Vibration
of an axially loaded viscoelastic nanobeam has been studied in this paper.
Viscoelasticity of the nanobeam has been modeled as a Kelvin-Voigt material. Equation
of motion and boundary conditions for an axially compressed nanobeam has been
obtained with help of Eringen’s Nonlocal Elasticity Theory. Viscoelasticity
effect on natural frequency and damping of nanobeam and critical buckling load
have been investigated. Nonlocality effect on nanobeam structure in the view of
viscoelasticity has been discussed.
Eringen A.C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics, 54, 4703–10, 1983. doi:10.1063/1.332803
Eringen A.C., Nonlocal polar elastic continua, International Journal of Engineering Science, 10, 1–16, 1972. doi:10.1016/0020-7225(72)90070-5
Lei Y., Murmu T., Adhikari S., Friswell M.I., Dynamic characteristics of damped viscoelastic nonlocal Euler-Bernoulli beams, European Journal of Mechanics, A/Solids, 42, 125–36, 2013. doi:10.1016/j.euromechsol.2013.04.006
Lei Y., Adhikari S., Friswell M.I., Vibration of nonlocal Kelvin-Voigt viscoelastic damped Timoshenko beams, International Journal of Engineering Science, 66–67, 1–13, 2013. doi:10.1016/j.ijengsci.2013.02.004
Chen C., Li S., Dai L., Qian C., Buckling and stability analysis of a piezoelectric viscoelastic nanobeam subjected to van der Waals forces, Communications in Nonlinear Science and Numerical Simulation, 19, 1626–37, 2014. doi:10.1016/j.cnsns.2013.09.017
Pavlović I., Pavlović R., Ćirić I., Karličić D., Dynamic stability of nonlocal Voigt-Kelvin viscoelastic Rayleigh beams, Applied Mathematical Modelling, 39, 6941–50, 2015. doi:10.1016/j.apm.2015.02.044
Civalek Ö., Demir C., Buckling and bending analyses of cantilever carbon nanotubes using the Euler-Bernoulli beam theory based on non-local continuum model, Asian Journal of Civil Engineering, 12, 651–62, 2011
Akgöz B., Civalek Ö., Buckling Analysis of Cantilever Carbon Nanotubes Using the Strain Gradient Elasticity and Modified Couple Stress Theories, Journal of Computational and Theoretical Nanoscience, 8, 1821–7, 2011. doi:10.1166/jctn.2011.1888
Mercan K., Civalek Ö., DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix, Composite Structures, 143, 300–9, 2016. doi:10.1016/j.compstruct.2016.02.040
Mercan K., Civalek Ö., Buckling analysis of Silicon carbide nanotubes (SiCNTs) with surface effect and nonlocal elasticity using the method of HDQ, Composites Part B: Engineering, 114, 34–45, 2017. doi:10.1016/j.compositesb.2017.01.067
Karličić D., Murmu T., Cajić M., Kozić P., Adhikari S., Dynamics of multiple viscoelastic carbon nanotube based nanocomposites with axial magnetic field, Journal of Applied Physics, 115, 234303, 2014. doi:10.1063/1.4883194
Ghorbanpour-Arani A.H., Rastgoo A., Sharafi M.M., Kolahchi R., Ghorbanpour Arani A., Nonlocal viscoelasticity based vibration of double viscoelastic piezoelectric nanobeam systems, Meccanica, 51, 25–40, 2016. doi:10.1007/s11012-014-9991-0
Mohammadi M., Safarabadi M., Rastgoo A., Farajpour A., Hygro-mechanical vibration analysis of a rotating viscoelastic nanobeam embedded in a visco-Pasternak elastic medium and in a nonlinear thermal environment, Acta Mechanica, 227, 2207–32, 2016. doi:10.1007/s00707-016-1623-4
Zhang Y., Pang M., Fan L., Analyses of transverse vibrations of axially pretensioned viscoelastic nanobeams with small size and surface effects, Physics Letters, Section A: General, Atomic and Solid State Physics, 380, 2294–9, 2016. doi:10.1016/j.physleta.2016.05.016
Ebrahimi F., Barati M.R., Vibration analysis of viscoelastic inhomogeneous nanobeams incorporating surface and thermal effects, Applied Physics A: Materials Science and Processing, 123, 1–10, 2017. doi:10.1007/s00339-016-0511-z
Ebrahimi F., Barati M.R., Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory, Composite Structures, 159, 433–44, 2017. doi:10.1016/j.compstruct.2016.09.092
Ebrahimi F., Barati M.R., Effect of three-parameter viscoelastic medium on vibration behavior of temperature-dependent non-homogeneous viscoelastic nanobeams in a hygro-thermal environment, Mechanics of Advanced Materials and Structures, 25, 361–74, 2018. doi:10.1080/15376494.2016.1255831
Ebrahimi F., Barati M.R., Vibration analysis of viscoelastic inhomogeneous nanobeams resting on a viscoelastic foundation based on nonlocal strain gradient theory incorporating surface and thermal effects, Acta Mechanica, 228, 1197–210, 2017. doi:10.1007/s00707-016-1755-6
Ebrahimi F., Barati M.R., Damping Vibration Behavior of Viscoelastic Porous Nanocrystalline Nanobeams Incorporating Nonlocal–Couple Stress and Surface Energy Effects, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 2017. doi:10.1007/s40997-017-0127-8
Attia M.A., Mahmoud F.F., Analysis of viscoelastic Bernoulli–Euler nanobeams incorporating nonlocal and microstructure effects, International Journal of Mechanics and Materials in Design, 13, 385–406, 2017. doi:10.1007/s10999-016-9343-4
Attia M.A., Abdel Rahman A.A., On vibrations of functionally graded viscoelastic nanobeams with surface effects, International Journal of Engineering Science, 127, 1–32, 2018. doi:10.1016/j.ijengsci.2018.02.005
Oskouie M.F., Ansari R., Linear and nonlinear vibrations of fractional viscoelastic Timoshenko nanobeams considering surface energy effects, Applied Mathematical Modelling, 43, 337–50, 2017. doi:10.1016/j.apm.2016.11.036
Oskouie M.F., Ansari R., Sadeghi F., Nonlinear vibration analysis of fractional viscoelastic Euler–Bernoulli nanobeams based on the surface stress theory, Acta Mechanica Solida Sinica, 30, 416–24, 2017. doi:10.1016/j.camss.2017.07.003
Ansari R., Faraji Oskouie M., Rouhi H., Studying linear and nonlinear vibrations of fractional viscoelastic Timoshenko micro-/nano-beams using the strain gradient theory, Nonlinear Dynamics, 87, 695–711, 2017. doi:10.1007/s11071-016-3069-6
Ansari R., Faraji Oskouie M., Gholami R., Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory, Physica E: Low-Dimensional Systems and Nanostructures, 75, 266–71, 2016. doi:10.1016/j.physe.2015.09.022
Ansari R., Faraji Oskouie M., Sadeghi F., Bazdid-Vahdati M., Free vibration of fractional viscoelastic Timoshenko nanobeams using the nonlocal elasticity theory, Physica E: Low-Dimensional Systems and Nanostructures, 74, 318–27, 2015. doi:10.1016/j.physe.2015.07.013
Cajic M., Karlicic D., Lazarevic M., Nonlocal vibration of a fractional order viscoelastic nanobeam with attached nanoparticle, Theoretical and Applied Mechanics, 42, 167–90, 2015. doi:10.2298/TAM1503167C
Marynowski K., Non-Linear Dynamic Analysis of an Axialy Moving Viscoelastic Beam, Journal of Theoretical and Applied Mechanics, 465–82, 2002
Eringen A.C., Nonlocal Continuum Field Theories. Springer New York, 2007
Civalek Ö., Demir Ç., Akgöz B., Static analysis of single walled carbon nanotubes (SWCNT) based on Eringen’s nonlocal elasticity theory, International Journal of Engineering and Applied Sciences, 1, 47–56, 2009
Akgöz B., Civalek Ö., Investigation of Size Effects on Static Response of Single-Walled Carbon Nanotubes Based on Strain Gradient Elasticity, International Journal of Computational Methods, 09, 1240032, 2012. doi:10.1142/S0219876212400324
Reddy J.N., Pang S.D., Nonlocal continuum theories of beams for the analysis of carbon nanotubes, Journal of Applied Physics, 103, 2008. doi:10.1063/1.2833431
Aydogdu M., A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration, Physica E: Low-Dimensional Systems and Nanostructures, 41, 1651–5, 2009. doi:10.1016/j.physe.2009.05.014
Arda M., Aydogdu M., Buckling of Eccentrically Loaded Carbon Nanotubes, Solid State Phenomena, 267, 151–6, 2017. doi:10.4028/www.scientific.net/SSP.267.151
Arda M., Aydogdu M., Nonlocal Gradient Approach on Torsional Vibration of CNTs, NOISE Theory and Practice, 3, 2–10, 2017
Lu P., Lee H.P., Lu C., Zhang P.Q., Dynamic properties of flexural beams using a nonlocal elasticity model, Journal of Applied Physics, 99, 073510, 2006. doi:10.1063/1.2189213
Eltaher M.A., Alshorbagy A.E., Mahmoud F.F., Vibration analysis of Euler-Bernoulli nanobeams by using finite element method, Applied Mathematical Modelling, 37, 4787–97, 2013. doi:10.1016/j.apm.2012.10.016
Romano G., Barretta R., Diaco M., Marotti de Sciarra F., Constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams, International Journal of Mechanical Sciences, 121, 151–6, 2017. doi:10.1016/j.ijmecsci.2016.10.036
Li C., A nonlocal analytical approach for torsion of cylindrical nanostructures and the existence of higher-order stress and geometric boundaries, Composite Structures, 118, 607–21, 2014. doi:10.1016/j.compstruct.2014.08.008
Li C., Torsional vibration of carbon nanotubes: Comparison of two nonlocal models and a semi-continuum model, International Journal of Mechanical Sciences, 82, 25–31, 2014. doi:10.1016/j.ijmecsci.2014.02.023
Challamel N., Reddy J.N., Wang C.M., Eringen’s Stress Gradient Model for Bending of Nonlocal Beams, Journal of Engineering Mechanics, 142, 04016095, 2016. doi:10.1061/(ASCE)EM.1943-7889.0001161
Eptaimeros K.G., Koutsoumaris C.C., Tsamasphyros G.J., Nonlocal integral approach to the dynamical response of nanobeams, International Journal of Mechanical Sciences, 115–116, 68–80, 2016. doi:10.1016/j.ijmecsci.2016.06.013
Shaat M., Faroughi S., Abasiniyan L., Paradoxes of differential nonlocal cantilever beams: Reasons and a novel solution, 1–17, 2017
Year 2018,
Volume: 10 Issue: 3, 252 - 263, 04.11.2018
Eringen A.C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics, 54, 4703–10, 1983. doi:10.1063/1.332803
Eringen A.C., Nonlocal polar elastic continua, International Journal of Engineering Science, 10, 1–16, 1972. doi:10.1016/0020-7225(72)90070-5
Lei Y., Murmu T., Adhikari S., Friswell M.I., Dynamic characteristics of damped viscoelastic nonlocal Euler-Bernoulli beams, European Journal of Mechanics, A/Solids, 42, 125–36, 2013. doi:10.1016/j.euromechsol.2013.04.006
Lei Y., Adhikari S., Friswell M.I., Vibration of nonlocal Kelvin-Voigt viscoelastic damped Timoshenko beams, International Journal of Engineering Science, 66–67, 1–13, 2013. doi:10.1016/j.ijengsci.2013.02.004
Chen C., Li S., Dai L., Qian C., Buckling and stability analysis of a piezoelectric viscoelastic nanobeam subjected to van der Waals forces, Communications in Nonlinear Science and Numerical Simulation, 19, 1626–37, 2014. doi:10.1016/j.cnsns.2013.09.017
Pavlović I., Pavlović R., Ćirić I., Karličić D., Dynamic stability of nonlocal Voigt-Kelvin viscoelastic Rayleigh beams, Applied Mathematical Modelling, 39, 6941–50, 2015. doi:10.1016/j.apm.2015.02.044
Civalek Ö., Demir C., Buckling and bending analyses of cantilever carbon nanotubes using the Euler-Bernoulli beam theory based on non-local continuum model, Asian Journal of Civil Engineering, 12, 651–62, 2011
Akgöz B., Civalek Ö., Buckling Analysis of Cantilever Carbon Nanotubes Using the Strain Gradient Elasticity and Modified Couple Stress Theories, Journal of Computational and Theoretical Nanoscience, 8, 1821–7, 2011. doi:10.1166/jctn.2011.1888
Mercan K., Civalek Ö., DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix, Composite Structures, 143, 300–9, 2016. doi:10.1016/j.compstruct.2016.02.040
Mercan K., Civalek Ö., Buckling analysis of Silicon carbide nanotubes (SiCNTs) with surface effect and nonlocal elasticity using the method of HDQ, Composites Part B: Engineering, 114, 34–45, 2017. doi:10.1016/j.compositesb.2017.01.067
Karličić D., Murmu T., Cajić M., Kozić P., Adhikari S., Dynamics of multiple viscoelastic carbon nanotube based nanocomposites with axial magnetic field, Journal of Applied Physics, 115, 234303, 2014. doi:10.1063/1.4883194
Ghorbanpour-Arani A.H., Rastgoo A., Sharafi M.M., Kolahchi R., Ghorbanpour Arani A., Nonlocal viscoelasticity based vibration of double viscoelastic piezoelectric nanobeam systems, Meccanica, 51, 25–40, 2016. doi:10.1007/s11012-014-9991-0
Mohammadi M., Safarabadi M., Rastgoo A., Farajpour A., Hygro-mechanical vibration analysis of a rotating viscoelastic nanobeam embedded in a visco-Pasternak elastic medium and in a nonlinear thermal environment, Acta Mechanica, 227, 2207–32, 2016. doi:10.1007/s00707-016-1623-4
Zhang Y., Pang M., Fan L., Analyses of transverse vibrations of axially pretensioned viscoelastic nanobeams with small size and surface effects, Physics Letters, Section A: General, Atomic and Solid State Physics, 380, 2294–9, 2016. doi:10.1016/j.physleta.2016.05.016
Ebrahimi F., Barati M.R., Vibration analysis of viscoelastic inhomogeneous nanobeams incorporating surface and thermal effects, Applied Physics A: Materials Science and Processing, 123, 1–10, 2017. doi:10.1007/s00339-016-0511-z
Ebrahimi F., Barati M.R., Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory, Composite Structures, 159, 433–44, 2017. doi:10.1016/j.compstruct.2016.09.092
Ebrahimi F., Barati M.R., Effect of three-parameter viscoelastic medium on vibration behavior of temperature-dependent non-homogeneous viscoelastic nanobeams in a hygro-thermal environment, Mechanics of Advanced Materials and Structures, 25, 361–74, 2018. doi:10.1080/15376494.2016.1255831
Ebrahimi F., Barati M.R., Vibration analysis of viscoelastic inhomogeneous nanobeams resting on a viscoelastic foundation based on nonlocal strain gradient theory incorporating surface and thermal effects, Acta Mechanica, 228, 1197–210, 2017. doi:10.1007/s00707-016-1755-6
Ebrahimi F., Barati M.R., Damping Vibration Behavior of Viscoelastic Porous Nanocrystalline Nanobeams Incorporating Nonlocal–Couple Stress and Surface Energy Effects, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 2017. doi:10.1007/s40997-017-0127-8
Attia M.A., Mahmoud F.F., Analysis of viscoelastic Bernoulli–Euler nanobeams incorporating nonlocal and microstructure effects, International Journal of Mechanics and Materials in Design, 13, 385–406, 2017. doi:10.1007/s10999-016-9343-4
Attia M.A., Abdel Rahman A.A., On vibrations of functionally graded viscoelastic nanobeams with surface effects, International Journal of Engineering Science, 127, 1–32, 2018. doi:10.1016/j.ijengsci.2018.02.005
Oskouie M.F., Ansari R., Linear and nonlinear vibrations of fractional viscoelastic Timoshenko nanobeams considering surface energy effects, Applied Mathematical Modelling, 43, 337–50, 2017. doi:10.1016/j.apm.2016.11.036
Oskouie M.F., Ansari R., Sadeghi F., Nonlinear vibration analysis of fractional viscoelastic Euler–Bernoulli nanobeams based on the surface stress theory, Acta Mechanica Solida Sinica, 30, 416–24, 2017. doi:10.1016/j.camss.2017.07.003
Ansari R., Faraji Oskouie M., Rouhi H., Studying linear and nonlinear vibrations of fractional viscoelastic Timoshenko micro-/nano-beams using the strain gradient theory, Nonlinear Dynamics, 87, 695–711, 2017. doi:10.1007/s11071-016-3069-6
Ansari R., Faraji Oskouie M., Gholami R., Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory, Physica E: Low-Dimensional Systems and Nanostructures, 75, 266–71, 2016. doi:10.1016/j.physe.2015.09.022
Ansari R., Faraji Oskouie M., Sadeghi F., Bazdid-Vahdati M., Free vibration of fractional viscoelastic Timoshenko nanobeams using the nonlocal elasticity theory, Physica E: Low-Dimensional Systems and Nanostructures, 74, 318–27, 2015. doi:10.1016/j.physe.2015.07.013
Cajic M., Karlicic D., Lazarevic M., Nonlocal vibration of a fractional order viscoelastic nanobeam with attached nanoparticle, Theoretical and Applied Mechanics, 42, 167–90, 2015. doi:10.2298/TAM1503167C
Marynowski K., Non-Linear Dynamic Analysis of an Axialy Moving Viscoelastic Beam, Journal of Theoretical and Applied Mechanics, 465–82, 2002
Eringen A.C., Nonlocal Continuum Field Theories. Springer New York, 2007
Civalek Ö., Demir Ç., Akgöz B., Static analysis of single walled carbon nanotubes (SWCNT) based on Eringen’s nonlocal elasticity theory, International Journal of Engineering and Applied Sciences, 1, 47–56, 2009
Akgöz B., Civalek Ö., Investigation of Size Effects on Static Response of Single-Walled Carbon Nanotubes Based on Strain Gradient Elasticity, International Journal of Computational Methods, 09, 1240032, 2012. doi:10.1142/S0219876212400324
Reddy J.N., Pang S.D., Nonlocal continuum theories of beams for the analysis of carbon nanotubes, Journal of Applied Physics, 103, 2008. doi:10.1063/1.2833431
Aydogdu M., A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration, Physica E: Low-Dimensional Systems and Nanostructures, 41, 1651–5, 2009. doi:10.1016/j.physe.2009.05.014
Arda M., Aydogdu M., Buckling of Eccentrically Loaded Carbon Nanotubes, Solid State Phenomena, 267, 151–6, 2017. doi:10.4028/www.scientific.net/SSP.267.151
Arda M., Aydogdu M., Nonlocal Gradient Approach on Torsional Vibration of CNTs, NOISE Theory and Practice, 3, 2–10, 2017
Lu P., Lee H.P., Lu C., Zhang P.Q., Dynamic properties of flexural beams using a nonlocal elasticity model, Journal of Applied Physics, 99, 073510, 2006. doi:10.1063/1.2189213
Eltaher M.A., Alshorbagy A.E., Mahmoud F.F., Vibration analysis of Euler-Bernoulli nanobeams by using finite element method, Applied Mathematical Modelling, 37, 4787–97, 2013. doi:10.1016/j.apm.2012.10.016
Romano G., Barretta R., Diaco M., Marotti de Sciarra F., Constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams, International Journal of Mechanical Sciences, 121, 151–6, 2017. doi:10.1016/j.ijmecsci.2016.10.036
Li C., A nonlocal analytical approach for torsion of cylindrical nanostructures and the existence of higher-order stress and geometric boundaries, Composite Structures, 118, 607–21, 2014. doi:10.1016/j.compstruct.2014.08.008
Li C., Torsional vibration of carbon nanotubes: Comparison of two nonlocal models and a semi-continuum model, International Journal of Mechanical Sciences, 82, 25–31, 2014. doi:10.1016/j.ijmecsci.2014.02.023
Challamel N., Reddy J.N., Wang C.M., Eringen’s Stress Gradient Model for Bending of Nonlocal Beams, Journal of Engineering Mechanics, 142, 04016095, 2016. doi:10.1061/(ASCE)EM.1943-7889.0001161
Eptaimeros K.G., Koutsoumaris C.C., Tsamasphyros G.J., Nonlocal integral approach to the dynamical response of nanobeams, International Journal of Mechanical Sciences, 115–116, 68–80, 2016. doi:10.1016/j.ijmecsci.2016.06.013
Shaat M., Faroughi S., Abasiniyan L., Paradoxes of differential nonlocal cantilever beams: Reasons and a novel solution, 1–17, 2017
Arda, M. (2018). Vibration Analysis of an Axially Loaded Viscoelastic Nanobeam. International Journal of Engineering and Applied Sciences, 10(3), 252-263. https://doi.org/10.24107/ijeas.468769
AMA
Arda M. Vibration Analysis of an Axially Loaded Viscoelastic Nanobeam. IJEAS. November 2018;10(3):252-263. doi:10.24107/ijeas.468769
Chicago
Arda, Mustafa. “Vibration Analysis of an Axially Loaded Viscoelastic Nanobeam”. International Journal of Engineering and Applied Sciences 10, no. 3 (November 2018): 252-63. https://doi.org/10.24107/ijeas.468769.
EndNote
Arda M (November 1, 2018) Vibration Analysis of an Axially Loaded Viscoelastic Nanobeam. International Journal of Engineering and Applied Sciences 10 3 252–263.
IEEE
M. Arda, “Vibration Analysis of an Axially Loaded Viscoelastic Nanobeam”, IJEAS, vol. 10, no. 3, pp. 252–263, 2018, doi: 10.24107/ijeas.468769.
ISNAD
Arda, Mustafa. “Vibration Analysis of an Axially Loaded Viscoelastic Nanobeam”. International Journal of Engineering and Applied Sciences 10/3 (November 2018), 252-263. https://doi.org/10.24107/ijeas.468769.
JAMA
Arda M. Vibration Analysis of an Axially Loaded Viscoelastic Nanobeam. IJEAS. 2018;10:252–263.
MLA
Arda, Mustafa. “Vibration Analysis of an Axially Loaded Viscoelastic Nanobeam”. International Journal of Engineering and Applied Sciences, vol. 10, no. 3, 2018, pp. 252-63, doi:10.24107/ijeas.468769.
Vancouver
Arda M. Vibration Analysis of an Axially Loaded Viscoelastic Nanobeam. IJEAS. 2018;10(3):252-63.