×

Thermoelastic vibrations in initially stressed rotating microbeams caused by laser irradiation. (English) Zbl 1536.74065

Summary: The current paper has been presented to illustrate the thermoelastic vibration of a rotating microbeam based on generalized thermoelasticity theory, taking into account Euler-Bernoulli’s assumptions. Using Hamilton’s principle, the equation of motion of the initially stressed rotating microbeams has been derived. The microbeam is exposed to femtosecond laser pulses and sinusoidal varying heat. The Laplace transform technique is applied to obtain an analytical solution to the field variables. The influence of properties of various parameters, such as axial load, laser pulse duration, angular velocity, and material variation on the thermal and elastic waves of the rotating microbeam has been displayed graphically and discussed in detail.
© 2021 Wiley-VCH GmbH

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74F05 Thermal effects in solid mechanics
74M25 Micromechanics of solids
74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
Full Text: DOI

References:

[1] Abrate, S.: Vibration of non‐uniform rods and beams. J. Sound Vib.4, 703-716 (1995) · Zbl 1049.74588
[2] Li, X., Bhushan, B., Takashima, K., Baek, C.‐W., Kim, Y.‐K.: Mechanical characterization of micro/nanoscale structures for MEMS/NEMS applications using nanoindentation techniques. Ultramicroscopy.97, 481-494 (2003)
[3] Ghadiri, M., Shafiei, N., Alireza Mousavi, S.: Vibration analysis of a rotating functionally graded tapered microbeam based on the modified couple stress theory by DQEM. Appl. Phys. A. 122, 836 (2016).
[4] Ghayesh, M.H.: Dynamical analysis of multilayered cantilevers. Commun. Nonlinear Sci. Numer. Simul.71, 244-253 (2018) · Zbl 1464.74092
[5] Ghayesh, M.H.: Nonlinear oscillations of FG cantilevers. Appl. Acoustics. 145, 393-398 (2019)
[6] Ghayesh, M.H., Amabili, M.: Nonlinear vibrations and stability of an axially moving Timoshenko beam with an intermediate spring support. Mech. Mach. Theory.67, 1-16 (2013)
[7] Kang, S., Lee, S.J., Prinz, F.B.: Size does matter: the pros and cons of miniaturization. ABB Rev.2, 54-62 (2001)
[8] Hosseini, S.M.H., Arvin, H.: Thermo‐rotational buckling and post‐buckling analyses of rotating functionally graded microbeams. Int J Mech Mater Des.17, 55-72 (2020)
[9] Zhang, X.C., Myers, E.B., Sader, J.E.Roukes, M.L.: Nanomechanical torsional resonators for frequency‐shift infrared thermal sensing. Nano Lett.13, 1528-1534 (2013)
[10] Dennis, J.‐O., Ahmed, A.‐Y., Khir, M.‐H.: Fabrication and characterization of a CMOS‐MEMS humidity sensor. Sensors.15, 16674-16687 (2015)
[11] Dejin, C., Kai, F., Shijie, Z.: Flapwise vibration analysis of rotating composite laminated Timoshenko microbeams with geometric imperfection based on a re‐modified couple stress theory and isogeometric analysis. Eur. J. Mech. A. Solids.76, 25-35 (2019) · Zbl 1470.74033
[12] Babaei, A., Yang, C.X.: Vibration analysis of rotating rods based on the nonlocal elasticity theory and coupled displacement field. Microsyst. Technol.25, 1077-1085 (2019)
[13] Narendar, S., Gopalakrishnan, S.: Nonlocal wave propagation in rotating nanotube. Results Physics.1(1), 17-25 (2011)
[14] Younesian, D., Esmailzadeh, E.: Vibration suppression of rotating beams using time varying internal tensile force. J. Sound Vib.330(2), 308-320 (2011)
[15] Shafiei, N., Kazemi, M., Ghadiri, M.: Comparison of modeling of the rotating tapered axially functionally graded Timoshenko and Euler-Bernoulli microbeams. Phys. E: Low‐Dimens. Syst. Nanostructures.83, 74-87 (2016)
[16] Dehrouyeh‐Semnani, A.M.: The influence of size effect on flapwise vibration of rotating microbeams. Int. J. Eng. Sci.94, 150-163 (2015) · Zbl 1423.74465
[17] Abouelregal, A.E., Ahmad, H.: Thermodynamic modeling of viscoelastic thin rotating microbeam based on non‐Fourier heat conduction. Appl. Math. Modell.91, 973-988 (2020) · Zbl 1481.74424
[18] Kaya, M.O.: Free vibration analysis of a rotating Timoshenko beam by differential transform method. Aircr. Eng. Aerosp. Technol.78, 194-203 (2006)
[19] Zarrinzadeh, H., Attarnejad, R., Shahba, A.: Free vibration of rotating axially functionally graded tapered beams. Proc Inst Mech Eng G J Aerosp Eng.226, 363-379 (2011)
[20] Ghafarian, M., Ariaei, A.: Free vibration analysis of a system of elastically interconnected rotating tapered Timoshenko beams using differential transform method. Int. J. Mech. Sci.107, 93-109 (2016)
[21] Hodges, D.Y., Rutkowski, M.Y.: Free‐vibration analysis of rotating beams by a variable‐order finite‐element method. AIAA Journal.19, 1459-1466 (1981) · Zbl 0468.73093
[22] Rajasekaran, S.: Differential transformation and differential quadrature methods for centrifugally stiffened axially functionally graded tapered beams. Int. J. Mech. Sci.74, 15-31 (2013)
[23] Librescu, L., Meirovitch, L., Na, S.S.: Control of cantilever vibration via structural tailoring and adaptive materials. AIAA Journal.35, 1309-1315 (1997) · Zbl 0903.73052
[24] Rajasekaran, S.: Free vibration of centrifugally stiffened axially functionally graded tapered Timoshenko beams using differential transformation and quadrature methods. Appl. Math. Model.37, 4440-4463 (2013) · Zbl 1307.74042
[25] Ghayesh, M.H.: Viscoelastic dynamics of axially FG microbeams. Int. J. Eng. Sci.135, 75-85 (2019) · Zbl 1423.74187
[26] Ghayesh, M.H.: Viscoelastic mechanics of Timoshenko functionally graded imperfect microbeams. Compos. Struct.225, 110974 (2019)
[27] Ghayesh, M.H.: Mechanics of viscoelastic functionally graded microcantilevers. Eur. J. Mech. A. Solids.73, 492-499 (2019) · Zbl 1406.74146
[28] Abouelregal, A.E.: Size‐dependent thermoelastic initially stressed micro‐beam due to a varying temperature in the light of the modified couple stress theory. Appl. Math. Mech.‐Engl. Ed.41, 1805-1820 (2020) · Zbl 1489.74008
[29] Abouelregal, A.E., Zenkour, A.M.: Fractional viscoelastic Voigt’s model for initially stressed microbeams induced by ultrashort laser heat source. Waves Random Complex Medium.30(4), 687-703 (2020) · Zbl 1504.74010
[30] Kocakaplan, S., Tassoulas, J.L.: Wave propagation in initially‐stressed elastic rods. J. Sound Vib.443, 293-309 (2019)
[31] Kundu, S., Maity, M.: Edge wave propagation in an initially stressed dry sandy plate. Procedia Eng.173, 1029-1033 (2017)
[32] Wang, C.M., Zhang, Y.Y., Kitipornchai, S.: Vibration of initially stressed micro‐ and nano‐beams. Int. J. Struct. Stab. Dyn.07(04), 555-570 (2007) · Zbl 1205.74019
[33] Taha, M.H.: Nonlinear vibration model for initially stressed beam‐foundation system. Open Appl Math J.6, 23-31 (2012) · Zbl 1322.74036
[34] Eftekhari, S.A., Jafari, A.A.: Vibration of an initially stressed rectangular plate due to an accelerated traveling mass. Scientia Iranica.19(5), 1195-1213 (2012)
[35] Benhamed, MM., Abouelregal, A.E.: Influence of temperature pulse on a nickel microbeams under couple stress theory. J. Appl. Comput. Mech.6(4), 777-787 (2020)
[36] Lord, H., Shulman, Y.: A generalized dynamical theory of thermoelasticity. J Mech Phys Solids.15(5), 299-309 (1967) · Zbl 0156.22702
[37] Biot, M.: Thermoelasticity and irreversible thermodynamics. J Appl Phys.27(3), 240-253 (1956) · Zbl 0071.41204
[38] Tzou, D.Y., Chiu, K.S.: Temperature‐dependent thermal lagging in ultrafast laser heating. Int. J. Heat. Mass. Tran.44, 1725-1732 (2001) · Zbl 1091.74508
[39] Tzou, D.Y., Chen, J.K., Beraun, J.E.: Hot‐electron blast induced by ultra short‐pulsed lasers in layered media. Int. J. Heat. Mass. Tran.45, 3369-3382 (2002) · Zbl 0993.76566
[40] Tzou, D.Y.: Macro‐ to Micro‐Scale Heat Transfer: The Lagging Behavior, John Wiley & Sons Ltd, USA, New Jersey; 61-124 (2014). Available from: http://doi.org/10.1002/9781118818275.ch2 · doi:10.1002/9781118818275.ch2
[41] Honig, G., Hirdes, U.: A method for the numerical inversion of the Laplace transform. J. Comp. Appl. Math.10, 113-132 (1984) · Zbl 0535.65090
[42] Ebrahimi, F., Haghi, P.: Elastic wave dispersion modeling within rotating functionally graded nanobeams in thermal environment. Adv. Nano Res.6(3), 201-217 (2018)
[43] Khaniki, H.B.: Vibration analysis of rotating nanobeam systems using Eringen’s two‐phase local/nonlocal model. Phys. E: Low‐Dimens. Syst. Nanostructures.99, 310-319 (2018)
[44] Safarabadi, M., Mohammadi, M., Farajpour, A., Goodarz, M.: Effect of surface energy on the vibration analysis of rotating nanobeam. J. Solid Mech.7(3), 299-311 (2015)
[45] Fang, J., Gu, J., Wang, H.: Size‐dependent three‐dimensional free vibration of rotating functionally graded microbeams based on a modified couple stress theory. Int. J. Mech. Sci.136, 188-199 (2018)
[46] Abouelregal, A.E., Zenkour, A.M.: Fractional viscoelastic Voigt’s modelfor initially stressed microbeams induced by ultrashort laser heat source. Waves Random Complex Medium.30, 687-703 (2020) · Zbl 1504.74010
[47] Abouelregal, A.E., Zenkour, A.M.: Dynamic characteristics of initially stressed viscoelastic microbeams induced by ultra‐intense lasers. Indian J. Phys.94, 779-788 (2020)
[48] Wang, C.M., Zhang, Y.Y., Kitipornchai, S.. Vibration of initially stressed micro‐ and nano‐beams. Int. J. Str. Stab. Dyn.7, 555-570 (2007) · Zbl 1205.74019
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.