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1
Content available Transient analysis of transversely functionally graded Timoshenko beam (TFGTB) in conjunction with finite element method
Khafaji Salwan Obaid Waheed, Al-Shujairi Mohammed A., Aubad Mohammed Jawad
Archive of Mechanical Engineering
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2020
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LXVII, nr 3
299--321
EN
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.
2
Content available remote Bending of beams with symmetrically varying mechanical properties under generalized load – shear effect
Magnucki Krzysztof, Lewinski Jerzy
Engineering Transactions
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2019
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Vol. 67, iss. 3
441--457
EN
The paper is devoted to simply supported beams with symmetrically varying mechanical properties in the depth direction. Generalized load of the beams includes the load types from uniformly distributed to point load (three-point bending). This load is analytically described with the use of a certain function including a dimensionless parameter. The value of the parameter is decisive for the load type. The individual nonlinear “polynomial” hypothesis is applied to deformation of a planar cross section. Based on the definitions of the bending moment and the shear transverse force the differential equation of equilibrium is obtained. The equation is analytically solved and the deflections are calculated for an exemplary beam family. The results of the study are specified in tables.
3
Content available Bending, buckling and free vibration of a beam with unsymmetrically varying mechanical properties
Magnucki K., Lewiński J., Magnucka-Blandzi E., Kędzia P.
Journal of Theoretical and Applied Mechanics
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2018
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Vol. 56 nr 4
1163--1178
EN
The subject of the paper is a beam with unsymmetrically varying mechanical properties in the depth direction. The nonlinear hypothesis of plane cross section deformation is assumed. Based on Hamilton’s principle, two differential equations of motion are obtained. The system of equations is analytically solved with a view to analyse the bending, buckling and free vibration problems of the beam. Moreover, the FEM model of the beam is developed and deflections, critical axial forces and natural frequencies of the beam are calculated. The results of these two methods are compared.
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