Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Microsystem Technologies
Erschienen in: Microsystem Technologies 4/2017

20.01.2016 | Technical Paper

Influence of surface effects on vibration behavior of a rotary functionally graded nanobeam based on Eringen’s nonlocal elasticity

verfasst von: Majid Ghadiri, Navvab Shafiei, Hamed Safarpour

Erschienen in: Microsystem Technologies | Ausgabe 4/2017

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This article presents a free vibration analysis of size-dependent functionally graded rotating nanobeams with all surface effects considerations on the basis of the nonlocal continuum model. By using constitutive differential model of Eringen, the nonlocal elastic behavior is described which enables the present model to become effective in design and analysis of nanoactuators and nanosensors. The material for this work is a functionally graded which according to power law distribution, it is assumed that its bottom surface is aluminum and the top one is silicon. Taking attention to Euler–Bernoulli beam theory, the modeled nanobeam and its equations of motion are derived using Hamilton’s principle. Novillity of this work is considering the effects of rotation and surface effects in addition to considering various boundary conditions of the FG nanobeam. The generalized differential quadrature method is used to discretize the model and to get a numerical approximation of the equation of motion. The model is validated by comparing the benchmark results with the obtained ones. Then influence of surfaces effects, nonlocal parameter, angular velocity, volume fraction index and boundary conditions on natural frequency ratio of the rotating FG nanobeams are investigated.
Vorheriger Artikel Research on the master–slave compound multi-cantilever piezoelectric energy harvester
Nächster Artikel Design and control of a novel piezo-driven XY parallel nanopositioning stage

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
Akgöz B, Civalek Ö (2012) Analysis of micro-sized beams for various boundary conditions based on the strain gradient elasticity theory. Arch Appl Mech 82(3):423–443CrossRefMATH
Aranda-Ruiz J, Loya J, Fernández-Sáez J (2012) Bending vibrations of rotating nonuniform nanocantilevers using the Eringen nonlocal elasticity theory. Compos Struct 94(9):2990–3001CrossRef
Asghari M et al (2010) On the size-dependent behavior of functionally graded micro-beams. Mater Des 31(5):2324–2329CrossRef
Asghari M et al (2011) Investigation of the size effects in Timoshenko beams based on the couple stress theory. Arch Appl Mech 81(7):863–874CrossRefMATH
Bath J, Turberfield AJ (2007) DNA nanomachines. Nat Nano 2(5):275–284CrossRef
Bellman R, Kashef B, Casti J (1972) Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. J Comput Phys 10(1):40–52MathSciNetCrossRefMATH
Chen L et al (2012) Engineering controllable bidirectional molecular motors based on myosin. Nat Nano 7(4):252–256CrossRef
Chen T, Chiu M-S, Weng C-N (2006) Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids. J Appl Phys 100(7):074308CrossRef
Chong A et al (2001) Torsion and bending of micron-scaled structures. J Mater Res 16(04):1052–1058CrossRef
Dehrouyeh-Semnani AM (2015) The influence of size effect on flapwise vibration of rotating microbeams. Int J Eng Sci 94:150–163MathSciNetCrossRef
Ebrahimi F, Salari E (2015) Thermo-mechanical vibration analysis of nonlocal temperature-dependent FG nanobeams with various boundary conditions. Compos B Eng 78:272–290CrossRef
Eltaher M et al (2013) Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams. Appl Math Comput 224:760–774MathSciNetMATH
Eltaher M, Emam SA, Mahmoud F (2012) Free vibration analysis of functionally graded size-dependent nanobeams. Appl Math Comput 218(14):7406–7420MathSciNetMATH
Eltaher M, Emam SA, Mahmoud F (2013) Static and stability analysis of nonlocal functionally graded nanobeams. Compos Struct 96:82–88CrossRef
Eringen AC (1983) On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys 54(9):4703–4710CrossRef
Fleck N et al (1994) Strain gradient plasticity: theory and experiment. Acta Metall Mater 42(2):475–487CrossRef
Ghadiri M, Shafiei N (2015a) Nonlinear bending vibration of a rotating nanobeam based on nonlocal Eringen’s theory using differential quadrature method. Microsyst Technol. doi:10.​1007/​s00542-015-2662-9
Ghadiri M, Shafiei N (2015b) Vibration analysis of rotating nanoplate based on eringen nonlocal elasticity appling differential quadrature method. J Vib Control. doi:10.​1177/​1077546315627723​
Goel A, Vogel V (2008) Harnessing biological motors to engineer systems for nanoscale transport and assembly. Nat Nano 3(8):465–475CrossRef
Guo J et al (2015) Ultra-durable rotary micromotors assembled from nanoentities by electric fields. Nanoscale 7(26):11363–11370CrossRef
Gurtin ME, Murdoch AI (1978) Surface stress in solids. Int J Solids Struct 14(6):431–440CrossRefMATH
Gurtin M, Weissmüller J, Larche F (1998) A general theory of curved deformable interfaces in solids at equilibrium. Philos Magn A 78(5):1093–1109CrossRef
Hosseini-Hashemi S, Nazemnezhad R, Bedroud M (2014) Surface effects on nonlinear free vibration of functionally graded nanobeams using nonlocal elasticity. Appl Math Model 38(14):3538–3553MathSciNetCrossRef
Lee Z et al (2006) Metallic NEMS components fabricated from nanocomposite Al–Mo films. Nanotechnology 17(12):3063CrossRef
Lee LK et al (2010) Structure of the torque ring of the flagellar motor and the molecular basis for rotational switching. Nature 466(7309):996–1000CrossRef
Lee H-L, Chang W-J (2010) Surface effects on frequency analysis of nanotubes using nonlocal Timoshenko beam theory. J Appl Phys 108(9):093503CrossRef
Lei X-W et al (2012) Surface effects on the vibrational frequency of double-walled carbon nanotubes using the nonlocal Timoshenko beam model. Compos B Eng 43(1):64–69CrossRef
Lubbe AS et al (2011) Control of rotor function in light-driven molecular motors. J Org Chem 76(21):8599–8610CrossRef
Lü C, Lim CW, Chen W (2009) Size-dependent elastic behavior of FGM ultra-thin films based on generalized refined theory. Int J Solids Struct 46(5):1176–1185CrossRefMATH
Miller RE, Shenoy VB (2000) Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11(3):139CrossRef
Narendar S (2011) Mathematical modelling of rotating single-walled carbon nanotubes used in nanoscale rotational actuators. Def Sci J 61(4):317–324CrossRef
Narendar S (2012) Differential quadrature based nonlocal flapwise bending vibration analysis of rotating nanotube with consideration of transverse shear deformation and rotary inertia. Appl Math Comput 219(3):1232–1243MathSciNetMATH
Narendar S, Gopalakrishnan S (2011) Nonlocal wave propagation in rotating nanotube. Res Phys 1(1):17–25
Natarajan S et al (2012) Size-dependent free flexural vibration behavior of functionally graded nanoplates. Comput Mater Sci 65:74–80CrossRef
Pradhan SC, Murmu T (2010) Application of nonlocal elasticity and DQM in the flapwise bending vibration of a rotating nanocantilever. Phys E 42(7):1944–1949CrossRef
Rahaeifard M, Kahrobaiyan M, Ahmadian M (2009) Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials. in ASME 2009 international design engineering technical conferences and computers and information in engineering conference. American Society of Mechanical Engineers
Reddy J (2010) Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates. Int J Eng Sci 48(11):1507–1518MathSciNetCrossRefMATH
Ru C (2010) Simple geometrical explanation of Gurtin-Murdoch model of surface elasticity with clarification of its related versions. Sci China Phys Mech Astron 53(3):536–544CrossRef
Safarabadi M et al (2015) Effect of surface energy on the vibration analysis of rotating nanobeam. J Solid Mech 7(3):299–311
Salamat-talab M, Nateghi A, Torabi J (2012) Static and dynamic analysis of third-order shear deformation FG micro beam based on modified couple stress theory. Int J Mech Sci 57(1):63–73CrossRef
Shafiei N, Kazemi M, Fatahi L (2015a) Transverse vibration of rotary tapered microbeam based on modified couple stress theory and generalized differential quadrature element method. Mechanics of Advanced Materials and Structures. doi:10.​1080/​15376494.​2015.​1128025
Shu C, Richards BE (1992) Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations. Int J Numer Meth Fluids 15(7):791–798CrossRefMATH
Shu C (2000) Application of Differential Quadrature Method to Structural and Vibration Analysis. Differential Quadrature and Its Application in Engineering. Springer, London, pp 186–223. doi:10.​1007/​978-1-4471-0407-0_​7
Şimşek M, Yurtcu H (2013) Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory. Compos Struct 97:378–386CrossRef
Tauchert TR (1974) Energy principles in structural mechanics. McGraw-Hill Companies, New York
Thai H-T (2012) A nonlocal beam theory for bending, buckling, and vibration of nanobeams. Int J Eng Sci 52:56–64MathSciNetCrossRef
Tierney HL et al (2011) Experimental demonstration of a single-molecule electric motor. Nat Nano 6(10):625–629CrossRef
van Delden RA et al (2005) Unidirectional molecular motor on a gold surface. Nature 437(7063):1337–1340CrossRef
Wang G-F, Feng X-Q (2007) Effects of surface elasticity and residual surface tension on the natural frequency of microbeams. Appl Phys Lett 90(23):231904CrossRef
Wang CM, Zhang YY, He XQ (2007) Vibration of nonlocal Timoshenko beams. Nanotechnology 18(10):105401CrossRef
Witvrouw A, Mehta A (2005) The use of functionally graded poly-SiGe layers for MEMS applications. In: Materials science forum, vol 492. Trans Tech Publications, Switzerland, pp 255–260
Xu X, Kim K, Fan D (2015) tunable release of multiplex biochemicals by plasmonically active rotary nanomotors. Angew Chem Int Ed 54(8):2525–2529CrossRef
Metadaten
Titel
Influence of surface effects on vibration behavior of a rotary functionally graded nanobeam based on Eringen’s nonlocal elasticity
verfasst von
Majid Ghadiri
Navvab Shafiei
Hamed Safarpour
Publikationsdatum
20.01.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
Microsystem Technologies / Ausgabe 4/2017
Print ISSN: 0946-7076
Elektronische ISSN: 1432-1858
DOI
https://doi.org/10.1007/s00542-016-2822-6

Weitere Artikel der Ausgabe 4/2017

Microsystem Technologies 4/2017 Zur Ausgabe

Technical Paper

Design and control of a novel piezo-driven XY parallel nanopositioning stage

Technical Paper

Gas-assisted light-cure microstructure transfer molding and transfer transformation

Technical Paper

An overview of additive manufacturing (3D printing) for microfabrication

Technical Paper

Transferring stress and temperature sensors for stress measurement of wafer level packaging

Technical Paper

Investigations of silicon wafer bonding utilizing sputtered Al and Sn films

Technical Paper

The analysis of the self-oscillation system for resonant pressure sensor

Neuer Inhalt

    Bildnachweise