Large-amplitude dynamics of a functionally graded microcantilever with an intermediate spring-support and a point-mass
Numerical modelling and simulations are conducted on the large-amplitude dynamics of a functionally graded microcantilever with a tip-mass, additionally supported by an intermediate spring; the functionally graded microsystem is subject to a base excitation. Since one end of the microsystem is free...
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| Published in | Acta mechanica Vol. 228; no. 12; pp. 4309 - 4323 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Vienna
Springer Vienna
01.12.2017
Springer Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0001-5970 1619-6937 |
| DOI | 10.1007/s00707-017-1858-8 |
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| Abstract | Numerical modelling and simulations are conducted on the large-amplitude dynamics of a functionally graded microcantilever with a tip-mass, additionally supported by an intermediate spring; the functionally graded microsystem is subject to a base excitation. Since one end of the microsystem is free to move, it undergoes large deformation; curvature-related nonlinearities play an important role. Taking into account this type of nonlinearity, using the Mori–Tanaka homogenisation scheme, as well as the modified couple stress theory, an energy technique is employed to derive the nonlinearly coupled equations for the longitudinal and transverse motions. An inextensibility assumption is applied for the functionally graded microcantilever, and hence, a nonlinear equation of motion for the transverse motion involving inertial (apart from stiffness) nonlinearity is obtained. For the functionally graded microsystem considered, effects of the length-scale parameter, the material gradient index, the tip-mass, and the stiffness of the spring-support on the nonlinear resonant responses are highlighted by means of a Houbolt’s finite difference scheme together with Newton–Raphson method. |
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| AbstractList | Numerical modelling and simulations are conducted on the large-amplitude dynamics of a functionally graded microcantilever with a tip-mass, additionally supported by an intermediate spring; the functionally graded microsystem is subject to a base excitation. Since one end of the microsystem is free to move, it undergoes large deformation; curvature-related nonlinearities play an important role. Taking into account this type of nonlinearity, using the Mori-Tanaka homogenisation scheme, as well as the modified couple stress theory, an energy technique is employed to derive the nonlinearly coupled equations for the longitudinal and transverse motions. An inextensibility assumption is applied for the functionally graded microcantilever, and hence, a nonlinear equation of motion for the transverse motion involving inertial (apart from stiffness) nonlinearity is obtained. For the functionally graded microsystem considered, effects of the length-scale parameter, the material gradient index, the tip-mass, and the stiffness of the spring-support on the nonlinear resonant responses are highlighted by means of a Houbolt's finite difference scheme together with Newton-Raphson method. |
| Audience | Academic |
| Author | Gholipour, Alireza Ghayesh, Mergen H. Farokhi, Hamed |
| Author_xml | – sequence: 1 givenname: Mergen H. surname: Ghayesh fullname: Ghayesh, Mergen H. email: mergen.ghayesh@adelaide.edu.au organization: School of Mechanical Engineering, University of Adelaide – sequence: 2 givenname: Hamed surname: Farokhi fullname: Farokhi, Hamed organization: Department of Mechanical Engineering, McGill University – sequence: 3 givenname: Alireza surname: Gholipour fullname: Gholipour, Alireza organization: School of Mechanical Engineering, University of Adelaide |
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| CitedBy_id | crossref_primary_10_1016_j_tws_2024_112005 crossref_primary_10_1016_j_compstruct_2018_11_079 crossref_primary_10_1007_s00419_022_02164_8 crossref_primary_10_1016_j_ijengsci_2018_12_001 crossref_primary_10_1016_j_tws_2021_108101 |
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| References | Ghayesh, Farokhi (CR12) 2016; 11 Tajalli, Rahaeifard, Kahrobaiyan, Movahhedy, Akbari, Ahmadian (CR24) 2013; 102 Ke, Wang, Yang, Kitipornchai (CR27) 2012; 50 Akgöz, Civalek (CR25) 2014; 85 Fernandes, Mousavi, El-Borgi (CR1) 2016; 227 Lü, Lim, Chen (CR2) 2009; 46 Lam, Yang, Chong, Wang, Tong (CR6) 2003; 51 Aghazadeh, Cigeroglu, Dag (CR28) 2014; 46 Ghayesh, Farokhi (CR19) 2015; 96 Witvrouw, Mehta (CR4) 2005; 492 Shafiei, Kazemi, Ghadiri (CR32) 2016; 101 Ghayesh, Farokhi (CR7) 2015; 227 Taati, Molaei Najafabadi, Basirat Tabrizi (CR11) 2014; 225 Ansari, Shojaei, Gholami (CR14) 2016; 136 Şimşek, Aydın, Yurtcu, Reddy (CR8) 2015; 226 Li, Li, Hu, Ding, Deng (CR21) 2017; 165 McFarland, Colton (CR5) 2005; 15 Arbind, Reddy (CR29) 2013; 98 Akgöz, Civalek (CR31) 2013; 98 Ghayesh, Amabili (CR17) 2014; 60 Şimşek, Reddy (CR26) 2013; 101 Farokhi, Ghayesh, Hussain (CR36) 2016; 106 Ghayesh, Amabili (CR35) 2012; 112–113 Farokhi, Ghayesh, Amabili (CR16) 2013; 113 Huang (CR3) 2008; 45 Ghayesh, Amabili (CR33) 2013; 49 Mirsalehi, Azhari, Amoushahi (CR22) 2017; 61 Fakhrabadi, Rastgoo, Ahmadian, Mashhadi (CR10) 2014; 225 Gholipour, Farokhi, Ghayesh (CR13) 2015; 79 Dai, Wang, Wang (CR37) 2015; 94 Ghayesh, Farokhi, Alici (CR23) 2016; 11 Darijani, Shahdadi (CR9) 2015; 226 Roque, Fidalgo, Ferreira, Reddy (CR15) 2013; 96 Asghari, Ahmadian, Kahrobaiyan, Rahaeifard (CR30) 2010; 31 Ghayesh, Farokhi, Gholipour, Hussain, Arjomandi (CR18) 2017; 12 Dehrouyeh-Semnani, Bahrami (CR20) 2016; 107 Ghayesh, Amabili, Farokhi (CR34) 2013; 51 M Mirsalehi (1858_CR22) 2017; 61 AM Dehrouyeh-Semnani (1858_CR20) 2016; 107 DCC Lam (1858_CR6) 2003; 51 MH Ghayesh (1858_CR33) 2013; 49 MH Ghayesh (1858_CR12) 2016; 11 L-L Ke (1858_CR27) 2012; 50 R Ansari (1858_CR14) 2016; 136 M Şimşek (1858_CR8) 2015; 226 N Shafiei (1858_CR32) 2016; 101 R Aghazadeh (1858_CR28) 2014; 46 DW Huang (1858_CR3) 2008; 45 M Şimşek (1858_CR26) 2013; 101 H Darijani (1858_CR9) 2015; 226 B Akgöz (1858_CR31) 2013; 98 A Witvrouw (1858_CR4) 2005; 492 HL Dai (1858_CR37) 2015; 94 H Farokhi (1858_CR16) 2013; 113 E Taati (1858_CR11) 2014; 225 CMC Roque (1858_CR15) 2013; 96 CF Lü (1858_CR2) 2009; 46 S Tajalli (1858_CR24) 2013; 102 MH Ghayesh (1858_CR35) 2012; 112–113 AW McFarland (1858_CR5) 2005; 15 B Akgöz (1858_CR25) 2014; 85 MH Ghayesh (1858_CR18) 2017; 12 R Fernandes (1858_CR1) 2016; 227 X Li (1858_CR21) 2017; 165 MH Ghayesh (1858_CR7) 2015; 227 A Arbind (1858_CR29) 2013; 98 MH Ghayesh (1858_CR19) 2015; 96 M Asghari (1858_CR30) 2010; 31 M Fakhrabadi (1858_CR10) 2014; 225 A Gholipour (1858_CR13) 2015; 79 MH Ghayesh (1858_CR23) 2016; 11 MH Ghayesh (1858_CR17) 2014; 60 H Farokhi (1858_CR36) 2016; 106 MH Ghayesh (1858_CR34) 2013; 51 |
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| SubjectTerms | Classical and Continuum Physics Computer simulation Control Curvature Deformation Dynamical Systems Engineering Engineering Thermodynamics Equations of motion Finite difference method Functionally gradient materials Heat and Mass Transfer Mathematical models Nonlinear equations Nonlinearity Numerical analysis Original Paper Simulation Solid Mechanics Spring supports Stiffness Theoretical and Applied Mechanics Vibration |
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| Title | Large-amplitude dynamics of a functionally graded microcantilever with an intermediate spring-support and a point-mass |
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