×

zbMATH — the first resource for mathematics

Nonlinear size-dependent forced vibrational behavior of microbeams based on a non-classical continuum theory. (English) Zbl 1348.74148
Summary: In this paper, the nonlinear forced-vibration of Euler-Bernoulli beams with large deflections is investigated based on the modified couple stress theory, a non-classical theory capable of capturing size effects. The classical theory is unable to predict the size effects. In systems with the dimensions in order of microns and sub-microns the size effects are very significant. For some specific beams subjected to a concentrated force at its middle as the harmonic exciter, the size-dependent responses are investigated for primary, super-harmonic and sub-harmonic resonances. The results show that the frequency-responses of the system are highly size-dependent.

MSC:
74H45 Vibrations in dynamical problems in solid mechanics
70J35 Forced motions in linear vibration theory
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] DOI: 10.1016/j.ijengsci.2010.09.025 · Zbl 1231.74258
[2] Asghari M, Archive of Applied Mechanics (2010)
[3] Banks H, ASME Journal of Applied Mechanics 58 pp 716– (1991) · Zbl 0741.73030
[4] Batra RC, Journal of Sound and Vibration 315 pp 939– (2008)
[5] Batra RC, Journal of Sound and Vibration 309 pp 600– (2008)
[6] Bauchau O, Non-linear Dynamics 6 pp 21– (1994)
[7] Begley MR, Journal of the Mechanics and Physics of Solids 46 pp 2049– (1998) · Zbl 0967.74043
[8] Chaterjee S, Journal of Sound and Vibration 322 pp 969– (2009)
[9] Chong ACM, Materials Research 14 (10) pp 4103– (1999)
[10] Fleck NA, Acta Metallurgica et Materialia 42 (2) pp 475– (1992)
[11] Gao Y, Journal of Sound and Vibration 283 pp 927– (2005)
[12] Hamdan MN, Journal of Sound and Vibration 329 pp 3121– (2010)
[13] Hao Z, Journal of Sound and Vibration 313 pp 77– (2008)
[14] Hassanpour PA, Journal of Sound and Vibration 329 pp 2547– (2010)
[15] Hino J, Journal of Sound and Vibration 100 (4) pp 477– (1985)
[16] Kahrobaiyan MH, International Journal of Engineering Science (2010)
[17] Ke L-L, International Journal of Engineering Science (2011)
[18] Khadem SE, Journal of Sound and Vibration 254 (4) pp 677– (2002)
[19] Koiter WT (1964) Couple-stresses in the theory of elasticity: I and II Proc. K. Ned. Akad. Wet. B 67 17–44.
[20] DOI: 10.1016/j.ijengsci.2007.10.002 · Zbl 1213.74189
[21] DOI: 10.1016/S0022-5096(03)00053-X · Zbl 1077.74517
[22] DOI: 10.1016/j.jmps.2008.09.007 · Zbl 1171.74367
[23] Mahdavi MH, Ultramicroscopy 109 pp 54– (2008)
[24] McFarland AW, Journal of Micromechanics and Microengineering 15 (5) pp 1060– (2005)
[25] Mindlin RD, Archive for Rational Mechanics and Analysis 11 (1) pp 415– (1962) · Zbl 0112.38906
[26] Moghimi Zand M, Mechanics Research Communications 36 pp 851– (2009) · Zbl 1273.74140
[27] Moghimi Zand M, Communications in Nonlinear Science and Numerical Simulation 14 pp 1664– (2009)
[28] Mojahedi M, Applied Mathematical Modelling 34 pp 1032– (2010) · Zbl 1185.74032
[29] Mook DT, Journal of Sound and Vibration 104 (2) pp 229– (1986) · Zbl 1235.70072
[30] Nayfeh AH, Nonlinear Oscillation (1979)
[31] Nix WD, Journal of the Mechanics and Physics of Solids 46 pp 411– (1998) · Zbl 0977.74557
[32] DOI: 10.1088/0960-1317/16/11/015
[33] Porfiri M, Journal of Sound and Vibration 315 pp 1071– (2008)
[34] Rao SS, Vibration of Continuous Systems (2007)
[35] Sinha A, Journal of Sound and Vibration 288 pp 387– (2005)
[36] DOI: 10.1016/S1359-6454(98)00153-0
[37] DOI: 10.1007/BF00253945 · Zbl 0112.16805
[38] Vogla A, Sensors and Actuators A 153 pp 155– (2009)
[39] DOI: 10.1016/j.jfluidstructs.2010.02.005
[40] Xia W, International Journal of Engineering Science (2010)
[41] DOI: 10.1016/S0020-7683(02)00152-X · Zbl 1037.74006
[42] Yiming F, Physica E 42 pp 1741– (2010)
[43] Zhou SJ, Journal of Shandong University of Technology 31 (5) pp 401– (2001)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.