DOI QR코드

DOI QR Code

Wave propagation in a microbeam based on the modified couple stress theory

  • Kocaturk, Turgut (Department of Civil Engineering, Yildiz Technical University, Davutpasa Campus) ;
  • Akbas, Seref Doguscan (Department of Civil Engineering, Yildiz Technical University, Davutpasa Campus)
  • 투고 : 2011.10.14
  • 심사 : 2013.04.24
  • 발행 : 2013.05.10

초록

This paper presents responses of the free end of a cantilever micro beam under the effect of an impact force based on the modified couple stress theory. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. The Kelvin-Voigt model for the material of the beam is used. The considered problem is investigated within the Bernoulli-Euler beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. In the study, the difference of the modified couple stress theory and the classical beam theory is investigated for the wave propagation. A few of the obtained results are compared with the previously published results. The influences of the material length scale parameter on the wave propagation are investigated in detail. It is clearly seen from the results that the classical beam theory based on the modified couple stress theory must be used instead of the classical theory for small values of beam height.

키워드

참고문헌

  1. Aydogdu, M. (2009), "A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration", Physica E., 41, 1651-1655. https://doi.org/10.1016/j.physe.2009.05.014
  2. Eringen, A.C. (1993), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", Journal of Applied Physics, 54, 4703-4710.
  3. Kocaturk, T., Eskin, A. and Akbas, S.D. (2011), "Wave propagation in a piecewise homegenous cantilever beam under impact force", International Journal of the Physical Sciences, 6, 4013-4020.
  4. Koiter, W.T. (1964), "Couple-stresses in the theory of elasticity: I and II", Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, 67B, 17-44.
  5. Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solids, 51, 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X
  6. Mindlin, R.D. (1963), "Influence of couple-stresses on stress concentrations", Experimental Mechanics, 3, 1-7. https://doi.org/10.1007/BF02327219
  7. Mindlin, R.D. and Tiersten, H.F. (1962), "Effects of couple-stresses in linear elasticity", Archive for Rational Mechanics and Analysis, 11, 415-448. https://doi.org/10.1007/BF00253946
  8. Newmark, N.M. (1959), "A method of computation for structural dynamics", ASCE Engineering Mechanics Division, 85, 67-94.
  9. Ostachowicz, W., Krawczuk, M., Cartmell, M. and Gilchrist, M. (2004), "Wave propagation in delaminated beam", Computers and Structures, 82, 475-483. https://doi.org/10.1016/j.compstruc.2003.11.001
  10. Ottosen, N.S., Ristinmaa, M. and Ljung, C. (2000), "Rayleigh waves obtained by the indeterminate couplestress theory", Eur. J. Mech. A/Solids, 19, 929-947. https://doi.org/10.1016/S0997-7538(00)00201-1
  11. Park, S.K. and Gao, X.L. (2006), "Bernoulli-Euler beam model based on a modified couple stress theory", J. Micromech. Microeng, 16, 2355-2359. https://doi.org/10.1088/0960-1317/16/11/015
  12. Palacz, M. and Krawczuk, M. (2002), "Analysis of longitudinal wave propagation in a cracked rod by the spectral element method", Computers and Structures, 80, 1809-1816. https://doi.org/10.1016/S0045-7949(02)00219-5
  13. Palacz, M., Krawczuk, M. and Ostachowicz, W. (2005a), "The spectral finite element model for analysis of flexural-shear coupled wave propagation", Part 1: Laminated Multilayer Composite, Composite Structures, 68, 37-44.
  14. Palacz, M., Krawczuk, M. and Ostachowicz, W. (2005b), "The spectral finite element model for analysis of flexural-shear coupled wave propagation. Part 2: Delaminated multilayer composite beam", Composite Structures, 68, 45-51. https://doi.org/10.1016/j.compstruct.2004.02.013
  15. Pei, J., Tian, F. and Thundat, T. (2004), "Glucose biosensor based on the microcantilever", Analytical Chemistry, 76, 292-297. https://doi.org/10.1021/ac035048k
  16. Reddy, J.N. (2007), "Nonlocal theories for bending, buckling and vibration of beams", International Journal of Engineering Science, 45, 288-307. https://doi.org/10.1016/j.ijengsci.2007.04.004
  17. Rezazadeh, G., Tahmasebi, A. and Zubtsov, M. (2006), "Application of piezoelectric layers in electrostatic MEM actuators: controlling of pull-in voltage", Journal of Microsystem Technologies, 12, 1163-1170. https://doi.org/10.1007/s00542-006-0245-5
  18. Simsek, M. (2010a), "Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory", International Journal of Engineering Science, 48, 1721-1732. https://doi.org/10.1016/j.ijengsci.2010.09.027
  19. Simsek, M. (2010b), "Vibration analysis of a single-walled carbon nanotube under action of a moving harmonic load based on nonlocal elasticity theory", Physica E, 43, 182-191. https://doi.org/10.1016/j.physe.2010.07.003
  20. Senturia, S.D. (1998), "CAD challenges for microsensors, microactuators, and microsystems", Proceedings of IEEE, 86, 1611-1626. https://doi.org/10.1109/5.704266
  21. Toupin, R.A. (1964), "Theories of elasticity with couple stress", Archive for Rational Mechanics and Analysis, 17, 85-112.
  22. Wang, Q. and Liew, K.M. (2007), "Application of nonlocal continuum mechanics to static analysis of micro- and nano-structures", Physics Letters A, 363, 236-242. https://doi.org/10.1016/j.physleta.2006.10.093
  23. Yang, F., Chong, M., Lam, D.C.C. and Tong, P. (2002), "Couple stress based strain gradient theory for elasticity", International Journal of Solids and Structures, 39, 2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X
  24. Yang, Y., Zhang, L. and Lim, C.W. (2011), "Wave propagation in double-walled carbon nanotubes on a novel analytically nonlocal Timoshenko-beam model", Journal of Sound and Vibration, 330, 1704-1717. https://doi.org/10.1016/j.jsv.2010.10.028
  25. Zook, J.D., Burns, D.W., Guckel, H., Smegowsky, J.J., Englestad, R.L. and Feng, Z. (1992), "Characteristics of polysilicon resonant microbeams", Sensors and Actuators, 35, 51-59. https://doi.org/10.1016/0924-4247(92)87007-4

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