Title

Nonlinear free vibration analysis of micro-beams resting on viscoelastic foundation based on the modified couple stress theory

Journal title

Archive of Mechanical Engineering

Yearbook

2017

Volume

vol. 64

Issue

No 2

Authors

Jam, Jafar Eskandari ; Noorabadi, Milad ; Namdaran, Nader

Affiliation

Jam, Jafar Eskandari : Composite Materials and Technology Cente, Malek Ashtar University of Technology, Tehran, Iran ; Noorabadi, Milad : Composite Materials and Technology Cente, Malek Ashtar University of Technology, Tehran, Iran ; Namdaran, Nader : Composite Materials and Technology Cente, Malek Ashtar University of Technology, Tehran, Iran

Keywords

nonlinear free vibration ; size dependent ; modified couple stress theory ; Euler-Bernoulli beam model ; Galerkin method

Divisions of PAS

Nauki Techniczne

Coverage

239-256

Publisher

Polish Academy of Sciences, Committee on Machine Building

Bibliography

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[32] B. Akgöz and Ö. Civalek. A new trigonometric beam model for buckling of strain gradient microbeams. International Journal of Mechanical Sciences, 81:88–94, 2014. doi: 10.1016/j.ijmecsci.2014.02.013.
[33] N. Shafiei, M. Kazemi, and M. Ghadiri. Nonlinear vibration of axially functionally graded tapered microbeams. International Journal of Engineering Science, 102:12–26, 2016. doi: 10.1016/j.ijengsci.2016.02.007.
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Date

2017

Type

Artykuły / Articles

Identifier

DOI: 10.1515/meceng-2017-0015 ; ISSN 0004-0738, e-ISSN 2300-1895

Source

Archive of Mechanical Engineering; 2017; vol. 64; No 2; 239-256

References

Kong (2008), The size - dependent natural frequency of Bernoulli Euler micro - beams, International Journal of Engineering Science, 20, 427, doi.org/10.1016/j.ijengsci.2007.10.002 ; Reddy (2010), Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates, International Journal of Engineering Science, 11, 1507, doi.org/10.1016/j.ijengsci.2010.09.020 ; Sedighi (2014), Modeling the size dependent static and dynamic pull - in instability of cantilever nanoactuator based on strain gradient theory, International Journal of Applied Mechanics, 14, 1450055, doi.org/10.1142/S1758825114500550 ; Thai (2013), Size - dependent functionally graded Kirchhoff and Mindlin plate models based on a modified couple stress theory, Composite Structures, 26, 142, doi.org/10.1016/j.compstruct.2012.08.023 ; Akgöz (2015), A novel microstructure - dependent shear deformable beam model, International Journal of Mechanical Sciences, 31, 10, doi.org/10.1016/j.ijmecsci.2015.05.003 ; Park (2006), Bernoulli Euler beam model based on a modified couple stress theory http stacks iop org, Journal of Micromechanics and Microengineering, 19, 2355. ; Taati (2014), Size - dependent generalized thermoelasticity model for Timoshenko micro - beams based on strain gradient and non - Fourier heat conduction theories, Composite Structures, 13, 116, doi.org/10.1016/j.compstruct.2014.05.040 ; Zhang (2001), A study of the static characteristics of a torsional micromirror A :, Sensors and Actuators Physical, 2, 73, doi.org/10.1016/S0924-4247(01)00453-8 ; Ke (2012), Nonlinear free vibration of size - dependent functionally graded microbeams, International Journal of Engineering Science, 18, 256, doi.org/10.1016/j.ijengsci.2010.12.008 ; Toupin (1962), Elastic materials with couple - stresses for and, Archive Rational Mechanics Analysis, 9, 385, doi.org/10.1007/BF00253945 ; Reddy (2012), A nonlinear modified couple stress - based third - order theory of functionally graded plates, Composite Structures, 24, 1128, doi.org/10.1016/j.compstruct.2011.10.006 ; Yong (2013), Gang Wen Hui Nonlinear free vibration of a microscale beam based on modified couple stress theory : Low - dimensional Systems and Nanostructures, Physica E, 35, 80, doi.org/10.1016/j.physe.2012.10.020 ; Fleck (1994), Strain gradient plasticity : theory and experiment, Acta Metallurgica et Materialia, 5, 475, doi.org/10.1016/0956-7151(94)90502-9 ; Taati (2016), Analytical solutions for the size dependent buckling and postbuckling behavior of functionally graded micro - plates ijengsci, International Journal of Engineering Science, 27, 45. ; Ma (2008), A microstructure - dependent Timoshenko beam model based on a modified couple stress theory the and of, Journal of Mechanics Physics Solids, 22, 3379, doi.org/10.1016/j.jmps.2008.09.007 ; Yang (2002), Couple stress based strain gradient theory for elasticity and, International Journal of Solids Structures, 10, 2731, doi.org/10.1016/S0020-7683(02)00152-X ; Akgöz (2014), A new trigonometric beam model for buckling of strain gradient microbeams, International Journal of Mechanical Sciences, 32, 81, doi.org/10.1016/j.ijmecsci.2014.02.013 ; Tilmans (1994), Electrostatically driven vacuum - encapsulated polysilicon resonators : Part II Theory and performance A :, Sensors and Actuators Physical, 4, 67, doi.org/10.1016/0924-4247(94)00813-2 ; Zhao (2004), A reduced - order model for electrically actuated microplates, Journal of Micromechanics and Microengineering, 3, 900, doi.org/10.1088/0960-1317/14/7/009 ; Ansari (2014), Nonlinear vibration analysis of Timoshenko nanobeams based on surface stress elasticity theory of Mechanics A /, European Journal Solids, 34, 143, doi.org/10.1016/j.euromechsol.2013.11.002 ; Ke (2011), Size effect on dynamic stability of functionally graded microbeams based on a modified couple stress theory, Composite Structures, 17, 342, doi.org/10.1016/j.compstruct.2010.09.008 ; Molaei Najafabadi (2014), Tabrizi Optimization of functionally graded materials in the slab symmetrically surface heated using transient analytical solution, Journal of Thermal Stresses, 16, 137, doi.org/10.1080/01495739.2013.839617 ; Reddy (2007), Nonlocal theories for bending , buckling and vibration of beams, International Journal of Engineering Science, 12, 288, doi.org/10.1016/j.ijengsci.2007.04.004 ; Eringen (1972), Nonlocal polar elastic continua, International Journal of Engineering Science, 10, 1, doi.org/10.1016/0020-7225(72)90070-5 ; Asghari (2013), A size - dependent model for functionally graded micro - plates for mechanical analyses, Journal of Vibration and Control, 23, 1614, doi.org/10.1177/1077546312442563 ; Lam (2003), Experiments and theory in strain gradient elasticity the and of, Journal of Mechanics Physics Solids, 8, 1477, doi.org/10.1016/S0022-5096(03)00053-X ; Shafiei (2016), Nonlinear vibration of axially functionally graded tapered microbeams, International Journal of Engineering Science, 33, 12, doi.org/10.1016/j.ijengsci.2016.02.007