Bending solutions of FGM Timoshenko beams from those of the homogenous Euler–Bernoulli beams

Liu, Shirong; Cao, Dafu; Wan, Ze-Qing

doi:10.1016/j.apm.2013.02.047

Cited by 49 publications

(21 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The static, dynamic and buckling response of FGM straight beams with material properties smoothly varying in the thickness direction has been extensively analyzed; e.g. see [9][10][11][12][13][14].…”

Section: General Audience Abstractmentioning

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

View full text Add to dashboard Cite

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

show abstract

Section: General Audience Abstractmentioning

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

View full text Add to dashboard Cite

show abstract

“…Because the characteristics of FGMs change continuously in the gradient direction, their fatigue properties are improved [1]. Extensive research works on FGM structures have been undertaken because of the wide range of applications of FGMs [2][3][4][5][6][7][8][9]. Benatta et al [2] investigated the static bending problem of composite beams composed of various fibers using analytical methods.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis for Cracked FGM Beams by Means of a Continuous Beam Model

Yang

Zhao

2015

Shock and Vibration

View full text Add to dashboard Cite

Based on Euler-Bernoulli beam theory and a continuous stiffness beam model, the free vibration of rectangular-section beams made of functionally graded materials (FGMs) containing open edge cracks is studied. Assuming the material gradients follow exponential distribution along beam thickness direction, the conversion relation between the vibration governing equations of a FGM beam and that of an isotropic homogenous beam is deduced. A continuous function is used to characterize the bending stiffness of an edge cracked FGM beam. Thus, the cracked FGM beam is treated as an intact beam with continuously varying bending stiffness along its longitudinal direction. The characteristic equations of beams with different boundary conditions are obtained by transfer matrix method. To verify the validity of the proposed method, natural frequencies for intact and cracked FGM beams are calculated and compared with those obtained by three-dimensional finite element method (3D FEM) and available data in the literature. After that, further discussions are carried out to analyze the influences of crack depth, crack location, material property, and slenderness ratio on the natural frequencies of the cracked FGM beams.

show abstract

“…The determination of the shear correction factor is investigated in [10] for various gradation laws. The static bending solutions of the FGM Timoshenko Beams are obtained analytically in terms of the homogeneous Euler Bernoulli beams by using mathematical similarity and load equivalence between the governing equations [11]. The static behaviour of the FGBs are also studied by using the quasi-3D theory to show the effects of shear deformation and thickness stretching on the displacement and stresses [12].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Bending Deflections of Functionally Graded Beams by Using Different Beam Theories and Symmetric Smoothed Particle Hydrodynamics

Karamanlı

2016

International Journal of Engineering Technologies IJET

View full text Add to dashboard Cite

Bending solutions of FGM Timoshenko beams from those of the homogenous Euler–Bernoulli beams

Cited by 49 publications

References 19 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 for Cracked FGM Beams by Means of a Continuous Beam Model

Analysis of Bending Deflections of Functionally Graded Beams by Using Different Beam Theories and Symmetric Smoothed Particle Hydrodynamics

Contact Info

Product

Resources

About