@ARTICLE{Khafaji_Salwan_Obaid_Waheed_Transient_2020,
 author={Khafaji, Salwan Obaid Waheed and Al-Shujairi, Mohammed A. and Aubad, Mohammed Jawad},
 volume={vol. 67},
 number={No 3},
 journal={Archive of Mechanical Engineering},
 pages={299-321},
 howpublished={online},
 year={2020},
 publisher={Polish Academy of Sciences, Committee on Machine Building},
 abstract={In this work, transient and free vibration analyses are illustrated for a functionally graded Timoshenko beam (FGM) using finite element method. The governing equilibrium equations and boundary conditions (B-Cs) are derived according to the principle of Hamilton. The materials constituents of the FG beam that vary smoothly along the thickness of the beam (along beam thickness) are evaluated using the rule of mixture method. Power law index, slenderness ratio, modulus of elasticity ratio, and boundary conditions effect of the cantilever and simply supported beams on the dynamic response of the beam are studied. Moreover, the influence of mass distribution and continuous stiffness of the FGM beam are deeply investigated. Comparisons between the current free vibration results (fundamental frequency) and other available studies are performed to check the formulation of the current mathematical model. Good results have been obtained. A significant effect is noticed in the transient response of both simply supported and cantilever beams at the smaller values of the power index and the modulus elasticity ratio.},
 type={Artykuły / Articles},
 title={Transient analysis of transversely functionally graded Timoshenko beam (TFGTB) in conjunction with finite element method},
 URL={http://journals.pan.pl/Content/115026/PDF/AME_2020_131694.pdf},
 doi={10.24425/ame.2020.131694},
 keywords={FGM beam, transient response, free vibration, fundamental frequency, finite element method, Timoshenko beam theory},
}