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Browsing Scopus by Subject "Adomian decomposition method"

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    Citation Count: 11
    Differential transform method and Adomian decomposition method for free vibration analysis of fluid conveying Timoshenko pipeline
    (Techno-Press, 2017) Bozyigit,B.; Yesilce,Y.; Catal,S.
    The free vibration analysis of fluid conveying Timoshenko pipeline with different boundary conditions using Differential Transform Method (DTM) and Adomian Decomposition Method (ADM) has not been investigated by any of the studies in open literature so far. Natural frequencies, modes and critical fluid velocity of the pipelines on different supports are analyzed based on Timoshenko model by using DTM and ADM in this study. At first, the governing differential equations of motion of fluid conveying Timoshenko pipeline in free vibration are derived. Parameter for the nondimensionalized multiplication factor for the fluid velocity is incorporated into the equations of motion in order to investigate its effects on the natural frequencies. For solution, the terms are found directly from the analytical solution of the differential equation that describes the deformations of the cross-section according to Timoshenko beam theory. After the analytical solution, the efficient and easy mathematical techniques called DTM and ADM are used to solve the governing differential equations of the motion, respectively. The calculated natural frequencies of fluid conveying Timoshenko pipelines with various combinations of boundary conditions using DTM and ADM are tabulated in several tables and figures and are compared with the results of Analytical Method (ANM) where a very good agreement is observed. Finally, the critical fluid velocities are calculated for different boundary conditions and the first five mode shapes are presented in graphs. © 2017 Techno-Press, Ltd.
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    Citation Count: 12
    Free vibrations of axial-loaded beams resting on viscoelastic foundation using Adomian decomposition method and differential transformation
    (Elsevier B.V., 2018) Bozyigit,B.; Yesilce,Y.; Catal,S.
    The aim of this paper is to reveal the effectiveness of Adomian decomposition method (ADM) and differential transform method (DTM) on free vibrations of axial-loaded Timoshenko beams resting on viscoelastic foundation. The effects of axial compressive load, modulus of subgrade reaction and foundation damping on natural frequencies of beam model are studied using various boundary conditions. The results of DTM and ADM are tabulated with exact results that obtained from analytical formulations where an excellent agreement is observed. Moreover, the dynamic stiffness method (DSM) which uses the exact mode shapes is applied to verify the analytical results. The accuracy of mathematical tools DTM and ADM is demonstrated by several numerical examples. The first four mode shapes are depicted. It is highlighted that application of DTM, ADM and DSM can be extended without any difficulties for free vibrations of beam assembly structures that resting on viscoelastic foundation. © 2018 Karabuk University