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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
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State-vector equation method for the frequency domain spectral element modeling of non-uniform one-dimensional structures
Taehyun Kim,Bitna Lee,Usik Lee +2 more
TL;DR: In this paper, a state vector equation method (SVEM)-based spectral element method was proposed to formulate frequency domain spectral element models for non-uniform 1-D structures.
Journal ArticleDOI
Numerical free vibration analysis of higher-order shear deformable beams resting on two-parameter elastic foundation
Mohammad Zakeri,Reza Attarnejad +1 more
TL;DR: In this paper, the free vibration analysis of higher-order shear deformation beam resting on one-and two-parameter elastic foundation is studied using differential transform method (DTM) as a part of a calculation procedure.
Journal ArticleDOI
Experimental and theoretical investigation of static deflection and natural frequency of stepped cantilever beam
TL;DR: A maximum static deflection and natural frequency of aluminium cantilever stepped beam (two steps) were investigated experimentally and theoretically for different values of small and large diameters as mentioned in this paper.
Journal ArticleDOI
Free Vibration Analysis of the Tube-In-Tube Tall Buildings with the Differential Transform Method:
TL;DR: In this paper, a tube-in-tube tall building was modeled as an orthotropic beam and the solution was completed in the governing equation written according to this model by applying the Differential Transform method to convert the differential equation into an algebraic equation.
Journal ArticleDOI
Comparison study of differential transform method with finite difference method for magnetoconvection in a vertical channel
TL;DR: In this paper, coupled nonlinear equations governing the flow for magnetoconvection in a vertical channel for open and short circuits are solved by using differential transformation method (DTM) which is a semi-numerical-analytical solution technique.
References
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Solutions of the system of differential equations by differential transform method
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Journal ArticleDOI
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.
Journal ArticleDOI
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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