Resonance of nanoscale beam due to various sources in modified couple stress thermoelastic diffusion with phase lags

• Autorzy: Kumar Rajneesh , Devi Shaloo , Sharma Veena

Identyfikatory

DOI

10.2478/mme-2019-0006

• Języki publikacji: EN

Abstrakty

EN

This paper deals with the study of thermoelastic thin beam in a modified couple stress with three-phaselag thermoelastic diffusion model subjected to thermal and chemical potential sources. The governing equations are derived by using the Euler-Bernoulli beam assumption and eigenvalue approach. The Laplace transform technique is employed to obtain the expressions for displacements, lateral deflection, temperature change, axial stress and chemical potential. A particular type of instantaneous and distributed sources is taken to show the utility of the approach. The general algorithm of the inverse Laplace transform is developed to compute the results numerically. The numerical results are depicted graphically to show the effects of phase lags, with and without energy dissipation on the resulting quantities. Some special cases are given.

Słowa kluczowe

EN

modified couple stress theory; thermoelastic thin beam; three-phase-lag; eigenvalue approach; Laplace transform

PL

zmodyfikowana teoria naprężeń momentowych; belka cieńka; opóźnienie trójfazowe; transformacja Laplace'a

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2019
• Tom: Vol. 23, nr 1
• Strony: 36--49
• Opis fizyczny: Bibliogr. 35 poz., 1 rys., wykr.

Twórcy

autor

Kumar Rajneesh

• Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, India

autor

Devi Shaloo

• Department of Mathematics & Statistics, Himachal Pradesh University Shimla, Shimla, Himachal Pradesh, India

autor

Sharma Veena

• Department of Mathematics & Statistics, Himachal Pradesh University Shimla, Shimla, Himachal Pradesh, India

Bibliografia

• [1] Voigt,W.: Theoretische Studienuber die Elasticitatsverhaltnisse der Krystalle. Abh. Ges. Wiss. Gottingen, 34, 1887.
• [2] Cosserat, E. and Cosserat, F.: Theory of Deformable Bodies. Hermann et Fils, Paris, 1909.
• [3] Toupin, R. A.: Elastic materials with couple-stresses, Arch. for Ratio. Mech. Analy., 11, 385-414, 1962.
• [4] Mindlin, R. D. and Tiersten, H. F.: Effects of couple-stresses in linear elasticity, Arch. for Ratio. Mech. and Analy., 11, 415-448, 1962.
• [5] Sengupta, P. R. and Ghosh, B.: Effect of couple stresses on surface waves in elastic media, Gerlands Beitr. Geophysik, Leipzig, 83, 309-318, 1974a.
• [6] Sengupta, P. R. and Ghosh, B.: Effect of couple stresses on propagation of waves in an elastic layer, Pure appl. Geophys, Leipzig, 1123, 331-338, 1974b.
• [7] Yang, F., Chong, A. C. M., Lam, D. C. C. and Tong, P.: Couple stress based strain gradient theory for elasticity, Int. J. Solids Struct., 39, 2731-2743, 2002.
• [8] Simsek, M. and Reddy, J. N.: Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory, Int. J. of Engg. Sci., 64, 37-53, 2013.
• [9] Kumar, R., Singh, R. and Chadha, T. K.: Eigenvalue approach to micropolar thermoelasticity without energy dissipation, Indian Journal of mathematics, 49(3), 355-369, 2007.
• [10] Hetnarski, R. B., Ignaczak, J.: Generalized thermoelasticity, J. Therm. Stresses, 22, 451-476, 1999.
• [11] Lord, H., Shulman, Y.: A generalized dynamical theory of thermoelasticity, J. Mech. Phys. Solids, 15, 299-309, 1967.
• [12] Green, A. E. and Lindsay, K. A.: Thermoelasticity, J. Elasticity, 2, 1-7, 1972.
• [13] Hetnarski, R. B. and Ignaczak, J.: Solution-like waves in a low temperature nonlinear thermoelastic solid, Int. J. Eng. Sci., 4, 1767-1787, 1996.
• [14] Green, A. E. and Naghdi, P. M.: On undamped heat waves in an elastic solid, J. Therm. Stresses, 15, 253-264, 1992.
• [15] Tzou, D. Y.: A unified field approach for heat conduction from micro to macroscales, ASME J. Heat Transf., 117, 8-16, 1995.
• [16] Roychoudhuri, S. K.: On a thermoelastic three-phase-lag model, J. of Thermal Stresses, 30, 231-238, 2007.
• [17] Nowacki, W.: Dynamical Problems of Thermo diffusion in Solids I, Bull Acad. Pol. Sci. Ser. Sci. Tech., 22, 55-64, 1974.
• [18] Sherief, H. H., Saleh, H. and Hamza, F.: The theory of generalized thermoelastic diffusion, Int. J. Engg. Sci., 42, 591-608, 2004.
• [19] Sherief, H. H. and Saleh, H.: A half-space problem in the theory of generalized thermoelastic diffusion, Int. J. of Solid and Structures, 42, 4484-4493, 2005.
• [20] Kumar, R. and Kansal, T.: Propagation of Lamb waves in transversely isotropic thermoelastic diffusion plate, Int. J. of Solid and Structures, 45, 2008, 5890-5913.
• [21] Sharma, K.: Analysis of deformation due to inclined load in generalized thermodiffusive elastic medium, Int. J. of Engineering Science and Technology, 3(2), 117-129, 2011.
• [22] Sarkar, N. and Lahiri, A.: (2012) Eigenvalue approach to two-temperature magneto-thermoelasticity, Vietnam Journal of Mathematics, 40(1), 13-30, 2012.
• [23] Rezazadeh, G., Vahdat, A. S., Tayefeh-rezaei, S., Cetinkaya, C.: Thermoelastic damping in a micro-beam resonator using modified couple stress theory, Acta Mechanica, 223(6), 1137-1152, 2012.
• [24] Abouelregal, A. E. and Zenkour, A. M.: (2014) Effect of phase lags on thermoelastic functionally graded microbeams subjected to ramp-type heating, Iranian Journal of Science and Technology: Transactions of Mechanical Engineering, 38(M2), 321-335, 2012.
• [25] Kumar, R. and Devi, S.: Interaction due to Hall current and rotation in a modified couple stress elastic half-space due to ramptype loading, Comp. methods in Sci. and Tech., 21(4), 229-240, 2015. DOI:10.12921/cmst.2015.21.04.007.
• [26] Reddy, J. N.,Romanoff, J. and Loya, J. A.: Nonlinear finite element analysis of functionally graded circular plates with modified couple stress theory, European Journal of Mechanics- A/Solids, 56, 92-104, 2016.
• [27] Chen, W. and Wang, Y.: A model of composite laminated Reddy plate of the global-local theory based on new modified couplestress theory, Mechanics of AdvancedMaterials and Structures, 23(6), 636-651, 2016.
• [28] Zenkour, A. M. and Abouelregal, A. E.: Effect of ramp-type heating on the vibration of functionally graded microbeams without energy dissipation, Mechanics of Advanced Materials and Structures, 23(5), 529-537, 2016.
• [29] Kumar, R.: Response of thermoelastic beam due to thermal source in modified couple stress theory, CMST, 22(2), 2016, 95- 101.
• [30] Green, A. E. and Naghdi, P. M.: Thermoelasticity without energy dissipation, J. Elast., 31, 189-209, 1993.
• [31] Sur, A. and Kanoria, M.: Three-phase-lag elasto-thermodiffusive response in an elastic solid under hydrostatic pressure, Int. J. of Advances in Applied Mathematics and Mechanics, 3(2), 121- 137, 2015.
• [32] Rao, S. S.: Vibration of Continuous Systems. JohnWiley & Sons, Inc. Hoboken, New Jersey, 2007.
• [33] Das, N. C., Lahiri, A. and Giri, R. R.: Eigenvalue approach to generalized thermoelasticity, Indian J. Pure Appl. Math., 28, 1573- 1594, 1997.
• [34] Honig, G. and Hirdes, U.: A method for the numerical inversion of the Laplace transform, J. Comput. Appl. Math., 10, 113-13, 19842.
• [35] Sur, A. and Kanoria, M.: Vibration of a gold-nanobeam induced by ramp type laser pulse three-phase-lag model, Int. J. of Appl. Math. and Mech., 10(5), 86-104, 2014.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).