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Application of Differential Transform Method in Free Vibration Analysis of Rotating Non-Prismatic Beams
Reza Attarnejad,Ahmad Shahba +1 more
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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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Journal ArticleDOI
Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory
Bekir Akgöz,Ömer Civalek +1 more
TL;DR: In this article, the vibration response of non-homogenous and non-uniform microbeams is investigated in conjunction with Bernoulli-Euler beam and modified couple stress theory, where boundary conditions of the microbeam are considered as fixed at one end and free at the other end.
Journal ArticleDOI
Free vibration and stability of tapered Euler–Bernoulli beams made of axially functionally graded materials
TL;DR: In this paper, the free vibration and stability of axially functionally graded tapered Euler-Bernoulli beams were studied through solving the governing differential equations of motion. But, the convergence rate of the conventional differential transform method (DTM) does not necessarily converge to satisfactory results, and a new approach based on DTM called differential transform element method (DTEM) is introduced which considerably improves the convergence of the method.
Journal ArticleDOI
Free vibration of centrifugally stiffened axially functionally graded tapered Timoshenko beams using differential transformation and quadrature methods
TL;DR: In this article, the free bending vibration of rotating axially functionally graded (FG) Timoshenko tapered beams (TTB) with different boundary conditions are studied using Differential Transformation method (DTM) and differential quadrature element method of lowest order (DQEL).
Journal ArticleDOI
Differential transformation and differential quadrature methods for centrifugally stiffened axially functionally graded tapered beams
TL;DR: In this article, the free bending vibration of rotating axially functionally graded (FG) Euler-Bernoulli tapered beams (ETB) with different boundary conditions are studied using Differential Transformation method (DTM) and differential quadrature element method of lowest order (DQEL).
Journal ArticleDOI
Dynamic basic displacement functions in free vibration analysis of centrifugally stiffened tapered beams; a mechanical solution
Reza Attarnejad,Ahmad Shahba +1 more
TL;DR: In this article, the free vibration analysis of rotating tapered beams is studied from a mechanical point of view, and exact shape functions are derived in terms of Basic Displacement Functions (BDFs).
References
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Journal ArticleDOI
On the two-dimensional differential transform method
TL;DR: Analytical form solutions of two diffusion problems have been obtained and the solutions are compared very well with those obtained by decomposition method.
Journal ArticleDOI
Free vibration of rotating tapered beams using the dynamic stiffness method
TL;DR: In this article, the free bending vibration of rotating tapered beams is investigated by using the dynamic stiffness method, and the expressions for bending rotation, shear force and bending moment at any cross-section of the beam are also obtained in explicit analytical form.
Journal ArticleDOI
Free vibration of centrifugally stiffened uniform and tapered beams using the dynamic stiffness method
TL;DR: In this article, the dynamic stiffness matrix of a uniform rotating Bernoulli-Euler beam is derived using the Frobenius method of solution in power series, which includes the presence of an axial force at the outboard end of the beam in addition to the usual centrifugal force arising from the rotational motion.
Journal ArticleDOI
Flapwise bending vibration analysis of a rotating tapered cantilever Bernoulli–Euler beam by differential transform method
Özge Özdemir,Mithat Kaya +1 more
TL;DR: In this article, the authors studied the vibration characteristics of a rotating tapered cantilever Bernoulli-Euler beam with linearly varying rectangular cross-section of area proportional to xn, where n equals to 1 or 2 covers the most practical cases.
Journal ArticleDOI
Free Vibration Analysis of Rotating Blades With Uniform Tapers
Gang Wang,Norman M. Wereley +1 more
TL;DR: In this paper, a spectral finite element method (SFEM) is proposed to develop a low-degree-of-freedom model for dynamic analysis of rotating tapered beams, which exploits semi-analytical progressive wave solutions of the governing partial differential equations.
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Flapwise bending vibration analysis of a rotating tapered cantilever Bernoulli–Euler beam by differential transform method
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