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).
About: This article is published in International Journal of Mechanical Sciences.The article was published on 2013-09-01. It has received 72 citations till now. The article focuses on the topics: Functionally graded material & Beam (structure).
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TL;DR: In this article, the effects of material property distribution, spring constants and porosity volume fraction on linear and nonlinear frequencies of functionally graded materials (FGMs) beams with porosity phases were investigated.
339 citations
TL;DR: In this paper, a coupled nonlinear longitudinal-transverse-rotational set of equations governing the motion of axially functionally graded (AFG) shear deformable tapered beams subjected to external harmonic excitations is derived.
145 citations
TL;DR: In this article, the free vibration of non-uniform functionally graded beams is analyzed via the Timoshenko beam theory, where bending stiffness and distributed mass density are assumed to obey a unified exponential law.
101 citations
TL;DR: In this article, the motion differential equations of the bi-directional functionally graded Timoshenko beam are established using Hamilton's principle using variable substitution method, and the influence of gradient parameters α, β on the fundamental frequency, mode shape and frequency response function is analyzed through the establishment of the dynamic stiffness matrix of the overall structure.
79 citations
TL;DR: In this paper, the free vibration analysis of functionally graded beams (FGBs) and frameworks containing FGBs is carried out by applying the dynamic stiffness method and deriving the elements of dynamic stiffness matrix in explicit algebraic form.
79 citations
Cites methods from "Differential transformation and dif..."
...amongst these are the applications of direct analytical procedure using the governing differential equations of motion [5e19], finite element [20e22], Rayleigh-Ritz [23], finite volume [24e26], differential quadrature [27], differential transformation [27,28] and transfer function [29,30] methods....
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Book•
14 Jan 2000
TL;DR: A Differential Quadrature Hierarchical Finite Element Method (DQEEM) based on Bernstein Polynomials is proposed in this paper for the analysis of doubly-curvel shell structures.
Abstract: Application of Differential Quadrature to Engineering ProblemsApplication of Differential Quadrature to the Analysis of Structural ComponentsTsinghua Science and TechnologyApplication of Differential Quadrature Method to the Analysis of Delamination Buckling of Laminated CompositesDifferential Quadrature and Differential Quadrature Based Element MethodsApplication of the Differential Quadratire Method to Problems in Engineering MechanicsProceedings of the International Conference on Advances in Computational Mechanics 2017Advanced Differential Quadrature MethodsA Differential Quadrature Hierarchical Finite Element MethodLaminated Composite Doubly-Curved Shell StructuresRecent Advances in Mathematics for EngineeringComputer Modeling in Engineering & SciencesMeshfree Approximation Methods with MatlabApplication of Differential Quadrature to the Analysis of Static Aeroelastic PhenomenaApplication of the Differential Quadrature Method to the Plane Elasticity ProblemMathematical Methods in Interdisciplinary SciencesDiQuMaSPABWave Propagation in Materials for Modern ApplicationsDifferential Quadrature Methods and Its ApplicationsA Generalization and Application of the Differential Quadrature MethodApplication of the Differential Quadrature Method to the Buckling Analysis of Cylindrical Shells and TanksBoundary Elements and Other Mesh Reduction Methods XXXVDifferential Quadrature and Its Application in EngineeringDifferential Quadrature Method in Computational MechanicsUse of Differential Quadrature in a Recursive FilterApplication of Differential Quadrature to Nuclear Engineering ProblemsMathematical PhysicsStructural Dynamics of Earthquake EngineeringDeterministic Flexibility AnalysisHandbook of Research on Computational Science and Engineering: Theory and PracticeNonlinear DynamicsInternational Petroleum Conference & Exhibition of MexicoVibration Analysis of Non-uniform Beams Using the Differential Quadrature MethodApplication of Differential Quadrature Method to the Analysis of Delamination Buckling of Laminated CompositesMechanical Vibration: Where Do We Stand?Scientific and Technical Aerospace ReportsA New Differential Quadrature Method Based on Bernstein PolynomialsA Primer on Radial Basis Functions with Applications to the GeosciencesMechanics of laminated Composite doubly-curvel shell structuresProceedings of the Sixth International Colloguium on Differential Equations
1,426 citations
TL;DR: The concept of functionally graded materials (FGMs) was proposed in 1984 by materials scientists in the Sendai area as a means of preparing thermal barrier materials as discussed by the authors, which results in gradients in such properties as mechanical strength and thermal conductivity.
Abstract: The concept of functionally graded materials (FGMs) was proposed in 1984 by materials scientists in the Sendai area as a means of preparing thermal barrier materials. Continuous changes in the composition, microstructure, porosity, etc. of these materials results in gradients in such properties as mechanical strength and thermal conductivity. In 1987, a national project was initiated entitled ‘Research on the Basic Technology for the Development of Functionally Gradient Materials for Relaxation of Thermal Stress’. In 1992 when the project was finished, samples of 300 mm square shell and 50 mm diameter hemispherical bowls for SiC-C FGM nose cones were prepared. The concept of FGMs is of interest not only in the practical design of super refractory materials, but also in the development of various functional materials. In 1993, the second national project was initiated for the research and development of FGMs as functional materials; ‘Research on Energy Conversion Materials with Functionally Gradient Structure’. This program aims to apply functionally graded structure technology to the improvement of energy conversion efficiency. The project will continue until the fiscal year 1997.
1,313 citations
1,113 citations
TL;DR: In this article, a simple approach is presented to solve natural frequencies of free vibration of axially functionally graded beams with non-uniform cross-section for various end supports including simply supported, clamped, and free ends.
285 citations
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.
Abstract: The method of Frobenius is used to solve for the exact frequencies and mode shapes for rotating beams in which both the flexural rigidity and the mass distribution vary linearly. Results are tabulated for a variety of situations including uniform and tapered beams, with root offset and tip mass, and for both hinged root and fixed root boundary conditions. The results obtained for the case of the uniform cantilever beam are compared with other solutions, and the results of a conventional finite-element code.
264 citations