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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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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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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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Book
Dynamics in engineering structures
TL;DR: In this paper, Dynamics in engineering structures are discussed in the context of engineering structures, where the authors propose a model for dynamic engineering structures in the engineering structures of buildings and their components.
Journal ArticleDOI
Flapwise bending vibration analysis of double tapered rotating Euler–Bernoulli beam by using the differential transform method
Ozge Ozdemir Ozgumus,Mithat Kaya +1 more
TL;DR: In this article, the out-of-plane free vibration analysis of a double tapered Euler-Bernoulli beam, mounted on the periphery of a rotating rigid hub is performed.
Journal ArticleDOI
Free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite elements
TL;DR: In this article, a spectral element for uniform and tapered rotating Euler-Bernoulli beams is presented, which takes into account the varying centrifugal force, mass and bending stiffness.
Journal ArticleDOI
Analysis of general elastically end restrained non-uniform beams using differential transform
Shing Huei Ho,Cha'o-Kuang Chen +1 more
TL;DR: In this paper, the authors introduced using differential transform to solve the free and forced vibration problems of a general elastically end restrained non-uniform beam, resting on a non-homogeneous elastic foundation and subjected to axial tensile and transverse forces.
Journal ArticleDOI
New rational interpolation functions for finite element analysis of rotating beams
TL;DR: In this article, a rotating beam finite element in which the interpolating shape functions are obtained by satisfying the governing static homogenous differential equation of Euler-Bernoulli rotating beams is developed.
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