Dynamic Analysis of a Viscoelastic Nanobeam

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Vibration of an axially loaded viscoelastic nanobeam is analyzed in this study. Viscoelasticity of the nanobeam is modeled as a Kelvin-Voigt material. Equation of motion and boundary conditions for viscoelastic nanobeam are provided with help of Eringen’s Nonlocal Elasticity Theory. Initial conditions are used in solution of governing equation of motion. Damping effect of the viscoelastic nanobeam structure is investigated. Nonlocal effect on natural frequency and damping of nanobeam and critical buckling load is obtained.

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223-229

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April 2019

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© 2019 Trans Tech Publications Ltd. All Rights Reserved

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[1] A.C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54:9 (1983) 4703–4710.

DOI: 10.1063/1.332803

Google Scholar

[2] A.C. Eringen, Nonlocal polar elastic continua. Int. J. Eng. Sci. 10:1 (1972) 1–16.

Google Scholar

[3] Y. Lei, T. Murmu, S. Adhikari, and M.I. Friswell, Dynamic characteristics of damped viscoelastic nonlocal Euler-Bernoulli beams. Eur. J. Mech. A/Solids 42:(2013) 125–136.

DOI: 10.1016/j.euromechsol.2013.04.006

Google Scholar

[4] Y. Lei, S. Adhikari, and M.I. Friswell, Vibration of nonlocal Kelvin-Voigt viscoelastic damped Timoshenko beams. Int. J. Eng. Sci. 66–67:(2013) 1–13.

DOI: 10.1016/j.ijengsci.2013.02.004

Google Scholar

[5] C. Chen, S. Li, L. Dai, and C. Qian, Buckling and stability analysis of a piezoelectric viscoelastic nanobeam subjected to van der Waals forces. Commun. Nonlinear Sci. Numer. Simul. 19:5 (2014) 1626–1637.

DOI: 10.1016/j.cnsns.2013.09.017

Google Scholar

[6] I. Pavlović, R. Pavlović, I. Ćirić, and D. Karličić, Dynamic stability of nonlocal Voigt-Kelvin viscoelastic Rayleigh beams. Appl. Math. Model. 39:22 (2015) 6941–6950.

DOI: 10.1016/j.apm.2015.02.044

Google Scholar

[7] A.H. Ghorbanpour-Arani, A. Rastgoo, M.M. Sharafi, R. Kolahchi, and A. Ghorbanpour Arani, Nonlocal viscoelasticity based vibration of double viscoelastic piezoelectric nanobeam systems. Meccanica 51:1 (2016) 25–40.

DOI: 10.1007/s11012-014-9991-0

Google Scholar

[8] Y. Zhang, M. Pang, and L. Fan, Analyses of transverse vibrations of axially pretensioned viscoelastic nanobeams with small size and surface effects. Phys. Lett. Sect. A Gen. At. Solid State Phys. 380:29–30 (2016) 2294–2299.

DOI: 10.1016/j.physleta.2016.05.016

Google Scholar

[9] M. Cajic, D. Karlicic, and M. Lazarevic, Nonlocal vibration of a fractional order viscoelastic nanobeam with attached nanoparticle. Theor. Appl. Mech. 42:3 (2015) 167–190.

DOI: 10.2298/tam1503167c

Google Scholar

[10] R. Ansari, M. Faraji Oskouie, and R. Gholami, Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory. Phys. E Low-Dimensional Syst. Nanostructures 75:(2016) 266–271.

DOI: 10.1016/j.physe.2015.09.022

Google Scholar

[11] M.F. Oskouie, R. Ansari, and F. Sadeghi, Nonlinear vibration analysis of fractional viscoelastic Euler–Bernoulli nanobeams based on the surface stress theory. Acta Mech. Solida Sin. 30:4 (2017) 416–424.

DOI: 10.1016/j.camss.2017.07.003

Google Scholar

[12] R. Ansari, M. Faraji Oskouie, F. Sadeghi, and M. Bazdid-Vahdati, Free vibration of fractional viscoelastic Timoshenko nanobeams using the nonlocal elasticity theory. Phys. E Low-Dimensional Syst. Nanostructures 74:(2015) 318–327.

DOI: 10.1016/j.physe.2015.07.013

Google Scholar

[13] R. Ansari, M. Faraji Oskouie, and H. Rouhi, Studying linear and nonlinear vibrations of fractional viscoelastic Timoshenko micro-/nano-beams using the strain gradient theory. Nonlinear Dyn. 87:1 (2017) 695–711.

DOI: 10.1007/s11071-016-3069-6

Google Scholar

[14] M.F. Oskouie and R. Ansari, Linear and nonlinear vibrations of fractional viscoelastic Timoshenko nanobeams considering surface energy effects. Appl. Math. Model. 43:(2017) 337–350.

DOI: 10.1016/j.apm.2016.11.036

Google Scholar

[15] Q. Gong et al., Nonlinear vibration control with nanocapacitive sensor for electrostatically actuated nanobeam. J. Low Freq. Noise, Vib. Act. Control 0:0 (2017) 146134841772595.

DOI: 10.1177/1461348417725953

Google Scholar

[16] C. Wang, C. Lin, C. Liu, and C. Hsu, Analysis of Pull-in Characteristics of Double-clamped Nanobeam Incorporating Casimir and van der Waals Effects. Sensors Mater. 30:11 (2018) 2627.

DOI: 10.18494/sam.2018.2081

Google Scholar

[17] K. Marynowski, Non-Linear Dynamic Analysis of an Axialy Moving Viscoelastic Beam. J. Theor. Appl. Mech. (2002) 465–482.

Google Scholar

[18] Ö. Civalek, Ç. Demir, and B. Akgöz, Static analysis of single walled carbon nanotubes (SWCNT) based on Eringen's nonlocal elasticity theory. Int. J. Eng. Appl. Sci. 1:2 (2009) 47–56.

Google Scholar

[19] M. Arda and M. Aydogdu, Buckling of Eccentrically Loaded Carbon Nanotubes. Solid State Phenom. 267:1 (2017) 151–156.

DOI: 10.4028/www.scientific.net/ssp.267.151

Google Scholar

[20] M. Arda and M. Aydogdu, Nonlocal Gradient Approach on Torsional Vibration of CNTs. NOISE Theory Pract. 3:3 (2017) 2–10.

Google Scholar