Journal of the Korea Academia-Industrial cooperation Society (한국산학기술학회논문지)

The Korea Academia-Industrial cooperation Society (한국산학기술학회)
권호 표지
DOI QR코드

DOI QR Code

Nonlocal elasticity effects on free vibration properties of sigmoid functionally graded material nano-scale plates

S형상 점진기능재료 나노-스케일 판의 자유진동 특성에 미치는 비국소 탄성 효과

  • Kim, Woo-Jung (Department of Civil Engineering, Gyeongnam National University of Science and Technology) ;
  • Lee, Won-Hong (Department of Civil Engineering, Gyeongnam National University of Science and Technology) ;
  • Park, Weon-Tae (Division of Construction and Environmental Engineering, Kongju National University) ;
  • Han, Sung-Cheon (Department of Civil & Railroad Engineering, Daewon University College)
  • 김우중 (경남과학기술대학교 토목공학과) ;
  • 이원홍 (경남과학기술대학교 토목공학과) ;
  • 박원태 (공주대학교 건설환경공학부) ;
  • 한성천 (대원대학교 철도건설과)
  • Received : 2014.01.03
  • Accepted : 2014.02.05
  • Published : 2014.02.28
Download PDF
⟨ Previous Next ⟩

Abstract

We study free vibration analysis of sigmoid functionally graded materials(S-FGM) nano-scale plates, using a nonlocal elasticity theory of Eringen in this paper. This theory has ability to capture the both small scale effects and sigmoid function in terms of the volume fraction of the constituents for material properties through the plate thickness. Numerical solutions of S-FGM nano-scale plate are presented using this theory to illustrate the effect of nonlocal theory on natural frequency of the S-FGM nano-scale plates. The relations between nonlocal and local theories are discussed by numerical results. Further, effects of (i) power law index (ii) nonlocal parameters, (iii) elastic modulus ratio and (iv) thickness and aspect ratios on nondimensional frequencies are investigated. In order to validate the present solutions, the reference solutions are compared and discussed. The results of S-FGM nano-scale plates using the nonlocal theory may be the benchmark test for the free vibration analysis.

본 논문에서는 S형상함수를 이용한 점진기능재료 나노-스케일 판의 자유진동 특성에 미치는 비국소 탄성 이론의 효과에 대하여 연구하였다. 비국소 탄성 이론은 미소 규모 효과를 고려할 수 있고 S형상함수는 점진기능재료의 정확한 특성변화를 고려할 수 있다. 이러한 이론을 이용하여 나노-스케일 판의 고유진동수에 미치는 비국소 이론의 효과를 제시하였고, 국소 탄성이론과의 관계를 수치해석 결과를 통하여 고찰하였다. 또한 (i) 거듭제곱 지수, (ii) 비국소 계수, (iii) 탄성계수 비 그리고 (iv) 나노-스케일 판의 두께 및 형상 변화 등이 나노-스케일 판의 무차원 진동수에 미치는 효과에 대하여 관찰하였다. 본 연구의 결과를 검증하기 위해 참고문헌의 결과들과 비교 분석하였으며 해석결과는 참고문헌의 결과들과 잘 일치함을 알 수 있었다. 비국소 이론에 의한 나노-스케일 판의 진동에 관한 연구는 향후 관련연구에 비교자료로 활용될 수 있을 것이다.

Keywords

References

  1. G. N. Praveen, J. N. Reddy, "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates", Int. J. Solids Struct., Vol. 35, pp. 4457-4476, 1988. DOI: http://dx.doi.org/10.1016/S0020-7683(97)00253-9
  2. F. Delale, F. Erdogan, "The crack problem for a nonhomogeneous plane", J. Appl. Mech.(ASME), Vol. 50, pp. 609-614, 1983. DOI: http://dx.doi.org/10.1115/1.3167098
  3. G. Bao, L. Wang, "Multiple cracking in functionally graded ceramic/metal coatings", Int. J. Solids Struct., Vol. 32, pp. 2853-2871, 1995. https://doi.org/10.1016/0020-7683(94)00267-Z
  4. Y. L. Chung, S. H. Chi, "The residual stress of functionally graded materials", Journal of Chinese Institute of Civil and Hydraulic Engineering, Vol. 13, pp. 1-9, 2001.
  5. S. H. Chi, Y. L. Chung, Y.L. "Cracking in sigmoid functionally graded coating". Journal of Mechanics, Vol. 18, pp. 41-53, 2002.
  6. A. M. Zenkour, "On vibration of functionally graded plates according to a refined trigonometric plate theory", Int. J. Struct. Stab. Dyna., Vol. 5, pp. 279-297, 2005. DOI: http://dx.doi.org/10.1142/S0219455405001581
  7. W. H. Lee, S. C. Han, W. T. Park, "Bending, Vibration and Buckling Analysis of Functionally Graded Material Plates, J. Korea Academia-Industrial cooperation Society, Vol. 9(4), pp. 1043-1049, 2008. DOI: http://dx.doi.org/10.5762/KAIS.2008.9.4.1043
  8. A. C. Eringen, "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., Vol. 54, pp. 4703-4710, 1983. DOI: http://dx.doi.org/10.1063/1.332803
  9. A. C. Eringen, Nonlocal Continuum Field Theories, Springer-Verlag, New York, 2002.
  10. H. Lu, H. Sun, A. Mao, H. Yang, H. Wang, X. Hu, "Preparation of plate-like nano a-Al2O3 using nanoaluminium seeds by wet-chemical methods", Mater. Sci.Eng., Vol. 406, pp. 19-23, 2005. DOI: http://dx.doi.org/10.1016/j.msea.2005.04.047
  11. T. Sumitomo, H. Kakisawa, Y. Owaki, Y. Kagawa, "Structure of natural nano-laminar composites", Mater. Sci. Eng., Vol. 561, pp. 713-716, 2007. DOI: http://10.4028/www.scientific.net/MSF.561-565.713
  12. Q. Wang, C. M. Wang. "The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes". Nanotechnology, Vol. 18, pp. 075702-075709, 2007. DOI: http://dx.doi.org/10.1088/0957-4484/18/7/075702
  13. W. H. Lee, S. C. Han, W. T. Park, "Application of nonlocal elasticity theory for buckling analysis of nano-scale plates, J. Korea Academia-Industrial cooperation Society, Vol. 13(11), pp. 5542-5550, 2012. DOI: http://dx.doi.org/10.5762/KAIS.2012.13.11.5542
  14. J. N. Reddy, Theory and Analysis of Elastic Plates and Shells, seconded, CRC Press, London, 2007.
  15. H. T. Thai, D. H. Choi, "Size-dependent functionally graded Kirchhoff and Mindlin plate models based on a modified couple stress theory", Comps. Struct., Vol. 95, pp. 142-153, 2013. DOI: http://dx.doi.org/10.1016/j.compstruct.2012.08.023