Open Access
Application of Differential Transform Method in Free Vibration Analysis of Rotating Non-Prismatic Beams
Reza Attarnejad,Ahmad Shahba +1 more
TLDR
In this paper, free vibration of non-prismatic rotating Euler-Bernoulli beams is studied by using differential transform method, a powerful numerical tool in solution of ordinary differential equations, for solving the governing equation of motion.Abstract:
Rotating beams are considerably used in different mechanical and aeronautical installations. In this paper, free vibration of non-prismatic rotating Euler-Bernoulli beams is studied. Dynamic stiffness matrix is evaluated by using differential transform method, a powerful numerical tool in solution of ordinary differential equations, for solving the governing equation of motion. The method is capable of modeling any beam whose cross-sectional area and moment of inertia vary along beam with any two arbitrary functions and any type of cross-section with just one or few elements so that it can be used in most of engineering applications. In order to verify the competency of the method, natural frequencies are obtained for two problems and the effects of rotational speed parameter and taper ratio on natural frequencies are investigated.read more
Citations
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Solution for Determining Modulus of Elasticity of Natural Materials Using Vibrations of Non-Uniform Circular Cross-Section Cantilevers
Jerzy Podgórski,Bartosz Kawecki +1 more
TL;DR: In this paper , a method for determining the modulus of elasticity of natural materials is presented based on vibrations of non-uniform circular cross-section cantilevers solved using Bessel functions.
Free vibration analysis of functionally graded rotating double tapered beam by using euler-bernoulli beam theory and differential transform method
F Ebrahimi,S Dashti +1 more
TL;DR: In this paper, the free vibration analysis of a functionally graded rotating double tapered beam is performed based on Euler-Bernoulli beam theory, and the results of this study are compared with the available results from the existing literature.
References
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Two-dimensional differential transform for partial differential equations
TL;DR: It is demonstrated that the differential transform is a feasible tool for obtaining the analytic form solutions of linear and nonlinear partial differential equation.
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Vibration Modes of Centrifugally Stiffened Beams
TL;DR: In this paper, the exact frequencies and mode shapes for rotating beams in which both the flexural rigidity and the mass distribution vary linearly were solved using the Frobenius method.
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Flapwise bending vibration analysis of a rotating tapered cantilever Bernoulli–Euler beam by differential transform method
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