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Thermo-mechanical vibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory
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 Title & Authors
Thermo-mechanical vibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory
Ebrahimi, Farzad; Jafari, Ali;
In this paper thermo-mechanical vibration analysis of a porous functionally graded (FG) Timoshenko beam in thermal environment with various boundary conditions are performed by employing a semi analytical differential transform method (DTM) and presenting a Navier type solution method for the first time. The temperature-dependent material properties of FG beam are supposed to vary through thickness direction of the constituents according to the power-law distribution which is modified to approximate the material properties with the porosity phases. Also the porous material properties vary through the thickness of the beam with even and uneven distribution. Two types of thermal loadings, namely, uniform and linear temperature rises through thickness direction are considered. Derivation of equations is based on the Timoshenko beam theory in order to consider the effect of both shear deformation and rotary inertia. Hamilton`s principle is applied to obtain the governing differential equation of motion and boundary conditions. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of several parameters such as porosity distributions, porosity volume fraction, thermal effect, boundary conditions and power-low exponent on the natural frequencies of the FG beams in detail. It is explicitly shown that the vibration behavior of porous FG beams is significantly influenced by these effects. Numerical results are presented to serve benchmarks for future analyses of FG beams with porosity phases.
thermo-mechanical vibration;functionally graded beam;porous material;DTM;thermal effect;
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Akgoz, B. and Civalek, O. (2014), "Shear deformation beam models for functionally graded microbeams with new shear correction factors", Compos. Struct, 112, 214-225. crossref(new window)

Akgoz, B. and Civalek, O. (2014), "Thermo-mechanical buckling behavior of functionally graded microbeams embedded in elastic medium", Int. J. Mech. Sci., 85, 90-104.

Atmane, H.A., Tounsi, A. and Bernard, F. (2015), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater. Des., 1-14.

Aydogdu, M. and Taskin, V. (2007), "Free vibration analysis of functionally graded beams with simply supported edges", Mater. Des., 28(5), 1651-1656. crossref(new window)

Civalek, O. and Kiracioglu, O. (2010), "Free vibration analysis of Timoshenko beams by DSC method", Int. J. Numer. Meth. Biomed. Eng., 26(12), 1890-1898.

Ebrahimi, F. and Mokhtari, M. (2014), "Transverse vibration analysis of rotating porous beam with functionally graded microstructure using the differential transform method", J. Braz. Soc. Mech. Sci. Eng., 1-10.

Ebrahimi, F. and Salari, E. (2015), "Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments", Compos. Struct., 128, 363-380. crossref(new window)

Ebrahimi, F., Ghasemi, F. and Salari, E. (2015), "Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities", Meccanica, 51(1), 223-249..

Ebrahimi, F., Naei, M.H. and Rastgoo, A. (2009), "Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation", J. Mech. Sci. Technol, 23(8), 2107-2124. crossref(new window)

Ebrahimi, F., Rastgoo, A. and Atai, A. (2009), "A theoretical analysis of smart moderately thick shear deformable annular functionally graded plate", Eur. J. Mech-A/Solid., 28(5), 962-973. crossref(new window)

Hassan, I.A.H. (2002), "On solving some eigenvalue problems by using a differential transformation", Appl. Math. Comput., 127(1), 1-22. crossref(new window)

Jha, D., Kant, T. and Singh, R. (2013), "A critical review of recent research on functionally graded plates", Compos. Struct., 96, 833-849. crossref(new window)

Ju, S.P. (2004), "Application of differential transformation to transient advective-dispersive transport equation", Appl. Math. Comput., 155(1), 25-38. crossref(new window)

Kiani, Y. and Eslami, M. (2013), "An exact solution for thermal buckling of annular FGM plates on an elastic medium", Compos. Part B: Eng., 45(1), 101-110. crossref(new window)

Komijani, M., Esfahani, S.E., Reddy, J.N., Liu, Y.P. and Eslami, M.R. (2014), "Nonlinear thermal stability and vibration of pre/post-buckled temperature-and microstructure-dependent functionally graded beams resting on elastic foundation", Compos. Struct., 112, 292-307. crossref(new window)

Magnucka-Blandzi, E. (2008), "Axi-symmetrical deflection and buckling of circular porous-cellular plate", Thin Wall. Struct., 46(3), 333-337. crossref(new window)

Magnucka-Blandzi, E. (2009), "Dynamic stability of a metal foam circular plate", J. Theor. Appl. Mech., 47, 421-433.

Magnucka-Blandzi, E. (2010), "Non-linear analysis of dynamic stability of metal foam circular plate", J. Theor. Appl. Mech., 48(1), 207-217.

Mechab, I., Mechab, B., Benaissa, S., Serier, B. and Bouiadjra, B.B. (2016), "Free vibration analysis of FGM nanoplate with porosities resting on Winkler Pasternak elastic foundations based on two-variable refined plate theories", J. Braz. Soc. Mech. Sci. Eng., 1-19.

Pradhan, K. and Chakraverty, S. (2013), "Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh-Ritz method", Compos. Part B: Eng., 51, 175-184. crossref(new window)

simsek, M. (2010), "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nucl. Eng. Des., 240(4), 697-705. crossref(new window)

simsek, M. (2010), "Non-linear vibration analysis of a functionally graded Timoshenko beam under action of a moving harmonic load", Compos. Struct., 92(10), 2532-2546. crossref(new window)

simsek, M. and T. Kocaturk, (2009), "Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load", Compos. Struct., 90(4), 465-473. crossref(new window)

Sina, S., Navazi, H. and Haddadpour, H. (2009), "An analytical method for free vibration analysis of functionally graded beams", Mater. Des., 30(3), 741-747. crossref(new window)

Tauchert, T.R. (1974), Energy Principles in Structural Mechanics, McGraw-Hill Co.

Thai, H.T. and Vo, T.P. (2012), "Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories", Int. J. Mech. Sci., 62(1), 57-66. crossref(new window)

Touloukian, Y.S. (1966), "Thermophysical properties of high temperature solid materials", 4, Oxides and Their Solutions and Mixtures, Part I. Simple Oxyg. Compd. Mix., DTIC Document.

Wattanasakulpong, N. and Chaikittiratana, A. (2015), "Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method", Meccanica, 50(5), 1-12. crossref(new window)

Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. crossref(new window)

Wattanasakulpong, N., Prusty, B.G., Kelly, D.W. and Hoffman, M. (2012), "Free vibration analysis of layered functionally graded beams with experimental validation", Mater. Des., 36, 182-190. crossref(new window)

Wei, D., Liu, Y. and Xiang, Z. (2012), "An analytical method for free vibration analysis of functionally graded beams with edge cracks", J. Sound Vib., 331(7), 1686-1700. crossref(new window)

Xiang, H. and Yang, J. (2008), "Free and forced vibration of a laminated FGM Timoshenko beam of variable thickness under heat conduction", Compos. Part B: Eng., 39(2), 292-303. crossref(new window)

Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143. crossref(new window)