Free vibration analysis of two directional functionally graded beams using a third order shear deformation theory

Karamanlı, Armağan

doi:10.1016/j.compstruct.2018.01.060

Cited by 85 publications

(29 citation statements)

References 34 publications

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“…Qian and Batra [16] [18]. Karamanli [19] has analyzed free vibration of bi-directional FGM straight beams using a third order shear deformation theory in which material properties vary exponentially along the beam thickness and length.…”

Section: List Of Tablesmentioning

confidence: 99%

Free vibration of bi-directional functionally graded material circular beams using shear deformation theory employing logarithmic function of radius

Fariborz

Batra

2019

Composite Structures

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Curved beams such as arches find ubiquitous applications in civil, mechanical and aerospace engineering, e.g., stiffened floors, fuselage, railway compartments, and wind turbine blades. The analysis of free vibrations of curved structures plays a critical role in their design to avoid transient loads with dominant frequencies close to their natural frequencies. One way to increase their applications and possibly make them lighter without sacrificing strength is to comprise them of Functionally Graded Materials (FGMs) that are composites with continuously varying material properties in one or more directions. In this thesis, we study free vibrations of FGM circular beams by using a logarithmic shear deformation theory that incorporates through-the-thickness logarithmic variation of the circumferential displacement, does not require a shear correction factor, and has a parabolic through-the-thickness distribution of the shear strain. The radial displacement of a point is assumed to depend only upon its CONTENTS

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Section: List Of Tablesmentioning

confidence: 99%

Free vibration of bi-directional functionally graded material circular beams using shear deformation theory employing logarithmic function of radius

Fariborz

Batra

2019

Composite Structures

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“…The use of FG materials eliminates interlaminar stress concentration and due to its unique properties provides strength and toughness of the structure [2]. A large number of studies related to vibration characteristics of intact and cracked FG uniform beams are available [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Furthermore the studies have been extended in mechanical analysis of small-sized structures [23][24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of cracked functionally graded non-uniform beams

Shabani

Cunedioĝlu

2020

Mater. Res. Express

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This paper presents the free vibration analysis of an edge cracked non-uniform symmetric beam made of functionally graded material. The Timoshenko beam theory is used for the finite element analysis of the multi-layered sandwich beam and the cantilever beam is modeled by 50 layers of material. The material properties vary continuously along the thickness direction according to the exponential and power laws. A MATLAB code is used to find the natural frequencies of two types of non-uniform beams, having a constant height but an exponential or linear width variation along the length of the beam. The natural frequencies of the beam are verified with ANSYS software as well as with available literature and good agreement is found. In the study, the effects of different parameters such as crack location, crack depth, power-law index, geometric index and taper ratio on natural frequencies are analyzed in detail.

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“…Ş imşek [12] studied vibration of Timoshenko beam under moving forces by considering the material properties varying in both the length and thickness directions by an exponential function. Free vibration analysis of bidirectional FGM beams was investigated by Karamanli [13] using a third-order shear deformation. Hao and Wei [14] assumed an exponential variation for the material properties in both the thickness and length directions in vibration analysis of FGM beams.…”

Section: Introductionmentioning

confidence: 99%

Free vibration of bidirectional functionally graded sandwich beams using a first-order shear deformation finite element formulation

Anh¹,

Ninh

Lăng³

et al. 2020

STCE

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Free vibration of bidirectional functionally graded sandwich (BFGSW) beams is studied by using a first-order shear deformation finite element formulation. The beams consist of three layers, a homogeneous core and two functionally graded skin layers with material properties varying in both the longitudinal and thickness directions by power gradation laws. The finite element formulation with the stiffness and mass matrices evaluated explicitly is efficient, and it is capable of giving accurate frequencies by using a small number of elements. Vibration characteristics are evaluated for the beams with various boundary conditions. The effects of the power-law indexes, the layer thickness ratio, and the aspect ratio on the frequencies are investigated in detail and highlighted. The influence of the aspect ratio on the frequencies is also examined and discussed. Keywords: BFGSW beam; first-order shear deformation theory; free vibration; finite element method.

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Free vibration analysis of two directional functionally graded beams using a third order shear deformation theory

Cited by 85 publications

References 34 publications

Free vibration of bi-directional functionally graded material circular beams using shear deformation theory employing logarithmic function of radius

Free vibration of bi-directional functionally graded material circular beams using shear deformation theory employing logarithmic function of radius

Free vibration analysis of cracked functionally graded non-uniform beams

Free vibration of bidirectional functionally graded sandwich beams using a first-order shear deformation finite element formulation

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