A Mechanical-Based Solution for Axially Functionally Graded Tapered Euler-Bernoulli Beams
10 May 2013-Mechanics of Advanced Materials and Structures (Taylor & Francis Group)-Vol. 20, Iss: 8, pp 696-707
TL;DR: In this paper, structural analysis of axially functionally graded tapered beams is studied from a mechanical point of view using a finite element method using the concept of basic displacement functions (BDFs).
Abstract: In this article, structural analysis of axially functionally graded tapered beams is studied from a mechanical point of view using a finite element method. Introducing the concept of basic displacement functions (BDFs), it is shown that exact shape functions could be explicitly obtained in terms of BDFs via application of basic principles of structural mechanics. BDFs are obtained using the unit-dummy-load method. Carrying out static analysis, it is verified that exact results are provided by applying one or a few elements. The competency of the present element in stability and free vibration analyses is verified through several numerical examples.
Citations
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TL;DR: In this article, the transverse vibration of a rotary tapered axially functionally graded (AFG) Euler-Bernoulli microbeam is studied based on the modified couple stress theory by considering the axial forces which are due to the rotation, in the form of true spatial variation.
94 citations
TL;DR: In this paper, the size dependent vibration behavior of a rotating non-uniform functionally graded (FG) Timoshenko and Euler-Bernoulli microbeam based on the modified couple stress theory is investigated.
76 citations
TL;DR: In this article, a new approach based on Chebyshev polynomials theory is introduced to analyze free vibration of axially functionally graded Euler-Bernoulli and Timoshenko beams with non-uniform cross-sections.
63 citations
TL;DR: In this article, large amplitude free vibration analysis is carried out on axially functionally graded (AFG) tapered slender beams under different boundary conditions, and the problem is addressed in two parts.
58 citations
TL;DR: In this article, the authors analyze transient analysis of axially functionally graded (AFG) Timoshenko beams with variable cross-section and apply complementary functions method to solve the differential equations in Laplace domain.
Abstract: The present study goals to analyze transient analysis of axially functionally graded (AFG) Timoshenko beams with variable cross-section. Both the materials and geometrical properties of the AFG tapered beam varying along the longitudinal direction. In the analysis, the influences of rotary inertia and shear deformation are taken into account. Complementary functions method (CFM) is applied to solve the differential equations in Laplace domain. By using the modified Durbin's algorithm, the results are transformed to the time domain. For the verification of the recommended method, numerous problems which were solved in the literature are handled with the developed method and benchmarked with the findings in the literature.
52 citations
References
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TL;DR: In this article, a unified approach for analyzing the static and dynamic behaviors of functionally graded beams (FGB) with the rotary inertia and shear deformation included is presented, where all material properties are arbitrary functions along the beam thickness.
450 citations
TL;DR: In this article, the free vibration of simply supported FG beam was investigated and the governing equations were found by applying Hamilton's principle, and different higher order shear deformation theories and classical beam theories were used in the analysis.
445 citations
01 Jan 2008
TL;DR: In this article, a beam theory different from the traditional first-order shear deformation beam theory is used to analyze free vibration of functionally graded beams, where the beam properties are varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents.
Abstract: Abstract A new beam theory different from the traditional first-order shear deformation beam theory is used to analyze free vibration of functionally graded beams. The beam properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. It is assumed that the lateral normal stress of the beam is zero and the governing equations of motion are derived using Hamilton’s principle. Resulting system of ordinary differential equations of free vibration analysis is solved using an analytical method. Different boundary conditions are considered and comparisons are made among different beam theories. Also, the effects of boundary conditions, volume fraction and shear deformation on natural frequencies and mode shapes are investigated.
347 citations
TL;DR: In this paper, a beam theory different from the traditional first-order shear deformation beam theory is used to analyze free vibration of functionally graded beams, where the beam properties are varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents.
312 citations