Transient dynamic analysis of functionally graded micro-beams considering small-scale effects

Eshraghi, I.; Dag, S.

doi:10.24423/aom.3786

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Transient dynamic analysis of functionally graded micro-beams considering small-scale effects

Autorzy

Eshraghi I. , Dag S.

Treść / Zawartość

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DOI

10.24423/aom.3786

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Abstrakty

A domain-boundary element method, based on modified couple stress theory, is developed for transient dynamic analysis of functionally graded micro-beams. Incorporating static fundamental solutions as weight functions in weighted residual expressions, governing partial differential equations of motion are converted to a set of coupled integral equations. A system of ordinary differential equations in time is obtained by domain discretization and solved using the Houbolt time marching scheme. Developed procedures are verified through comparisons to the results available in the literature for micro- and macro-scale beams. Numerical results illustrate elastodynamic responses of graded micro-beams subjected to various loading types. It is shown that metal-rich micro-beams and those with a smaller length scale parameter ratio undergo higher displacements and are subjected to larger normal stresses.

Słowa kluczowe

boundary element method functionally graded materials Timoshenko micro-beam vibrations modified couple stress theory

Wydawca

Instytut Podstawowych Problemów Techniki PAN

Czasopismo

Archives of Mechanics

Rocznik

2021

Tom

Vol. 73, nr 4

Strony

303--337

Opis fizyczny

Bibliogr. 58 poz., rys., wykr.

Twórcy

autor

Eshraghi I.

ieshraghi@ut.ac.ir

School of Engineering Science, College of Engineering, University of Tehran, P.O. Box 11155-4563,Tehran, Iran

autor

Dag S.

sdag@metu.edu.tr

Department of Mechanical Engineering, Middle East Technical University, Ankara 06800, Turkey

Bibliografia

1. J.A.M. Carrer, S.A. Fleischfresser, L.F.T. Garcia, W.J. Mansur, Dynamic analysis of Timoshenko beams by the boundary element method, Engineering Analysis with Boundary Elements, 37, 12, 1602–1616, 2013.
2. I. Eshraghi, S. Dag, Domain-boundary element method for elastodynamics of functionally graded Timoshenko beams, Computers & Structures, 195, 113–125, 2018.
3. Z. Ahmed, I. Eshraghi, S. Dag, Domain-boundary element method for forced vibrations of fiber-reinforced laminated beams, International Journal of Computational Methods In Engineering Science and Mechanics, 21, 3, 141–158, 2020.
4. J.A.M. Carrer, W.J. Mansur, Scalar wave equation by the boundary element method: A D-BEM approach with constant time-weighting functions, International Journal for Numerical Methods in Engineering, 81, 10, 1281–1297, 2010.
5. J.A.M. Carrer, W.J. Mansur, R.J. Vanzuit, Scalar wave equation by the Bondary element method: a D-BEM approach with non-homogeneous initial conditions, Computational Mechanics, 44, 1, 31–44, 2009.
6. I. Eshraghi, S. Dag, Forced vibrations of functionally graded annular and circular plater by domain-boundary element method, ZAMM – Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 100, 8, e201900048, 2020.
7. C.P. Providakis, Transient dynamic response of elastoplastic thick plates resting on Winkler-type foundation, Nonlinear Dynamics, 23, 3, 285–302, 2000.
8. G.D. Hatzigeorgiou, D.E. Beskos, Dynamic elastoplastic analysis of 3-D structures by the domain/boundary element method, Computers & Structures, 80, 3–4, 339–347, 2002.
9. C.P. Providakis, D.E. Beskos, Dynamic analysis of elasto-plastic flexural plates by the D/BEM, Engineering Analysis with Boundary Elements, 14, 1, 75–80, 1994.
10. D. Soares, J.A.M. Carrer, W.J. Mansur, Non-linear elastodynamic analysis by the BEM: an approach based on the iterative coupling of the D-BEM and TD-BEM formulations, Engineering Analysis with Boundary Elements, 29, 8, 761–774, 2005.
11. R. Pettres, L.A. De Lacerda, J.A.M. Carrer, A boundary element formulation for the heat equation with dissipative and heat generation terms, Engineering Analysis with Boundary Elements, 51, 191–198, 2015.
12. P. Oyarzún, F.S. Loureiro, J.A.M. Carrer, W.J. Mansur, A time-stepping scheme based on numerical Green’s functions for the domain boundary element method: the ExGA-DBEM Newmark approach, Engineering Analysis with Boundary Elements, 35, 3, 533–542, 2011.
13. D.P.N. Kontoni, Elastoplastic dynamic analysis by the DR-BEM in modal co-ordinates, WIT Transactions on Modelling and Simulation, WIT Press, 3, 191–202, 1993.
14. M. Kögl, L. Gaul, A boundary element method for transient piezoelectric analysis, Engineering Analysis with Boundary Elements, 24, 7–8, 591–598, 2000.
15. C.-C. Chien, Y.-H. Chen, C.-C. Chuang, Dual reciprocity BEM analysis of 2D transie nt elastodynamic problems by time-discontinuous Galerkin FEM, Engineering Analysis with Boundary Elements, 27, 6, 611–624, 2003.
16. E.L. Albuquerque, P. Sollero, M.H. Aliabadi, Dual boundary element method for anisotropic dynamic fracture mechanics, International Journal for Numerical Methods In Engineering, 59, 9, 1187–1205, 2004.
17. X. Lu, W.-L. Wu, A subregion DRBEM formulation for the dynamic analysis of twodimensional cracks, Mathematical and Computer Modelling, 43, 1–2, 76–88, 2006.
18. J. Useche, E.L. Albuquerque, Dynamic analysis of shear deformable plates using the dual reciprocity method, Engineering Analysis with Boundary Elements, 36, 5, 627–632, 2012.
19. J. Useche, E.L. Albuquerque, Transient dynamic analysis of shear deformable shallow shells using the boundary element method, Engineering Structures, 87, 1–7, 2015.
20. P.H. Wen, M.H. Aliabadi, A. Young, A boundary element method for dynamic plate bending problems, International Journal of Solids and Structures, 37, 37, 5177–5188, 2000.
21. P.H. Wen, M.H. Aliabadi, Boundary element frequency domain formulation for dynamic analysis of Mindlin plates, International Journal for Numerical Methods in Engineering, 67, 11, 1617–1640, 2006.
22. P.H. Wen, M.H. Aliabadi, Laplace domain boundary element method for Winkler and Pasternak foundation thick plates, in: Recent Developments in Boundary Element Methods, E.J. Sapountzakis [ed.], 43, 323–333, 2010.
23. L. Igumnov, I. Markov, A. Konstantinov, Boundary element modeling of dynamic bending of a circular piezoelectric plate, DYMAT 2018 International Conference, EPJWeb of Conferences, 183, paper no: 01025, 2018.
24. E.J. Sapountzakis, J.A. Dourakopoulos, Shear deformation effect in flexural-torsional vibrations of composite beams by boundary element method, Journal of Vibration and Control, 16, 12, 1763–1789, 2010.
25. E.J. Sapountzakis, V.J. Tsipiras, A.K. Argyridi, Torsional vibration analysis of bars including secondary torsional shear deformation effect by the boundary element method, Journal of Sound Vibration, 355, 208–231, 2015.
26. K.M. Rasmussen, S.R.K. Nielsen, P.H. Kirkegaard, Boundary element method solution in the time domain for a moving time-dependent force, Computers & Structures, 79, 7, 691–701, 2001.
27. Y. Qu, W. Zhang, Z. Peng, G. Meng, Time-domain structural acoustic analysis of composite plates subjected to moving dynamic loads, Composite Structures, 208, 574–584, 2019.
28. C.A. Brebbia, D. Nardini, Dynamic analysis in solid mechanics by an alternative boundary element procedure, Engineering Analysis with Boundary Elements, 24, 4, 513–518, 2000.
29. S. Hamzehei Javaran, S. Shojaee, The solution of elastostatic and dynamic problems using the boundary element method based on spherical Hankel element network, International Journal for Numerical Methods in Engineering, 112, 13, 2067–2086, 2017.
30. Y. Fu, H. Du, S. Zhang, Functionally graded TiN/TiNi shape memory alloy films, Materials Letters, 57, 20, 2995–2999, 2003.
31. A. Witvrouw, A. Mehta, The use of functionally graded poly-SiGe layers for MEMS applications, Materials Science Forum, 492–493, 255–260, 2005.
32. H. Hassanin, K. Jiang, Net shape manufacturing of ceramic micro parts with tailored graded layers, Journal of Micromechanics and Microengineering, 24, 1, 015018, 2014.
33. F. Yang, A.C.M. Chong, D.C.C. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39, 10, 2731–2743, 2002.
34. H.M. Ma, X.L. Gao, J.N. Reddy, A microstructure-dependent Timoshenko beam model based on a modified couple stress theory, Journal of the Mechanics and Physics of Solids, 56, 12, 3379–3391, 2008.
35. M. Asghari, M.H. Kahrobaiyan, M.T. Ahmadian, A nonlinear Timoshenko beam formulation based on the modified couple stress theory, International Journal of Engineering Science, 48, 12, 1749–1761, 2010.
36. M. Asghari, M. Rahaeifard, M.H. Kahrobaiyan, M.T. Ahmadian, The modified couple stress functionally graded Timoshenko beam formulation, Materials & Design, 32, 3, 1435–1443, 2011.
37. M. Simsek, T. Kocatürk, S.D. Akbas, Static bending of a functionally graded microscale Timoshenko beam based on the modified couple stress theory, Composite Structures, 95, 740–747, 2013.
38. M. Simsek, J.N. Reddy, Bending and vibration of functionally graded microbeams Rusing a new higher order beam theory and the modified couple stress theory, International Journal of Engineering Science, 64, 37–53, 2013.
39. R. Aghazadeh, E. Cigeroglu, S. Dag, Static and free vibration analyses of small-scale functionally graded beams possessing a variable length scale parameter using different beam theories, European Journal of Mechanics – A/Solids, 46, 1–11, 2014.
40. A. Babaei, M.R.S. Noorani, A. Ghanbari, Temperature-dependent free vibration analysis of functionally graded micro-beams based on the modified couple stress theory, Microsystem Technologies, 23, 10, 4599–4610, 2017.
41. M.H. Ghayesh, M. Amabili, H. Farokhi, Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory, International Journal of Engineering Science, 63, 52–60, 2013.
42. R. Vatankhah, M.H. Kahrobaiyan, A. Alasty, M.T. Ahmadian, Nonlinear forced vibration of strain gradient microbeams, Applied Mathematical Modelling, 37, 18–19, 8363–8382, 2013.
43. S. Rajasekaran, H.B. Khaniki, Size-dependent forced vibration of non-uniform bidirectional functionally graded beams embedded in variable elastic environment carrying a moving harmonic mass, Applied Mathematical Modelling, 72, 129–154, 2019.
44. D. Das, Nonlinear forced vibration analysis of higher order shear-deformable functionally graded microbeam resting on nonlinear elastic foundation based on modified coupe stress theory, Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 233, 9, 1773–1790, 2019.
45. G.G. Sheng, X. Wang, Nonlinear forced vibration of size-dependent functionally graded microbeams with damping effects, Applied Mathematical Modelling, 71, 421–437, 2019.
46. J.C. Houbolt, A recurrence matrix solution for the dynamic response of elastic aircraft, Journal of the Aeronautical Sciences, 17, 9, 540–550, 1950.
47. M. Kerdjoudj, F.M.L. Amirouche, Implementation of the boundary element metod in the dynamics of flexible bodies, International Journal for Numerical Methods in Engineering, 39, 2, 321–354, 1996.
48. K.J. Bathe, E.L. Wilson, Stability and accuracy analysis of direct integration methods, Earthquake Engineering & Structural Dynamics, 1, 3, 283–291, 1972.
49. D.E. Johnson, A proof of the stability of the Houbolt method, AIAA Journal, 4, 8, 1450–1451, 1966.
50. T. Mori, K. Tanaka, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metallurgica, 21, 5, 571–574, 1973.
51. G.H. Paulino, Z.-H. Jin, R.H. Dodds Jr., Failure of functionally graded materials, in: Comprehensive Structural Integrity, I. Milne, R.O. Ritchie, B. Karihaloo [eds.], 2, 607–644, 2003.
52. H.-S. Shen, Z.-X. Wang, Assessment of Voigt and Mori-Tanaka models for vibration analysis of functionally graded plates, Composite Structures, 94, 7, 2197–2208, 2012.
53. J.N. Reddy, Z.-Q. Cheng, Frequency of functionally graded plates with threedimensional asymptotic approach, Journal of Engineering Mechanics, 129, 8, 896–900, 2003.
54. A.J.M. Ferreira, R.C. Batra, C.M.C. Roque, L.F. Qian, R.M.N. Jorge, Natural frequencies of functionally graded plates by a meshless method, Composite Structures, 75, 1–4, 593–600, 2006.
55. C. Zhang, Q. Wang, Free vibration analysis of elastically restrained functionally graded curved beams based on the Mori–Tanaka scheme, Mechanics of Advanced Materials and Structures, 26, 21, 1821–1831, 2019.
56. J. Song, Y. Wei, A method to determine material length scale parameters in elastic strain gradient theory, Journal of Applied Mechanics, Transactions of the ASME, 87, Paper No: 031010, 2020.
57. R. Ansari, R. Gholami, S. Sahmani, Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory, Composite Structures, 94, 1, 221–228, 2011.
58. L. Garcia, S. Villaça, Introduction to the theory of elasticity, COPPE/UFRJ, 2000 [In Portuguese].

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).

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Bibliografia

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