Dynamic Response of Shear Deformable Functionally Graded Porous Beams

Abstract:

This paper analyzes the dynamic response of a shear deformable functionally graded porous beam under a point harmonic load. Timoshenko beam theory is employed to include the effect of transverse shear strain. The elasticity moduli and mass density of the porous beam vary continuously in the thickness direction based on two different porosity distributions. The relationship between porosity and density coefficients are determined according to the mechanical property of an open-cell metal foam. The equations of motion are derived and solved by applying Ritz method in the space domain and Newmark-β method in the time domain. The dynamic deflections are obtained for porous beams with different boundary conditions. A detailed numerical analysis is presented to show the effects of porosity coefficient and slenderness ratio on the dynamic response of porous beams. The influence of porosity distribution pattern is highlighted to shed a useful insight into the design of functionally graded porous structures.

• Periodical: Applied Mechanics and Materials (Volume 846)
• Pages: 434-439
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.846.434
• Online since: July 2016
• Authors: Da Chen, Sritawat Kitipornchai, Jie Yang*
• Keywords: Dynamic Analysis, Functionally Graded Porous Beam, Harmonic Load, Porosity Distribution, Timoshenko Beam Theory

References

[1] K. Magnucki, P. Stasiewicz, Elastic buckling of a porous beam, Journal of Theoretical and Applied Mechanics. 42 (2004) 859-868.

[2] E. Magnucka-Blandzi, Non-linear analysis of dynamic stability of metal foam circular plate, Journal of Theoretical and Applied Mechanics. 48 (2010) 207-217.

[3] E. Magnucka-Blandzi, Axi-symmetrical deflection and buckling of circular porous-cellular plate, Thin-Walled Structures. 46 (2008) 333-337.

DOI: 10.1016/j.tws.2007.06.006

[4] M. Jabbari, A. Mojahedin, A. Khorshidvand, M. Eslami, Buckling analysis of a functionally graded thin circular plate made of saturated porous materials, Journal of Engineering Mechanics. 140 (2014) 287-295.

DOI: 10.1061/(asce)em.1943-7889.0000663

[5] D. Chen, J. Yang, S. Kitipornchai, Elastic buckling and static bending of shear deformable functionally graded porous beam, Composite Structures. 133 (2015) 54-61.

DOI: 10.1016/j.compstruct.2015.07.052

[6] L. Cui, S. Kiernan, M. D. Gilchrist, Designing the energy absorption capacity of functionally graded foam materials, Materials Science and Engineering: A. 507 (2009) 215-225.

DOI: 10.1016/j.msea.2008.12.011

[7] M. Şimşek, T. Kocatürk, Ş. Akbaş, Dynamic behavior of an axially functionally graded beam under action of a moving harmonic load, Composite Structures. 94 (2012) 2358-2364.

DOI: 10.1016/j.compstruct.2012.03.020

[8] L. -L. Ke, J. Yang, S. Kitipornchai, Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams, Composite Structures. 92 (2010) 676-683.

DOI: 10.1016/j.compstruct.2009.09.024

[9] T. Yan, S. Kitipornchai, J. Yang, X. Q. He, Dynamic behaviour of edge-cracked shear deformable functionally graded beams on an elastic foundation under a moving load, Composite Structures. 93 (2011) 2992-3001.

DOI: 10.1016/j.compstruct.2011.05.003

[10] L. J. Gibson, M. Ashby, The mechanics of three-dimensional cellular materials, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. 382 (1982) 43-59.

[11] J. Choi, R. Lakes, Analysis of elastic modulus of conventional foams and of re-entrant foam materials with a negative Poisson's ratio, International Journal of Mechanical Sciences. 37 (1995) 51-59.

DOI: 10.1016/0020-7403(94)00047-n