Influences of Dynamic Moving Forces on the Functionally Graded Porous-Nonuniform Beams
Keywords:
functionally graded material, porous-nonuniform beam, porosity, dynamic analysis, finite element modelAbstract
The dynamic response of functionally graded (FG) porous-nonuniform beams subjected to moving forces is investigated. The beam cross-section is assumed to vary longitudinally in the width direction by a linear or quadratic function. A modified rule of mixture, taking the effect of porosities into account, is adopted in evaluating the effective material properties. Based on Timoshenko beam theory, governing equations of motion are derived from Hamilton's principle, and they are solved by a finite element model. The dynamic response of a simply supported FG porous beam is computed with the aid of the Newmark method. The validation of the derived formulation is confirmed by comparing the obtained numerical results with the data available in the literature. A parametric study is conducted to highlight the effect of the material inhomogeneity, porosity volume fraction, section profile and loading parameters on the dynamic behavior of the beams.References
L. Frýba, Vibration of solids and structures under moving loads, 3rd ed. Prague: Thomas Telford House, 1999.
W. H. Lin and M. W. Trethewey, “Finite element analysis of elastic beams subjected to moving dynamic loads,” Journal of Sound and Vibration, vol. 136, no. 2, pp. 323-342, January 1990.
D. Thambiratnam and Y. Zhuge, “Dynamic analysis of beams on elastic foundation subjected to moving loads.” Journal of Sound and Vibration, vol. 198, no. 2, pp. 149-169, November 1996.
S. Ziaei-Rad, A. Ariaei, and M. Imregun, “Vibration analysis of Timoshenko beams under uniform partially distributed moving masses, ” Proc. of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, vol. 221, no. 4, pp. 551-566, December 2007.
M. Moghaddas, R. Sedaghati, and E. Esmailzadeh, “Finite element analysis of a Timoshenko beam traversed by a moving vehicle,” Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics, vol. 223, no. 3, pp. 231-243, September 2009.
M. Moghaddas, E. Esmailzadeh, R. Sedaghati, and P. Khosravi, “Vibration control of Timoshenko beam traversed by moving vehicle using optimized tuned mass damper,” Journal of Vibration and Control, vol. 18, no. 6, pp. 757-773, May 2012.
D. Roshandel, M. Mofid, and A. Ghannadiasl, “Dynamic response of a non-uniform Timoshenko beam, subjected to moving mass,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 229, no. 14, pp. 2499-2513, October 2015.
M. Koizumi, “FGM activities in Japan,” Composites Part B: Engineering, vol. 28, no. 1-2, pp. 1-4, 1997.
D. K. Jha,T. Kant, and R.K. Singh, “A critical review of recent research on functionally graded plates,” Composite Structures, vol. 96, pp. 833-849, 2013.
A. Chakraborty, S. Gopalakrishnan, and J. N. Reddy, “A new beam finite element for the analysis of functionally graded materials,” International Journal of Mechanical Science, vol. 45, no. 3, pp. 519-539, March 2003.
R. Kadoli, K. Akhtar, and N. Ganesan, “Static analysis of functionally graded beams using higher order shear deformation
beam theory,” Applied Mathematical Modelling, vol. 32, no. 12, pp. 2509-2525, December 2008.
A. E. Alshorbagy, M. A. Eltaher, and F. F. Mahmoud, “Free vibration characteristics of a functionally graded beam by finite element method,” Applied Mathematical Modelling, vol. 35, no. 1, pp. 412-425, January 2011.
A. Shahba, R. Attarnejad, M. T. Marvi, and S. Hajilar, “Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions,” Composites Part B: Engineering, vol. 42, no. 4, pp. 801-808, June 2011.
D. K. Nguyen, “Large displacement response of tapered cantilever beams made of axially functionally graded material,” Composites Part B: Engineering, vol. 55, pp. 298-305, December 2013.
D. K. Nguyen, “Large displacement behaviour of tapered cantilever Euler-Bernoulli beams made of functionally graded material,” Applied Mathematics and Computation, vol. 237, pp. 340-355, June 2014
D. K. Nguyen and B. S. Gan, “Large deflections of tapered functionally graded beams subjected to end forces,” Applied Mathematical Modelling, vol. 38, pp. 3054-3066, June 2014.
M. Şimşek and T. Kocatürk, “Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load,” Composite Structures, vol. 90, no. 4, pp. 465-473, October 2009.
M. Şimşek, “Vibration analysis of a functionally graded beam under a moving mass by using different beam theories,” Composite Structures, vol. 92, no. 4, pp. 904-917, March 2010.
M. Şimşek, “Non-linear vibration analysis of a functionally graded Timoshenko beam under action of a moving harmonic load,” Composite Structures, vol. 92, no. 10, pp. 2532-2546, September 2010.
S. M. R. Khalili, A. A. Jafari, and S. A. Eftekhari, “A mixed Ritz-DQ method for forced vibration of functionally graded beams carrying moving loads,” Composite Structures, vol. 92, no. 10, pp. 2497-2511, September 2010.
K. Rajabi, M. H. Kargarnovin, and M. Gharini, “Dynamic analysis of a functionally graded simply supported Euler-Bernoulli beam to a moving oscillator,” Acta Mechanica, vol. 224, pp. 425-446, February 2013.
D. K. Nguyen, B. S. Gan, and T. H. Le, “Dynamic response of non-uniform functionally graded beams subjected to a variable speed moving load,” Journal of ComputationalScience and Technology (JSME), vol. 7, no. 1, pp. 12-27, January 2013.
T. H. Le, B. S. Gan, T. H. Trinh, and D. K. Nguyen, “Finite element analysis ofmulti-span functionally graded beams under a moving harmonic load,” Mechanical Engineering Journal (JSME), vol. 1, no. 3, pp. 1-13, June 2014.
B. S. Gan, T. H. Trinh, T. H. Le, and D. K. Nguyen, “Dynamic response of non-uniform Timoshenko beams made of axially FGM subjected to multiple moving point loads,” Structural Engineering and Mechanics, vol. 53, no. 5, pp. 981-995, March 2015.
N. Wattanasakulpong and V. Ungbhakorn, “Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities,” Aerospace Science and Technology, vol. 32, no. 1, pp. 111-120, January 2014.
N. Wattanasakulpong and A. Chaikittiratana, “Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method,” Meccanica, vol. 50, no. 5, pp. 1331-1342, May 2015.
D. Chen, J. Yang and S. Kitipornchai, “Elastic buckling and static bending of shear deformable functionally graded porous beam,” Composite Structures, vol. 133, pp. 54-61, December 2015.
H. A. Atmane, A. Tounsi, and F. Bernard, “Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations,” International Journal of Mechanics and Materials in Design, pp. 1-14,July 2015.
F. Ebrahimi and M. Zia, “Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities,” ActaAstronautica, vol. 116, pp. 117-125, November 2015.
F. Ebrahimi, F. Ghasemi, and E. Salari, “Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities,” Meccanica, vol. 51, no. 1, pp. 223-249, January 2016.
J. B. Kosmatka, “An improve two-node finite element for stability and natural frequencies of axial-loaded Timoshenko beams,” Computers & Structures, vol. 57, no. 1, pp. 141-149, October 1995.
M. Géradin and D. Rixen, Mechanical Vibrations: Theory and Application toStructural Dynamics, 2nd ed. Chichester: John Willey & Sons, 1997.
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