Influence of Temperature Pulse on a Nickel Microbeams under Couple Stress Theory

Document Type: Research Paper


1 Department of Mathematics, College of Science and Arts, Jouf University, Gurayat, Saudi Arabia

2 Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El Manar, LR03ES04, 2092 Tunis, Tunisia

3 Department of Mathematics, Faculty of Science, Mansoura University Mansoura 35516, Egypt


In this paper, the vibration of microbeams due to a temperature pulse has been investigated. The thermoelastic coupled equations for microbeam resonator have been derived via the modified theory of couple stress in connection with the generalized thermoelasticity with relaxation time. The analytical expressions for studied fields due to modified couple stress for the microbeam have been obtained by applying the Laplace transform method. In addition, some comparisons have been displayed in graphs to estimate the effects of different parameters such as the couple stress parameter and pulse of temperature on the considered fields. Numerical conclusions demonstrate that the estimation of deflection expected by the new theory is lower than that of the classical one. Comparisons are made with the results of different models in the absence and presence of couple stress theory. Particular cases of interest are also derived.


Main Subjects

[1] A. M. Zenkour, A. E. Abouelregal, Effect of harmonically varying heat on FG nanobeams in the context of a nonlocal two-temperature thermoelasticity theory, European Journal of Computational Mechanics, 23(1-2), 2014, 1–14.

[2] E. Carrera, A. E. Abouelregal, I. A. Abbas, A. M. Zenkour, Vibrational analysis for an axially moving microbeam with two temperatures, Journal of Thermal Stresses, 38, 2014, 569–590.

[3] A. E. Abouelregal, A. M. Zenkour, Thermoelastic problem of an axially moving microbeam subjected to an external transverse excitation, Journal of Theoretical and Applied Mechanics, 53(1), 2015, 167–178.

[4] A. E. Abouelregal, A. M. Zenkour, 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), 2014, 321–335.

[5] W.H. Duan, C.M. Wang, Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on non-local plate theory, Nanotechnology,18(38), 2007, 385-704.

[6] Q. Wang, K. M. Liew, Application of nonlocal continuum mechanics to static analysis of micro-and nano-structures, Physics Letter A, 363, 2007, 236–242.

[7] G. Rezazadeh, F. Khatami, A. Tahmasebi, Investigation of the torsion and bending effects on static stability of electrostatic torsional micro-mirrors, Microsystem Technologies, 13, 2007, 715-722.

[8] J. Y. Chen, Y. C. Hsu, S. S. Lee, T. Mukherjee, G. K. Fedder, Modeling and simulation of a condenser microphone, Sensors and Actuators A, 145, 2008, 224-230.

[8] H. M. Sedighi, Size-dependent dynamic pull-in instability of vibrating electrically actuated microbeams based on the strain gradient elasticity theory, Acta Astronautica, 95, 2014, 111-123.

[9] H.M. Sedighi, F. Daneshmand, J. Zare, The influence of dispersion forces on the dynamic pull-in behavior of vibrating nano-cantilever based NEMS including fringing field effect, Archives of Civil and Mechanical Engineering, 14, 2014, 766-775.

[10] H. M. Sedighi, A. Koochi, F. Daneshmand, M. Abadyan, Non-linear dynamic instability of a double-sided nano-bridge considering centrifugal force and rarefied gas flow, International Journal of Non-Linear Mechanics, 77, 2015, 96–106.

[11] H. M. Sedighi, A. Bozorgmehri, Dynamic instability analysis of doubly clamped cylindrical nanowires in the presence of Casimir attraction and surface effects using modified couple stress theory, Acta Mechanica, 227(6), 2016, 1575–1591.

[12] H. M. Sedighi, A. Koochi, M. Abadyan, Modeling the size dependent static and dynamic pull-in instability of cantilever nanoactuator based on strain gradient theory, International Journal of Applied Mechanics, 6(5), 2014, 1450055.

[13] A. Chong, D. C. Lam, Strain gradient plasticity effect in indentation hardness of polymers, Journal of Materials Research, 14(10), 1999, 4103-4110.

[14] A.W. McFarland, J. S. Colton, Role of material microstructure in plate stiffness with relevance to micro-cantilever sensors, Journal of Micromechanics and Microengineering, 15(5), 2005, 10-60.

[15] R. Mindlin, H. Tiersten, Effects of couple-stresses in linear elasticity, Archive for Rational Mechanics and Analysis, 11(1), 1962, 415-448.

[16] R. A. Toupin, Elastic materials with couple-stresses, Archive for Rational Mechanics and Analysis, 11(1), 1962, 385-414.

[17] R. Kumar, Response of thermoelastic beam due to thermal source in modified couple stress theory, Computational Methods in Science and Technology, 22(2), 2016, 95-101.

[18] S. K. Park, X. L. Gao, Bernoulli-Euler beam model based on a modified couple stress theory, Journal of Micromechanics and Microengineering, 16, 2006, 2355-2359.

[15] A. R. Hadjesfandiari, G. F. Dargush, Couple stress theory for solids, International Journal of Solids and Structures, International Journal of Solids and Structures, 48(18), 2011, 2496-2510.

[19] F. Yang, A. Chong, D. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39, 2002, 2731–2743.

[20] M. H. Sad, Elasticity Theory Application and Numeric,Elsevier Inc, 2009.

[21] H.W. Lord, Y. Shulman, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids, 15, 1967, 299–309.

[22] G. Honig, U. Hirdes, A method for the numerical inversion of the Laplace transform, Journal of Computational and Applied Mathematics, 10, 1984, 113-132.

[23] D.Y. Tzou, Experimental support for the Lagging behavior in heat propagation, Journal of Thermophysics and Heat Transfer, 9, 1995, 686–693. 

[24] M. Najafi, G. Rezazadeh, R. Shabani, Thermo-elastic Damping in a Capacitive Micro-beam Resonator Considering Hyperbolic Heat Conduction Model and Modified Couple Stress Theory, Journal of Solid Mechanics, 4(4), 2012, 386-401.

[25] A. E. Abouelregal, Response of thermoelastic microbeams to a periodic external transverse excitation based on MCS theory, Microsystem Technologies, 24(4), 2018, 1925–1933.