Structural Engineering and Mechanics

  • 제18권2호
  • /
  • Pages.195-209
  • /
  • 2004
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Analytical solutions to magneto-electro-elastic beams

  • Jiang, Aimin (West Branch of Zhejiang University of Technology) ;
  • Ding, Haojiang (Department of Civil Engineering, Zhejiang University)
  • 투고 : 2003.10.23
  • 심사 : 2004.01.19
  • 발행 : 2004.08.25
⟨ 이전 논문 다음 논문 ⟩

초록

By means of the two-dimensional basic equations of transversely isotropic magneto-electro-elastic media and the strict differential operator theorem, the general solution in the case of distinct eigenvalues is derived, in which all mechanical, electric and magnetic quantities are expressed in four harmonic displacement functions. Based on this general solution in the case of distinct eigenvalues, a series of problems is solved by the trial-and-error method, including magneto-electro-elastic rectangular beam under uniform tension, electric displacement and magnetic induction, pure shearing and pure bending, cantilever beam with point force, point charge or point current at free end, and cantilever beam subjected to uniformly distributed loads. Analytical solutions to various problems are obtained.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China

참고문헌

  1. Chen, J.Y., Ding, H.J. and Hou, P.F. (2003), "Analytical solutions of simply supported magneto-electro-elastic circular plate under uniform loads", J. of Zhejiang University SCIENCE, 4(5), 560-564. https://doi.org/10.1631/jzus.2003.0560
  2. Ding, H.J., Wang, G.Q. and Chen, W.Q. (1997a), "General solution of plane problem of piezoelectric media expressed by "harmonic functions"", Applied Mathematics and Mechanics, 18, 757-764. https://doi.org/10.1007/BF00763127
  3. Ding, H.J., Wang, G.Q. and Chen, W.Q. (1997b), "Green's functions for a two-phase infinite piezoelectric plane", Proc. of Royal Society of London(A), 453, 2241-2257. https://doi.org/10.1098/rspa.1997.0120
  4. Hou, P.F., Leung, Andrew Y.T. and Ding, H.J. (2003), "The elliptical Hertizan contact of transversely isotropic magneto-electro-elastic bodies", Int. J. Solids Struct., 40, 2833-2850. https://doi.org/10.1016/S0020-7683(02)00670-4
  5. Kogan, L., Hui, C.Y. and Molkov, V. (1996), "Stress and induction field of a spheroidal inclusion or a pennyshaped crack in a transversely isotropic piezoelectric material", Int. J. Solids Struct., 33(19), 2719-2737. https://doi.org/10.1016/0020-7683(95)00182-4
  6. Liu, J.X., Liu, X.L. and Zhao, Y.B. (2001), "Green's functions for anisotropic magneto-electro-elastic solids with an elliptical cavity or a crack", Int. J. Eng. Sci., 39, 1405-1418. https://doi.org/10.1016/S0020-7225(01)00005-2
  7. Pan, E. (2001), "Exact solution for simply supported and multilayered magneto-electro-elastic plates", J. Appl. Mech., ASME, 68, 608-618. https://doi.org/10.1115/1.1380385
  8. Pan, E. (2002a), "Three-dimensional Green's function in anisotropic magneto-electro-elastic bimaterials", Z. Angew. Math. Phys., 53, 815-838. https://doi.org/10.1007/s00033-002-8184-1
  9. Pan, E. (2002b), "Free vibrations of simply supported and multilayered magneto-electro-elastic plates", J. of Sound Vib., 252(3), 429-442. https://doi.org/10.1006/jsvi.2001.3693
  10. Sosa, H.A. and Castro, M.A. (1994), "On concentrated loads at the boundary of a piezoelectric half-plane", J. Mech. Phys. Solids, 42(7), 1105-1122. https://doi.org/10.1016/0022-5096(94)90062-0
  11. Timoshenko, S.P. and Goodier, T.N. (1970), Theory of Elasticity, 3rd McGraw-Hill Book Co., N.Y.
  12. Wang, X. and Shen, Y.P. (2002), "The general solution of three-dimensional problems in magneto-electro-elastic media", Int. J. Eng. Sci., 40, 1069-1080. https://doi.org/10.1016/S0020-7225(02)00006-X
  13. Wang, X. and Shen, Y.P. (2003), "Inclusion of arbitrary shape in magneto-electro-elastic composite materials", Int. J. Eng. Sci., 41, 85-102. https://doi.org/10.1016/S0020-7225(02)00110-6

피인용 문헌

  1. Free vibration response of two-dimensional magneto-electro-elastic laminated plates vol.292, pp.3-5, 2006, https://doi.org/10.1016/j.jsv.2005.08.004
  2. Simplified Gurtin-type generalized variational principles for fully dynamic magneto-electro-elasticity with geometrical nonlinearity vol.47, pp.22-23, 2010, https://doi.org/10.1016/j.ijsolstr.2010.07.011
  3. A one-dimensional model for dynamic analysis of generally layered magneto-electro-elastic beams vol.332, pp.2, 2013, https://doi.org/10.1016/j.jsv.2012.09.004
  4. Steady-state analysis of a three-layered electro-magneto-elastic strip in a thermal environment vol.16, pp.2, 2007, https://doi.org/10.1088/0964-1726/16/2/006
  5. Harmonic Response of Three-phase Magneto-electro-elastic Beam Under Mechanical, Electrical and Magnetic Environment vol.20, pp.10, 2009, https://doi.org/10.1177/1045389X09103307
  6. Studies on Magnetoelectric Effect for Magneto‐Electro‐Elastic Cylinder using Finite Element Method vol.5, pp.3, 2009, https://doi.org/10.1163/157361109789016970
  7. On the dualism of voltage oscillations and kinematical variables of a 1D-beam piezofilm vol.127, 2015, https://doi.org/10.1016/j.compstruct.2015.03.053
  8. A beam finite element for magneto-electro-elastic multilayered composite structures vol.94, pp.12, 2012, https://doi.org/10.1016/j.compstruct.2012.06.011
  9. Free vibration analysis of magneto-electro-elastic microbeams subjected to magneto-electric loads vol.75, 2016, https://doi.org/10.1016/j.physe.2015.09.019
  10. Behaviour of magneto-electro-elastic sensors under transient mechanical loading vol.150, pp.1, 2009, https://doi.org/10.1016/j.sna.2008.11.035
  11. Buckling behavior of smart MEE-FG porous plate with various boundary conditions based on refined theory vol.5, pp.4, 2016, https://doi.org/10.12989/amr.2016.5.4.279
  12. Two-dimensional analysis of simply supported piezoelectric beams with variable thickness vol.35, pp.9, 2011, https://doi.org/10.1016/j.apm.2011.03.012
  13. Free vibration behaviour of multiphase and layered magneto-electro-elastic beam vol.299, pp.1-2, 2007, https://doi.org/10.1016/j.jsv.2006.06.044
  14. On the fundamental equations of electromagnetoelastic media in variational form with an application to shell/laminae equations vol.47, pp.3-4, 2010, https://doi.org/10.1016/j.ijsolstr.2009.10.014
  15. Free vibrations of simply supported layered and multiphase magneto-electro-elastic cylindrical shells vol.15, pp.2, 2006, https://doi.org/10.1088/0964-1726/15/2/027
  16. Decay rate of saint-venant end effects for plane deformations of piezoelectric-piezomagnetic sandwich structures vol.23, pp.5, 2010, https://doi.org/10.1016/S0894-9166(10)60043-2
  17. Magnetic field effects on dynamic behavior of inhomogeneous thermo-piezo-electrically actuated nanoplates vol.39, pp.6, 2017, https://doi.org/10.1007/s40430-016-0646-z
  18. Influence of neutral surface position on dynamic characteristics of in-homogeneous piezo-magnetically actuated nanoscale plates 2017, https://doi.org/10.1177/0954406217728977
  19. Magnetic field effects on buckling behavior of smart size-dependent graded nanoscale beams vol.131, pp.7, 2016, https://doi.org/10.1140/epjp/i2016-16238-8
  20. Effect of Displacement Current in Magneto-Electro-Elastic 3D Beam Subjected to Dynamic Loading vol.20, pp.3, 2013, https://doi.org/10.1080/15376494.2011.584145
  21. Green's functions for two-phase transversely isotropic magneto-electro-elastic media vol.29, pp.6, 2005, https://doi.org/10.1016/j.enganabound.2004.12.010
  22. Optimization of magneto-electro-elastic composite structures using differential evolution vol.107, 2014, https://doi.org/10.1016/j.compstruct.2013.08.005
  23. Buckling Analysis of Smart Size-Dependent Higher Order Magneto-Electro-Thermo-Elastic Functionally Graded Nanosize Beams vol.33, pp.01, 2017, https://doi.org/10.1017/jmech.2016.46
  24. Dynamic modeling of a thermo–piezo-electrically actuated nanosize beam subjected to a magnetic field vol.122, pp.4, 2016, https://doi.org/10.1007/s00339-016-0001-3
  25. Virtual boundary element-integral collocation method for the plane magnetoelectroelastic solids vol.30, pp.8, 2006, https://doi.org/10.1016/j.enganabound.2006.03.004
  26. Analytical solution for functionally graded magneto-electro-elastic plane beams vol.45, pp.2-8, 2007, https://doi.org/10.1016/j.ijengsci.2007.03.005
  27. Static analysis of anisotropic functionally graded magneto-electro-elastic beams subjected to arbitrary loading vol.29, pp.3, 2010, https://doi.org/10.1016/j.euromechsol.2009.12.002
  28. Discrete Layer Solution to Free Vibrations of Functionally Graded Magneto-Electro-Elastic Plates vol.13, pp.3, 2006, https://doi.org/10.1080/15376490600582750
  29. Free Vibration Analysis of Smart Porous Plates Subjected to Various Physical Fields Considering Neutral Surface Position vol.42, pp.5, 2017, https://doi.org/10.1007/s13369-016-2348-3
  30. Transient Dynamic Response of Cantilever Magneto-Electro-Elastic Beam Using Finite Elements vol.10, pp.3, 2009, https://doi.org/10.1080/15502280902797207
  31. Virtual boundary element-equivalent collocation method for the plane magnetoelectroelastic solids vol.22, pp.1, 2006, https://doi.org/10.12989/sem.2006.22.1.001
  32. An inhomogeneous cell-based smoothed finite element method for the nonlinear transient response of functionally graded magneto-electro-elastic structures with damping factors pp.1530-8138, 2018, https://doi.org/10.1177/1045389X18812712
  33. An Efficient Cell-Based Smoothed Finite Element Method for Free Vibrations of Magneto-Electro-Elastic Beams pp.1793-6969, 2020, https://doi.org/10.1142/S0219876219500014
  34. Closed-form solutions for vibrations of a magneto-electro-elastic beam with variable cross section by means of Green’s functions pp.1530-8138, 2018, https://doi.org/10.1177/1045389X18803456
  35. An effective cell-based smoothed finite element model for the transient responses of magneto-electro-elastic structures vol.29, pp.14, 2018, https://doi.org/10.1177/1045389X18781258
  36. Coupling magneto-electro-elastic cell-based smoothed radial point interpolation method for static and dynamic characterization of MEE structures pp.1619-6937, 2019, https://doi.org/10.1007/s00707-018-2351-8
  37. Analytical solutions for density functionally gradient magneto-electro-elastic cantilever beams vol.3, pp.2, 2007, https://doi.org/10.12989/sss.2007.3.2.173
  38. Investigating vibration behavior of smart imperfect functionally graded beam subjected to magnetic-electric fields based on refined shear deformation theory vol.5, pp.4, 2017, https://doi.org/10.12989/anr.2017.5.4.281
  39. Free vibration and static analysis of functionally graded skew magneto-electro-elastic plate vol.21, pp.4, 2004, https://doi.org/10.12989/sss.2018.21.4.493
  40. Thermal buckling analysis of magneto-electro-elastic porous FG beam in thermal environment vol.8, pp.1, 2004, https://doi.org/10.12989/anr.2020.8.1.083
  41. On the static analysis of inhomogeneous magneto-electro-elastic plates in thermal environment via element-free Galerkin method vol.134, pp.None, 2004, https://doi.org/10.1016/j.enganabound.2021.11.002