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Kamali, Farhad, Shahabian, Farzad. (1400). Free Vibration of Axially Functionally Graded Tapered Micro-Beams Considering Uncertain Properties. نشریه مهندسی عمران امیرکبیر, 5(4), 543-556. doi: 10.22060/ajce.2022.18056.5657
Farhad Kamali; Farzad Shahabian. "Free Vibration of Axially Functionally Graded Tapered Micro-Beams Considering Uncertain Properties". نشریه مهندسی عمران امیرکبیر, 5, 4, 1400, 543-556. doi: 10.22060/ajce.2022.18056.5657
Kamali, Farhad, Shahabian, Farzad. (1400). 'Free Vibration of Axially Functionally Graded Tapered Micro-Beams Considering Uncertain Properties', نشریه مهندسی عمران امیرکبیر, 5(4), pp. 543-556. doi: 10.22060/ajce.2022.18056.5657
Kamali, Farhad, Shahabian, Farzad. Free Vibration of Axially Functionally Graded Tapered Micro-Beams Considering Uncertain Properties. نشریه مهندسی عمران امیرکبیر, 1400; 5(4): 543-556. doi: 10.22060/ajce.2022.18056.5657

Free Vibration of Axially Functionally Graded Tapered Micro-Beams Considering Uncertain Properties

AUT Journal of Civil Engineering
مقاله 1، دوره 5، شماره 4، اسفند 2021، صفحه 543-556    اصل مقاله (1.25 M)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22060/ajce.2022.18056.5657
نویسندگان
Farhad Kamali؛ Farzad Shahabian*
Civil Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran.
چکیده
Experimental observations reveal that the classical continuum theory cannot accurately describe the mechanical behavior of micro/nanoscale structures. In fact, the size-effect will arise when the order of structure dimensions is the same as the material characteristic length. The current work presents free vibration and stability of axially functionally graded (AFG) tapered micro-beams with random properties. The size-dependent behavior of the micro-structure is modeled by the modified couple stress theory. The mathematical formulations are developed based on the Euler-Bernoulli beam model and von Kármán geometric nonlinearity. The minimum total potential energy principle is employed to obtain governing differential equations and the corresponding boundary conditions. The governing equations are solved by the Galerkin method. Due to the complexity of the fabrication process of FGMs, their mechanical and structural properties may vary from sample to sample significantly. Hence, achieving the desired FGMs specification is almost impossible and they are not deterministic, inherently. To incorporate uncertainties in the mathematical model of this study, a First-Order Second-Moment (FOSM) technique is applied to estimate the reliability index of the micro-structure, stochastically. Finally, numerical examples are presented for both deterministic and reliability analysis to show the effects of geometry, length scale parameter, material distribution, and axial load on the natural frequency of vibration and the reliability index of the AFG tapered micro-beam. It can be concluded that by increasing the coefficient of variation (COV) of random variables, the reliability index will decrease. Indeed, by enhancing the length scale parameter, a higher natural frequency of vibration is expected.
کلیدواژه‌ها
Axially functionally graded؛ Micro-beam؛ Size-dependent behavior؛ Modified couple stress theory؛ First-Order Second-Moment technique؛ Reliability index
مراجع
  1. Michael, CY. Kwok, Piezoelectric micro-lens actuator, Sensors and Actuators A: Physical, 236 (2015) 116-129.
  2. Fan, Y. Luo, L. Li, Q. Wu, Z. Ren, B. Peng, Large-range fiber microsphere micro-displacement sensor, Optical Fiber Technology, 48 (2019) 173-178.
  3. Ma, T. Huang, S. Guo, C. Yang, Y. Ding, C. Hu, Atomic force microscope study of the aging/rejuvenating effect on asphalt morphology and adhesion performance, Construction and Building Materials, 205 (2019) 642-655.
  4. Li, Y. Liu, L. Dong, C. Shen, F. Li, M. Huang, C. Ma, B. Yang, X. An, W. Sand, Recent advances on photocatalytic fuel cell for environmental applications-The marriage of photocatalysis and fuel cells, Science of the Total Environment, 668 (2019) 966-978.
  5. Ding, Y. Tian, L.S. Wang, X. Huang, H.R. Zheng, K. Song, X.G. Zeng, Micro-mechanism of the effect of grain size and temperature on the mechanical properties of polycrystalline TiAl, Computational Materials Science, 158 (2019) 76-87.
  6. Kabel, Y. Yang, M. Balooch, C. Howard, T. Koyanagi, K.A. Terrani, Y. Katoh, P. Hosemann, Micro-mechanical evaluation of SiC-SiC composite interphase properties and debond mechanisms, Composites Part B: Engineering, 131 (2017) 173-183.
  7. C. Eringen, Linear theory of micropolar elasticity, Mathematics and Mechanics of Solids, 15 (6) (1966) 909-923.
  8. D. Mindlin, N.N. Eshel, On first strain-gradient theories in linear elasticity, International Journal of Solids and Structures, 4 (1) (1968) 109-124.
  9. Cosserat, F. Cosserat, Théorie des corps déformables, (1909).
  10. T. Koiter, Couple-stress in the theory of elasticity, Proc K Ned Akad Wet C, 67 (1964) 17-44.
  11. D. Mindlin, Second gradient of strain and surface-tension in linear elasticity, International Journal of Solids and Structures, 1 (4) (1965) 417-438.
  12. A. Toupin, Elastic materials with couple-stresses, Archive for Rational Mechanics and Analysis, 11 (1) (1962) 385-414.
  13. Qiu, J. Tani, T. Ueno, T. Morita, H. Takahashi, H. Du, Fabrication and high durability of functionally graded piezoelectric bending actuators, Smart Materials and Structures, 12 (1) (2003) 115-121.
  14. Xu, Y. Qian, J. Chen, G. Song, Stochastic dynamic characteristics of FGM beams with random material properties, Composite Structures, 133 (2015) 585-594.
  15. Ferrante, L. Graham-Brady, Stochastic simulation of non-Gaussian/nonstationary properties in a functionally graded plate, Computer Methods in Applied Mechanics and Engineering, 194(12) (2005) 1675-1692.
  16. Kitipornchai, J. Yang, K. Liew, Random vibration of the functionally graded laminates in thermal environments, Computer Methods in Applied Mechanics and Engineering, 195(9) (2006) 1075-1095.
  17. S. Nowak, K.R. Collins, Reliability of structures, CRC Press (2012).
  18. Wang, J. Zhao, S. Zhou, A micro scale Timoshenko beam model based on strain gradient elasticity theory, European Journal of Mechanics - A/Solids, 29 (4) (2010) 591–599.
  19. N. Patel, D. Pandit, S.M. Srinivasan, A simplified moment-curvature based approach for large deflection analysis of micro-beams using the consistent couple stress theory, European Journal of Mechanics - A/Solids, 66 (2017) 45–54.
  20. Arvin, Free vibration analysis of micro rotating beams based on the strain gradient theory using the differential transform method: Timoshenko versus Euler-Bernoulli beam models, European Journal of Mechanics - A/Solids, 65 (2017) 336–348.
  21. Talimian, P. Béda, Dynamic stability of a size-dependent micro-beam, European Journal of Mechanics - A/Solids, 72 (2018) 245-251.
  22. Shafiei, M. Kazemi, Nonlinear buckling of functionally graded nano-/micro-scaled porous beams, Composite Structures, 178 (2017) 483-492.
  23. Kamali, F. Shahabian, Analytical solutions for surface stress effects on buckling and post-buckling behavior of thin symmetric porous nano-plates resting on elastic foundation, Archive of applied mechanics, 91 (2021) 2853-2880.
  24. Li, L. Li, Y. Hu, Z. Ding, W. Deng, Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory, Composite Structures, 165 (2017) 250-265.
  25. Rezaiee-Pajand, F. Kamali, Exact solution for thermal-mechanical post-buckling of functionally graded micro-beams, CEAS Aeronautical Journal, 12 (2021) 85-100.
  26. Yang, D. He, Free vibration and buckling analyses of a size-dependent axially functionally graded beam incorporating transverse shear deformation, Results in Physics, 7 (2017) 3251-3263.
  27. Sınır, M. Çevik, B.G. Sınır, Nonlinear free and forced vibration analyses of axially functionally graded Euler-Bernoulli beams with non-uniform cross-section, Composites Part B: Engineering, 148 (2018) 123-131.
  28. A. Momeni, M. Asghari, The second strain gradient functionally graded beam formulation, Composite Structures, 188 (2018) 15-24.
  29. L. Jia, L.L. Ke, X.L. Zhong, Y. Sun, J. Yang, S. Kitipornchai, Thermal-mechanical-electrical buckling behavior of functionally graded micro-beams based on modified couple stress theory, Composite Structures, 202 (2018) 625-634.
  30. Al-shujairi, Dynamic stability of sandwich functionally graded micro-beam based on the nonlocal strain gradient theory with thermal effect, Composite Structures, 201 (2018) 1018-1030.
  31. Bhattacharya, D. Das, Free vibration analysis of bidirectional-functionally graded and double-tapered rotating micro-beam in thermal environment using modified couple stress theory, Composite Structures, 215 (2019) 471-492.
  32. L. Shegokar, A. Lal, Stochastic nonlinear bending response of piezoelectric functionally graded beam subjected to thermoelectromechanical loadings with random material properties, Composite Structures, 100 (2013) 17-33.
  33. Xu, Y. Qian, J. Chen, G. Song, Stochastic dynamic characteristics of FGM beams with random material properties, Composite Structures, 133 (2015) 585-594.
  34. Zhou, X. Zhang, Natural frequency analysis of functionally graded material beams with axially varying stochastic properties, Applied Mathematical Modelling, 67 (2019) 85-100.
  35. Mohammadi, M. Eghtesad, H. Mohammadi, Stochastic analysis of pull-in instability of geometrically nonlinear size-dependent FGM micro beams with random material properties, Composite Structures, 200 (2018) 466-479.
  36. S. Rao, Vibration of continuous systems, New York: Wiley, (2007)
  37. Kong, S. Zhou, Z. Nie, K. Wang, The size-dependent natural frequency of Bernoulli-Euler micro-beams, International Journal of Engineering Science, 46 (2008) 427-437.
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