This study presents free vibration analysis of rotating functionally graded Timoshenko beam made of porous material using the semi-analytical differential transform method.The material properties are supposed to vary along the thickness direction of the beam according to the rule of mixture, which is modified to approximate the material properties with the porosity phases. The frequency equation is obtained using Hamilton’s principle. It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of porous FG rotating beams. The good agreement between the results of this article and those available in literature validated the presented approach. Detailed mathematical derivations are presented and numerical investigations are performed, while emphasis is placed on investigating the effect of the several parameters such as porosity, functionally graded microstructure, thickness ratio, rotational speed and hub radius on the normalized natural frequencies of porous FG rotating beams in detail.
Porous material Functionally graded material Rotating beam Differential transform method
This is a preview of subscription content, log in to check access.
Banerjee JR (2001) Dynamic stiffness formulation and free vibration analysis of centrifugally stiffened Timoshenko beams. J Sound Vib 247(1):97–115CrossRefGoogle Scholar
Ebrahimi F (2013) Analytical investigation on vibrations and dynamic response of functionally graded plate integrated with piezoelectric layers in thermal environment. Mech Adv Mater Struct 20(10):854–870MathSciNetCrossRefGoogle Scholar
Ebrahimi F, Rastgoo A, Atai AA (2009) A theoretical analysis of smart moderately thick shear deformable annular functionally graded plate. Eur J Mech A Solids 28(5):962–973CrossRefGoogle Scholar
Ebrahimi F, Naei MH, Rastgoo A (2009) Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation. J Mech Sci Technol 23(8):2107–2124CrossRefGoogle Scholar
Ho SH, Chen COK (2006) Free transverse vibration of an axially loaded non-uniform spinning twisted Timoshenko beam using differential transform. Int J Mech Sci 48(11):1323–1331CrossRefzbMATHGoogle Scholar
Hodges DY, Rutkowski MY (1981) Free-vibration analysis of rotating beams by a variable-order finite-element method. AIAA J 19(11):1459–1466CrossRefzbMATHGoogle Scholar
Mei C (2008) Application of differential transformation technique to free vibration analysis of a centrifugally stiffened beam. Comput Struct 86(11):1280–1284CrossRefGoogle Scholar
Şimşek M (2010) Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nucl Eng Des 240(4):697–705CrossRefGoogle Scholar
Wattanasakulpong N, Ungbhakorn V (2014) Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities. Aerosp Sci Technol 32(1):111–120CrossRefGoogle Scholar
Wattanasakulpong N, Gangadhara Prusty B, Kelly DW, Hoffman M (2012) Free vibration analysis of layered functionally graded beams with experimental validation. Mater Des 36:182–190CrossRefGoogle Scholar
Zhou JK (1986) Differential transformation and its applications for electrical circuits. Huazhong University Press, Wuhan, ChinaGoogle Scholar