Application of the differential transform method to the free vibration analysis of functionally graded Timoshenko beams

Őzdemir, Őzge

doi:10.15632/jtam-pl.54.4.1205

Cited by 3 publications

(1 citation statement)

References 25 publications

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“…In this section, energy expressions are given both for a rotating Euler-Bernoulli beam and a rotating Timoshenko beam. Details of the derivations can be found in the studies of [17] and [18].…”

Section: Energy Expressionsmentioning

confidence: 99%

Archive of Mechanical Engineering

Kılıç¹,

Őzdemir²

2021

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Design considerations, material properties and dynamic properties of engineering applications, rotating components, turbine blades, helicopter blades, etc., have significant effects on system efficiency. Structures made of functionally graded materials have recently begun to take place in such engineering applications, resulting from the development of composite material technology. In this study, vibration and buckling characteristics of axially functionally graded beams whose material properties change along the beam length is analyzed. Beam structural formulations and functionally graded material formulations are obtained for the Classical and the First Order Shear Deformation Theories. Finite element models are derived to carry out the vibratory and stability characteristic analyses. Effects of several parameters, i.e., rotational speed, hub radius, material properties, power law index parameter and boundary conditions are investigated and are displayed in several figures and tables. The calculated results are compared with the ones in open literature and very good agreement is observed.

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Section: Energy Expressionsmentioning

confidence: 99%

Archive of Mechanical Engineering

Kılıç¹,

Őzdemir²

2021

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Vibration and Buckling Analyses of Rotating Axially Functionally Graded Nonuniform Beams

Őzdemir

2022

J. Vib. Eng. Technol.

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Vibration Analysis of Rotating Timoshenko Beams With Different Material Distribution Properties

Őzdemir¹

2019

Scitech

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In this study, vibration characteristics of functionally graded rotating Timoshenko beams that undergoes flapwise bending vibration are analysed. Beam models with different material distribution properties are considered. The energy expressions are derived by introducing several explanotary figures and tables. Applying the Hamilton's Principle to the derived energy expressions, governing differential equations of motion and the boundary conditions are obtained. Related formulation is coded by using MATLAB and in the solution part, the equations of motion, including the parameters for the rotary inertia, shear deformation, power law index parameter and slenderness ratio are solved using an efficient mathematical technique, called the differential transform method (DTM). Natural frequencies of the modeled beams are obtained. Increasing effects of the slenderness ratio and the rotational speed and the decreasing effect of the power-law index on the natural frequencies are investigated. Moreover, differences between the natural frequencies of the beam models with different material distribution characteristics is noticed and examined. Obtained results are distributed in several tables.

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Application of the differential transform method to the free vibration analysis of functionally graded Timoshenko beams

Cited by 3 publications

References 25 publications

Archive of Mechanical Engineering

Archive of Mechanical Engineering

Vibration and Buckling Analyses of Rotating Axially Functionally Graded Nonuniform Beams

Vibration Analysis of Rotating Timoshenko Beams With Different Material Distribution Properties

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