/10.1016/j.ijengsci.2017.01.004 https://www.proquest.com/docview/1932193975 |
| Volume | 115 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3PT8IwFG4IXvRg_BlRJDt4HWxru7ZHghLUyEkSbk3XtQSCQAAPXvzb7ds6g8aEg4cl27LXLF-7974u33sPoTsdkSw2iQiz2G1RiObujFIaCqUdm2Ca2KJn5MswHYzI05iOa6hX5cKArNL7_tKnF97a3-l4NDur6RRyfJOIJVByC0M-MCT8EsJglbc_d2QeWHiZRxTC0ztZwrP2dGYWEzc4SLxYUb7TN2z7I0D9ctVF_OmfoGNPHINu-W6nqGYWZ-hop5zgOYrvy_bym2BpAwhY5X---UcwWavc5MEbqO9CANP5AtBjXKBR_-G1Nwh9S4RQO-6_DbWjczyD5FRrCMu5wpmJsLZKxZpzrROVZnlmMhKz1GJNsebK5iwWTHFh3Ib0EtUXy4W5QoGxVGkaW02FIJQYrlKBhaZcKJzTyDQQrXCQ2tcLh7YVc1kJw2aywk8CfjKKpcOvgTrfdquyYsZeC1HBLH_MvXRufa9ts5oX6b--jQRS6g7B6PU_hr5Bh3BV6sKaqL5dv5tbx0C2WatYYi100H18Hgy_AN4y23g |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3PT8IwFH5BOKgH48-Iou7gdbKt69YeCUqG_DhBwq3puo5AcBDAg_-97dYpGhMOHpYsW16zfN1evy7f-x7Ao3D82JUetWNXbVF8QdQZxtimXCg2EQo_zXtGDoZBNPZfJ3hSgXZZC6NllSb3Fzk9z9bmStOg2VzNZrrG13NCT1tuIV0PTA6gpt2pcBVqrW4vGn4rPRA1Sg_H1gE7hcLzp9lcZlM1vlZ5hbmDp-nZ9sca9Stb50tQ5xRODHe0WsXjnUFFZudwvOMoeAHuc9FhfmMtU0uvWcWvvsWHNV3zRCbWmxbg2RpPlQ60JOMSxp2XUTuyTVcEWyj6v7WFYnQk1vWpqfTDhHAUSweJlHNXECKEx4M4iWXsu2GQIoGRIDxNQpeGnFCp9qRXUM2WmbwGS6aYC-ymAlOqoJOEBxRRgQnlKMGOrAMucWDCWIbrzhULVmrD5qzEj2n8mOMyhV8dml9xq8I0Y28ELWFmP6afqcy-N7ZRzgszH-CGaV6qDhrim38M_QCH0WjQZ_3usHcLR_pOIRNrQHW7fpd3ipBs43vzwn0CbHXeKQ |
| 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=Dynamics+of+functionally+graded+micro-cantilevers&rft.jtitle=International+journal+of+engineering+science&rft.au=Farokhi%2C+Hamed&rft.au=Ghayesh%2C+Mergen+H.&rft.au=Gholipour%2C+Alireza&rft.date=2017-06-01&rft.issn=0020-7225&rft.volume=115&rft.spage=117&rft.epage=130&rft_id=info:doi/10.1016%2Fj.ijengsci.2017.01.004&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_ijengsci_2017_01_004 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0020-7225&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0020-7225&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0020-7225&client=summon |