TEMPERATURE-DEPENDENT PHYSICAL CHARACTERISTICS OF THE ROTATING NONLOCAL NANOBEAMS SUBJECT TO A VARYING HEAT SOURCE AND A DYNAMIC LOAD

Ahmed E. Abouelregal, Hamid Mohammad-Sedighi, Seyed Ali Faghidian, Ali Heidari Shirazi

DOI Number
https://doi.org/10.22190/FUME201222024A
First page
633
Last page
656

Abstract


In this article, the influence of thermal conductivity on the dynamics of a rotating nanobeam is established in the context of nonlocal thermoelasticity theory. To this end, the governing equations are derived using generalized heat conduction including phase lags on the basis of the Euler–Bernoulli beam theory. The thermal conductivity of the proposed model linearly changes with temperature and the considered nanobeam is excited with a variable harmonic heat source and exposed to a time-dependent load with exponential decay. The analytic solutions for bending moment, deflection and temperature of rotating nonlocal nanobeams are achieved by means of the Laplace transform procedure. A qualitative study is conducted to justify the soundness of the present analysis while the impact of nonlocal parameter and varying heat source are discussed in detail. It also shows the way in which the variations of physical properties due to temperature changes affect the static and dynamic behavior of rotating nanobeams. It is found that the physical fields strongly depend on the nonlocal parameter, the change of the thermal conductivity, rotation speed and the mechanical loads and, therefore, it is not possible to neglect their effects on the manufacturing process of precise/intelligent machines and devices.

Keywords

Nonlocal Elasticity, Rotating Nanobeam, Thermoelasticity, Variable Thermal Conductivity, Varying Load

Full Text:

PDF

References


Lord, H.W., Shulman, Y.H.,1967, A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids,15(5), pp. 299–309.

Tzou, D.Y.,1992, Thermal shock phenomena under high rate response in solids, Annual Rev. Heat Transf., 4(4), pp. 111–185.

Tzou, D.Y.,1995, A unified field approach for heat conduction from macro-to micro-scales, J. Heat Transf., 117(1), pp. 8–16.

Tzou, D.Y.,1995, The generalized lagging response in small-scale and high-rate heating, Int. J. Heat Mass Transf., 38(17), pp. 3231–3240.

Abouelregal, A.E. 2019, Two-temperature thermoelastic model without energy dissipation including higher order time-derivatives and two phase-lags, Materials Research Express, 6(11), 116535.

Abouelregal, A.E.,2020, On Green and Naghdithermoelasticity model without energy dissipation with higher order time differential and phase-lags, Journal of Applied and Computational Mechanics, 6(3),pp. 445–56.

Abouelregal, A.E.,2019, A novel generalized thermoelasticity with higher-order time-derivatives and three-phase lags, Multidiscipline Modeling in Materials and Structures, doi: 10.1108/MMMS-07-2019-0138.

Abouelregal, A.E.,2019, Three-phase-lag thermoelastic heat conduction model with higher-order time-fractional derivatives, Indian J. Phys. https://doi.org/10.1007/s12648-019-01635-z.

Berman, R.,1953, The thermal conductivity of dielectric solids at low temperatures, Advances in Physics, 2(5), pp. 103-140.

Younis, M.I.,2011, MEMS Linear and Non-linear Statics and Dynamics, Springer, New York, USA.

Allameh, S.M.,2003, An introduction to mechanical-properties-related issues in MEMS structures, J. Mater. Sci., 38, pp. 4115–4123.

Sedighi, H.M., Bozorgmehri, A., 2016, Dynamic instability analysis of doubly clamped cylindrical nanowires in the presence of Casimir attraction and surface effects using modified couple stress theory,Acta Mech., 227, pp. 1575-1591.

Malikan, M., Uglov, N. S., Eremeyev, V.A., 2020,On instabilities and post-buckling of piezomagnetic and flexomagnetic nanostructures, International Journal of Engineering Science, 157, 103395.

Malikan, M., Eremeyev, V. A.,Żur, K. K.,2020,Effect of Axial Porosities on Flexomagnetic Response of In-Plane Compressed PiezomagneticNanobeams, Symmetry, 12(12), 1935.

Malikan, M., &Eremeyev, V.A., 2020,On Nonlinear Bending Study of a Piezo-FlexomagneticNanobeam Based on an Analytical-Numerical Solution, Nanomaterials, 10(9), 1762.

Malikan, M., Eremeyev, V.A., 2020,On the Dynamics of a Visco–Piezo–FlexoelectricNanobeam, Symmetry, 12(4), 643.

Eringen,A.C.,1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, J Appl Phys, 54, pp. 4703–4710.

Eringen, A.C.,1972, Nonlocal polar elastic continua,Int J EngSci, 10, pp. 1–16.

Sedighi, H.M., Keivani, M., Abadyan, M.R., 2015, Modified continuum model for stability analysis of asymmetric FGM double-sided NEMS: Corrections due to finite conductivity, surface energy and nonlocal effect, Composites Part B: Engineering, 83, pp. 117-133.

Abouelregal, A.E., Marin, M.,2020, The size-dependent thermoelastic vibrations of nanobeams subjected to harmonic excitation and rectified sine wave heating, Mathematics; 8(7), 1128.

Barretta, R., Faghidian, S.A., Marotti de Sciarra, F., Pinnola, F.P., 2020, Timoshenko nonlocal strain gradient nanobeams: variational consistency, exact solutions and carbon nanotube Young moduli, Mechanics of Advanced Materials and Structures, 2020, doi: 10.1080/15376494.2019.1683660.

Abouelregal, A.E., Mohammed, W.W., 2020, Effects of nonlocal thermoelasticity on nanoscale beams based on couple stress theory, Mathematical Methods in the Applied Sciences, doi:10.1002/mma.6764.

Abouelregal A.E., Marin M.,2020, The response of nanobeams with temperature-dependent properties using state-space method via modified couple stress theory, Symmetry, 12(8), 1276.

Barretta, R., Faghidian, S.A., Marotti de Sciarra, F., Penna, R., Pinnola, F.P., 2020,On torsion of nonlocal Lam strain gradient FG elastic beams, Composite Structures, 233, 111550.

Shabani, S., Cunedioglu, Y. 2020, Free vibration analysis of cracked functionally graded non-uniform beams, Mater. Res. Express, 7, 015707.

Romano, G., Barretta, R., 2017, Nonlocal elasticity in nanobeams: the stress-driven integral model, International Journal of Engineering Science, 115, pp. 14-27.

Barretta, R., Feo, L., Luciano, R., Marotti de Sciarra, F., Penna, R., 2017, Nano-beams under torsion: a stress-driven nonlocal approach, PSU Research Review, 1(2), pp. 164-169.

Drexler, K. E., 1992, Nanosystems: Molecular Machinery, Manufacturing, and Computation, Wiley, New York, USA.

Han, J., Globus, A., Jaffe, R., Deardorff, G., 1997, Molecular dynamics simulations of carbon nanotube-based gears, Nanotechnology, 8, pp. 95–102.

Srivastava, D., 1997, A phenomenological model of the rotation dynamics of carbon nanotube gears with laser electric fields, Nanotechnology, 8, pp. 186–192.

Lohrasebi, A. Rafii-Tabar, H., 2008, Computational modeling of an iondrivennanomotor, J. Mol. Graphics Modell., 27, pp. 116–123.

Yokoyama, T.,1988, Free vibration characteristics of rotating Timoshenko beams, Int. J. Mech. Sci. 30, pp. 743–755.

Gunda J.B., Ganguli R.,2008, New rational interpolation functions for finite element analysis of rotating beams, Int. J. Mech. Sci., 50, 578–588.

Yoo, H.H., Park, J.H., Park J.,2001, Vibration analysis of rotating pre-twisted blades, Comput. Struct., 79(19), pp. 1811–1819.

Lee, S.Y., Lin, S.M., Lin, Y.S.,2009, Instability and vibration of a rotating Timoshenko beam with precone, Int. J. Mech. Sci. 51, pp. 114–121.

Avramov, K.V., Pierre, C., Shyriaieva, N.,2007, Flexural-flexural-torsional nonlinear vibrations of pre-twisted rotating beams with asymmetric cross-sections, J. Vib. Control., 13, pp. 329–364.

Mohammadi, M., Safarabadi, M., Rastgoo, A., Farajpour, A.,2016, Hygro-mechanical vibration analysis of a rotating viscoelastic nanobeam embedded in a visco-Pasternak elastic medium and in a nonlinear thermal environment,ActaMechanica, 227(8), pp. 2207–2232.

Faroughia, S., Rahmani, A., Friswell, M.I.,2020, On wave propagation in two-dimensional functionally graded porous rotating nano-beams using a general nonlocal higher-orderbeam model, Applied Mathematical Modelling, 80, pp. 169-190.

Ebrahimi, F., Haghi, P.,2017, Wave propagation analysis of rotating thermoelastically-actuated nanobeams based on nonlocal strain gradient theory,ActaMechanicaSolidaSinica, 30(6), pp. 647–657.

Azimi, M., Mirjavadi, S. S., Shafiei, N., Hamouda, A. M. S., Davari, E.,2017, Vibration of rotating functionally graded Timoshenko nano-beams with nonlinear thermal distribution, Mechanics of Advanced Materials and Structures, 25(6), pp. 467–480.

Narendar, S., Gopalakrishnan, S.,2011, Nonlocal wave propagation in rotating nanotube, Results in Physics, 1, pp. 17–25.

Ebrahimi, F., Dabbagh, A.,2018, Wave dispersion characteristics of rotating heterogeneous magneto-electro-elastic nanobeams based on nonlocal strain gradient elasticity theory, J. Electromag. Waves Appl., 32(2), pp. 138-169.

Noda, N.,1986, Thermal stress in material with temperature dependent properties, In: R.B. Hetnarski (Ed.), Thermal stresses, Elsevier Science, North Holland, Amsterdam, pp. 391-483.

Berman, R.,1953, The thermal conductivity of dielectric solids at low temperatures, Advances in Physics, 2(5), pp. 103-140.

Sharma, J.N., Kaur, R.,2015, Response of anisotropic thermoelastic micro-beam resonators under dynamic loads, Applied Mathematical Modelling, 39, pp. 2929–2941.

Honig, G., Hirdes, U.,1984, A method for the numerical inversion of Laplace Transform, J. Comp. Appl. Math., 10, 113-132.

Tzou, D.Y.,1995, Experimental support for the lagging behavior in heat propagation, J. Thermophys. Heat Transf. 9(4), pp. 686–693.

Wang, Y., Liu, D. Wang, Q., Zhou, J.,2016, Asymptotic solutions for generalized thermoelasticity with variable thermal material properties, Archives of Mechanics, 68(3), pp. 181–202.

Abo‐Dahab, S.M., Abouelregal, A.E., Ahmad, H.,2020, Fractional heat conduction model with phase lags for a half‐space with thermal conductivity and temperature dependent, Mathematical Methods in the Applied Sciences, doi:10.1002/mma.6614

Ebrahimi, F. Haghi, P. 2018, Elastic wave dispersion modelling within rotating functionally graded nanobeams in thermal environment, Advances in Nano Research, 6(3), pp. 201-217.

Shafiei, N., Kazemi, M., Ghadiri, M.,2016, Comparison of modeling of the rotating tapered axially functionally graded Timoshenko and Euler–Bernoulli microbeams,Physica E: Lowdimensional Systems and Nanostructures, 83, pp. 74-87.

Younesian, D., Esmailzadeh, E.,2011, Vibration suppression of rotating beams using timevarying internal tensile force, Journal of Sound and Vibration, 330(2), pp. 308-320.

Khaniki, H.B.,2018, Vibration analysis of rotating nanobeam systems using Eringen’s two-phase local/nonlocal model,Physica E: Low-Dimensional Systems and Nanostructures, 99, pp. 310–319.

Safarabadi, M., Mohammadi, M., Farajpour, A., Goodarz, M.,2015, Effect of Surface Energy on the Vibration Analysis of Rotating Nanobeam, Journal of Solid Mechanics, 7(3) pp. 299-311.

Fang, J., Gu,J., Wang, H.,2018, Size-dependent three-dimensional free vibration of rotating functionally graded microbeams based on a modified couple stress theory, International Journal of Mechanical Sciences, 136, pp. 188-199.

Abouelregal, A.E. 2020, A novel model of nonlocal thermoelasticity with time derivatives of higher order, Mathematical Methods in the Applied Sciences, doi:10.1002/mma.6416.

Borjalilou, V., Asghari, M., Taati, E.,2020, Thermoelastic damping in nonlocal nanobeams considering dual-phase-lagging effect, Journal of Vibration and Control, 26(11–12), pp. 1042–1053.

Abouelregal, A.E., Zenkour, A.M.,2017, Thermoelastic response of nanobeam resonators subjected to exponential decaying time varying load, Journal of Theoretical and Applied Mechanics, 55(3), pp. 937-948, Warsaw.

Hahn, D.W.,Özişik, M. N., 2012, Heat conduction, (3rd ed.),Hoboken, N.J., Wiley.




DOI: https://doi.org/10.22190/FUME201222024A

Refbacks

  • There are currently no refbacks.


ISSN: 0354-2025 (Print)

ISSN: 2335-0164 (Online)

COBISS.SR-ID 98732551

ZDB-ID: 2766459-4