A single layer shear deformation plate theory with superposed shape functions for laminated compo... more A single layer shear deformation plate theory with superposed shape functions for laminated composite plates has been proposed. Some of the previously developed, five degrees of freedom shear deformation theories, including parabolic [1], hyperbolic [2], exponential [3] and trigonometric [4] plate theories have been superposed by applying different theories in the different in-plane directions of the composite plate. Statics and dynamics of composite plate problems have been investigated. It was obtained that using different shape functions in the different in-plane directions may decrease the percentage error of stress and deflection. Present hyperbolic-exponential and parabolic-exponential theories predict stiffer properties (give lower bending and stress values, and higher frequency, and buckling loads when compared to the 3-D elasticity). Some improvements were determined for y-z component of the transverse shear stress using hyperbolic-exponential and parabolic-exponential theories for symmetric cross-ply composite plates when compared to available single shape function plate models. Global behaviours (vibration frequency and critical buckling loads) are predicted within %5 accuracy similar to plate theories with single shape functions.
Abstract This paper is focused on the static and the dynamic behaviour of an axial lattice (with ... more Abstract This paper is focused on the static and the dynamic behaviour of an axial lattice (with direct neighbouring interaction) loaded by some distributed forces and in interaction with an elastic medium. Some exact analytical solutions are provided both in static and in dynamic settings, for the finite lattice system under general boundary conditions including fixed- and free-end boundary conditions. A nonlocal rod model based on the introduction of one additional length scale, is then constructed by continualization scheme of the lattice difference equations, to capture the scale effects associated with the lattice spacing. The continualized nonlocal model coincides with a phenomenological Eringen's nonlocal model, except eventually for the boundary conditions. These new continualized nonlocal boundary conditions are derived from the end lattice boundary conditions. The enriched nonlocal wave equation augmented by the elastic medium interaction has a spatial derivative which coincides with the local wave equation, thus avoiding the need of higher-order boundary conditions. The static and the dynamic responses of the equivalent nonlocal bar are also analytically studied and compared to the lattice problem. It is shown that the nonlocal solution efficiently fits the lattice one, both in static and in dynamic settings. The nonlocal model can be also introduced from variational arguments, thus leading to a nonlocal optimal Rayleigh quotient. For very high frequencies, the nonlocal model is corrected by a two-length scale model, which is shown to capture efficiently the frequency spectra of the lattice model for all frequency range.
The absorption (L) of the wave in the ionosphere has been calculated. The 5.47 MHz wave is transm... more The absorption (L) of the wave in the ionosphere has been calculated. The 5.47 MHz wave is transmitted from Erciş, Turkey (39.03 • N, 43.37 • E) and received at Elazıg, Turkey (38.70 • N, 39.20 • E). The field strength of this wave is measured by ITU-Compliant HF Field Strength Monitoring Terminal, and the absorption L in the ionosphere has been calculated. It is observed that the field strength of the wave is least around noon time and it increases at night times at all seasons. The diurnal and seasonal variations of the calculated absorption L shows that the maximum absorption in the wave occurs around noon time. The behaviour of the diurnal and seasonal variations of the field strength of the wave can be explained with the diurnal and seasonal variations of the calculated absorption L in the ionosphere. Equation (22) in this paper can be used to obtain the imaginary part (β) of the refractive index of the ionospheric plasma, and it can be applied to the HF radio waves propagations in the ionosphere for absorption L.
Carbon nanotubes may hold scientific promise in nanotechnology as nanopipes conveying fluid. In t... more Carbon nanotubes may hold scientific promise in nanotechnology as nanopipes conveying fluid. In this paper, the wave propagation in double-walled carbon nanotubes (DWCNTs) conveying fluid is studied based on the Euler–Bernoulli beam theory. The influences of internal moving fluids, such as flow velocity and mass density of fluids, on the sound wave propagation of DWCNTs or the DWCNTs embedded in an elastic matrix are investigated in detail. The DWCNTs are considered as a two-shell model coupled together through the van der Waals interaction between two adjacent nanotubes. According to the proposed theoretical approach, the results indicate that fluid flow through carbon nanotubes affects the wave speed and the critical frequency in the carbon nanotubes. The amplitude ratios of the inner to outer nanotubes are largely affected by the fluid velocity and density when the vibrational frequency in nanotubes is larger than 1.5 Hz. The theoretical investigation may give a useful reference ...
Abstract In this study, the effect of size and fraction of SiCp on compressive behavior of compos... more Abstract In this study, the effect of size and fraction of SiCp on compressive behavior of composite metal foam were investigated. Compare to the same relative density of composite foam, plateau stress and energy absorption increased with increasing fraction of SiCp. ...
The mechanics of a laminated composite beam attached to inside of a rotating rim and directed to ... more The mechanics of a laminated composite beam attached to inside of a rotating rim and directed to the inward direction is investigated. The Ritz method is utilized in the solution of the problem. Simple algebraic polynomials are used in the displacement field. Clamped-free boundary conditions are considered. First, Reddy (third order) and classical beam theories are used in the formulation. Cross-ply lamination configurations are considered. Effects of rotation speed, hub ratio, orthotropy ratio, beam theory and length to thickness ratio are analyzed in detail. Mode shapes of composite rotating beams are given. It is obtained that composite beams may buckle due to compressive centrifugal force for the some combinations of rotation speed and hub ratio.
The free vibration of a rotating laminated composite beam with an attached point mass is investig... more The free vibration of a rotating laminated composite beam with an attached point mass is investigated. The Ritz method with algebraic polynomials is used in the formulation. The boundary conditions are considered as clamped-free. Different shear deformation theories (first order and third order) and classical beam theories are used in the formulation. Cross-ply lamination configurations are considered. Effects of the ratio of attached mass to the beam mass, rotation speed, hub ratio, orthotropy ratio, position of attached mass, beam theory and length to thickness ratio are analyzed in detail. Some typical mode shapes are presented in order to illustrate the effects of the attached mass.
The torsional vibration analysis of double carbon nanotube system (CNT system) is carried out in ... more The torsional vibration analysis of double carbon nanotube system (CNT system) is carried out in the present work. Carbon nanotubes are connected to each other with elastic matrix material. Eringen's Nonlocal Elasticity Theory is used in modeling of the system. The effects of nonlocal parameter and stiffness of elastic medium to the non-dimensional frequencies of the system are investigated in detail. Two frequency set are obtained for double carbon nanotube system for a given half wave number. It is also shown that some mode shapes are anti-phase and some of them are in-phase. The present results can be useful in design of nanoelectromechanical systems like rotary servomotors.
Turkish Journal of Engineering and Environmental Sciences, May 1, 2007
To determine the cardiovascular risk (CVR) in patients with rheumatoid arthritis (RA) and its cor... more To determine the cardiovascular risk (CVR) in patients with rheumatoid arthritis (RA) and its correlation with disease activity and functional ability by using the Framingham risk score (FRS) and to compare the CVR of the RA patients with the control group with the help of the FRS. Materials and methods: Seventy-four RA patients, who were in conformity with the criteria of the American College of Rheumatology, were included in this study at Bezmialem Vakıf University Hospital. A total of 39 subjects without inflammatory arthritis were included as the control group. The FRS was calculated by evaluating age, smoking habits, diabetes, cholesterol and blood pressure measurements. The disease activity score-28 (DAS-28) and the health assessment questionnaire (HAQ-DI) were applied to the RA patients. Results: We could not find any significant difference between the case and control groups in terms of FRS. The means of erythrocyte sedimentation rate (ESR) and blood pressure of participants in the study group were significantly higher than those of the control group. There was not any significant difference in terms of C-reactive protein (CRP) and cholesterol levels between the groups. DAS-28, HAQ-DI, CRP, ESR, and disease duration were not significantly correlated with FRS. Conclusion: For patients who have inflammatory arthritis, new risk score calculation that consists of other disease-specific risk factors, in addition to traditional ones, is needed.
Journal of Reinforced Plastics and Composites, Oct 1, 2006
The free vibrations of angle-ply laminated cylindrical shells are studied numerically and experim... more The free vibrations of angle-ply laminated cylindrical shells are studied numerically and experimentally. The material of the cylindrical shell is a carbon fiber reinforced plastic (CFRP). First, the material properties for the lamina of the cylindrical shell are measured. Secondly, using the measured material properties of the lamina, the natural frequencies and mode shapes of the angle-ply laminated cylindrical shells with clamped edges are computed by the finite element method (FEM). Finally, the vibration tests of the angle-ply laminated cylindrical shells with clamped edges are carried out. By applying the experimental modal analysis technique, natural frequencies and mode shapes of the shells are obtained. From the comparison between experimental and numerical results, one can see the good agreement between these results. Furthermore, the effects of length of the angle-ply laminated cylindrical shells with clamped edges on the natural frequencies and mode shapes are investigated numerically and experimentally. An approximate frequency equation for the shell's length is proposed.
Mechanics of Advanced Materials and Structures, Sep 29, 2015
In this study, vibration of symmetrically laminated composite plates with attached mass is studie... more In this study, vibration of symmetrically laminated composite plates with attached mass is studied. The Ritz method with algebraic polynomial displacement field is used. The plates with at least two adjacent free edges are considered in the formulations. The effect of various parameters (material, number of layers, ratio of attached mass to the plate mass, position of attached mass, fiber orientation) upon the frequencies is investigated.
Dynamic response of a cylindrical tube surrounded by an unbounded elastic medium due to plane har... more Dynamic response of a cylindrical tube surrounded by an unbounded elastic medium due to plane harmonic SH-Waves is studied. A two-dimensional mathematical model is considered. Cylindrical coordinates are used for convenience. The surrounding medium is assumed to be homogeneous, isotropic and linear elastic. The tube is assumed to be made of linear elastic Functionally Graded Materials (FGMs) such that shear modulus and shear wave velocity are assumed to change linearly from inner surface to outer surface. Material properties are constant along circumferential direction. It is assumed that the inner surface of the tube is traction-free and there is a welded contact between the tube and the surrounding medium. Governing equations are slightly different in the tube region and the unbounded region. Both of the governing equations are solved by applying Finite Fourier Transform in circumferential direction. The exact solution series are presented in terms of Fourier-Bessel series in the unbounded region and power series in the tube region. The presented numerical results show that when the incoming wave lengths decrease, shear stresses at the tube increase significantly. It was shown that for the shorter incoming wave lengths, tubes made of FGMs are subjected to smaller shear stresses compared to the tubes homogeneously made of outer surface material of the FG cases.
Abstract In the present study, vibration of rotating composite beams is studied. Different beam t... more Abstract In the present study, vibration of rotating composite beams is studied. Different beam theories are used in the formulation including Euler–Bernoulli, Timoshenko and Reddy beam theories. Ritz method is used in the solution of the problem. Simple polynomials are chosen for the displacement field. The continuity of transverse stresses is satisfied among the layers. Results are obtained for different orthotropy ratios, rotation speed, hub ratio, length to thickness ratio of the rotating composite beam and different boundary conditions.
Mechanics Based Design of Structures and Machines, Jun 18, 2019
Abstract Since the two-directional functionally graded (2D-FG) materials can satisfy the new requ... more Abstract Since the two-directional functionally graded (2D-FG) materials can satisfy the new requirements raised based on the elimination of the stress concentration, delamination and cracking problems accompanying with the low cost and lightweight on the structures without sacrificing the stiffness and strength, the structural analyses of these structures become more important than ever. Moreover, the usage of the micro-electromechanical systems composed of 2D-FG materials has been increasing in automotive, military, space, biomedical, and nuclear energy industries. Within this study, the free vibration and buckling behaviors of 2D-FG porous microbeams are investigated based on the modified couple stress theory by employing a transverse shear-normal deformation beam theory and using finite element method. The effects of the thickness to material length scale parameter (MLSP) accompanying with the micro-porosity volume fraction ratio, boundary condition, aspect ratio, and gradient index on the dimensionless fundamental frequencies and dimensionless critical buckling loads of the 2D-FG porous microbeams are investigated. Moreover, with assumption of the variable material length scale parameters (VMLSP), the computed results are compared with ones obtained by employing constant MLSP. It is found that VMLSP increases the stiffness of the 2D-FG porous microbeams and effects the free vibration and buckling responses of these structures.
This paper is dedicated to study the elastic buckling behavior of isotropic, laminated composite ... more This paper is dedicated to study the elastic buckling behavior of isotropic, laminated composite and sandwich beams subjected to various axially varying in-plane loads and boundary conditions (BCs). The formulation of the problem is derived by using the Ritz method with the displacement field based on a shear and normal deformable beam theory (SNDBT). Polynomial functions are employed to present the displacement field. The convergence studies are performed and then obtained results are compared with those of reported works. Results from extensive analysis are presented for different BCs, aspect ratios, orthotropy ratios, fiber angles and loading conditions. It is observed that the type of the axially variable in-plane load significantly affects the critical buckling loads and mode shapes of the beams depending on the BCs. The normal deformation effect depends on not only the aspect ratio but also BCs and the fiber orientation angles.
This paper presents free vibration of composite beams under axial load using a four-unknown shear... more This paper presents free vibration of composite beams under axial load using a four-unknown shear and normal deformation theory. The constitutive equation is reduced from the 3D stress-strain relations of orthotropic lamina. The governing differential equations of motion are derived using the Hamilton's principle. A two-node C 1 beam element is developed by using a mixed interpolation with linear and Hermite-cubic polynomials for unknown variables. Numerical results are computed and compared with those available in the literature and commercial finite element software (ANSYS and ABAQUS). The comparison study illustrates the effects of normal strain, lay-ups and Poisson's ratio on the natural frequencies and load-frequency curves of composite beams.
In the present study, buckling of eccentrically loaded nanobeams in which the load is not applied... more In the present study, buckling of eccentrically loaded nanobeams in which the load is not applied at the centroid of cross section, has been studied. Eringen’s Nonlocal Elasticity Theory has been used in the formulation of governing equation of motion of the nanobeam. Simply supported and free boundary conditions for nanobeam have been taken consideration. The effect of nonlocal parameter, eccentricity of the load, nanobeam length on the buckling deflection and critical buckling load on nanobeam have been investigated. Present results can be useful in the design of nano-structures.
A single layer shear deformation plate theory with superposed shape functions for laminated compo... more A single layer shear deformation plate theory with superposed shape functions for laminated composite plates has been proposed. Some of the previously developed, five degrees of freedom shear deformation theories, including parabolic [1], hyperbolic [2], exponential [3] and trigonometric [4] plate theories have been superposed by applying different theories in the different in-plane directions of the composite plate. Statics and dynamics of composite plate problems have been investigated. It was obtained that using different shape functions in the different in-plane directions may decrease the percentage error of stress and deflection. Present hyperbolic-exponential and parabolic-exponential theories predict stiffer properties (give lower bending and stress values, and higher frequency, and buckling loads when compared to the 3-D elasticity). Some improvements were determined for y-z component of the transverse shear stress using hyperbolic-exponential and parabolic-exponential theories for symmetric cross-ply composite plates when compared to available single shape function plate models. Global behaviours (vibration frequency and critical buckling loads) are predicted within %5 accuracy similar to plate theories with single shape functions.
Abstract This paper is focused on the static and the dynamic behaviour of an axial lattice (with ... more Abstract This paper is focused on the static and the dynamic behaviour of an axial lattice (with direct neighbouring interaction) loaded by some distributed forces and in interaction with an elastic medium. Some exact analytical solutions are provided both in static and in dynamic settings, for the finite lattice system under general boundary conditions including fixed- and free-end boundary conditions. A nonlocal rod model based on the introduction of one additional length scale, is then constructed by continualization scheme of the lattice difference equations, to capture the scale effects associated with the lattice spacing. The continualized nonlocal model coincides with a phenomenological Eringen's nonlocal model, except eventually for the boundary conditions. These new continualized nonlocal boundary conditions are derived from the end lattice boundary conditions. The enriched nonlocal wave equation augmented by the elastic medium interaction has a spatial derivative which coincides with the local wave equation, thus avoiding the need of higher-order boundary conditions. The static and the dynamic responses of the equivalent nonlocal bar are also analytically studied and compared to the lattice problem. It is shown that the nonlocal solution efficiently fits the lattice one, both in static and in dynamic settings. The nonlocal model can be also introduced from variational arguments, thus leading to a nonlocal optimal Rayleigh quotient. For very high frequencies, the nonlocal model is corrected by a two-length scale model, which is shown to capture efficiently the frequency spectra of the lattice model for all frequency range.
The absorption (L) of the wave in the ionosphere has been calculated. The 5.47 MHz wave is transm... more The absorption (L) of the wave in the ionosphere has been calculated. The 5.47 MHz wave is transmitted from Erciş, Turkey (39.03 • N, 43.37 • E) and received at Elazıg, Turkey (38.70 • N, 39.20 • E). The field strength of this wave is measured by ITU-Compliant HF Field Strength Monitoring Terminal, and the absorption L in the ionosphere has been calculated. It is observed that the field strength of the wave is least around noon time and it increases at night times at all seasons. The diurnal and seasonal variations of the calculated absorption L shows that the maximum absorption in the wave occurs around noon time. The behaviour of the diurnal and seasonal variations of the field strength of the wave can be explained with the diurnal and seasonal variations of the calculated absorption L in the ionosphere. Equation (22) in this paper can be used to obtain the imaginary part (β) of the refractive index of the ionospheric plasma, and it can be applied to the HF radio waves propagations in the ionosphere for absorption L.
Carbon nanotubes may hold scientific promise in nanotechnology as nanopipes conveying fluid. In t... more Carbon nanotubes may hold scientific promise in nanotechnology as nanopipes conveying fluid. In this paper, the wave propagation in double-walled carbon nanotubes (DWCNTs) conveying fluid is studied based on the Euler–Bernoulli beam theory. The influences of internal moving fluids, such as flow velocity and mass density of fluids, on the sound wave propagation of DWCNTs or the DWCNTs embedded in an elastic matrix are investigated in detail. The DWCNTs are considered as a two-shell model coupled together through the van der Waals interaction between two adjacent nanotubes. According to the proposed theoretical approach, the results indicate that fluid flow through carbon nanotubes affects the wave speed and the critical frequency in the carbon nanotubes. The amplitude ratios of the inner to outer nanotubes are largely affected by the fluid velocity and density when the vibrational frequency in nanotubes is larger than 1.5 Hz. The theoretical investigation may give a useful reference ...
Abstract In this study, the effect of size and fraction of SiCp on compressive behavior of compos... more Abstract In this study, the effect of size and fraction of SiCp on compressive behavior of composite metal foam were investigated. Compare to the same relative density of composite foam, plateau stress and energy absorption increased with increasing fraction of SiCp. ...
The mechanics of a laminated composite beam attached to inside of a rotating rim and directed to ... more The mechanics of a laminated composite beam attached to inside of a rotating rim and directed to the inward direction is investigated. The Ritz method is utilized in the solution of the problem. Simple algebraic polynomials are used in the displacement field. Clamped-free boundary conditions are considered. First, Reddy (third order) and classical beam theories are used in the formulation. Cross-ply lamination configurations are considered. Effects of rotation speed, hub ratio, orthotropy ratio, beam theory and length to thickness ratio are analyzed in detail. Mode shapes of composite rotating beams are given. It is obtained that composite beams may buckle due to compressive centrifugal force for the some combinations of rotation speed and hub ratio.
The free vibration of a rotating laminated composite beam with an attached point mass is investig... more The free vibration of a rotating laminated composite beam with an attached point mass is investigated. The Ritz method with algebraic polynomials is used in the formulation. The boundary conditions are considered as clamped-free. Different shear deformation theories (first order and third order) and classical beam theories are used in the formulation. Cross-ply lamination configurations are considered. Effects of the ratio of attached mass to the beam mass, rotation speed, hub ratio, orthotropy ratio, position of attached mass, beam theory and length to thickness ratio are analyzed in detail. Some typical mode shapes are presented in order to illustrate the effects of the attached mass.
The torsional vibration analysis of double carbon nanotube system (CNT system) is carried out in ... more The torsional vibration analysis of double carbon nanotube system (CNT system) is carried out in the present work. Carbon nanotubes are connected to each other with elastic matrix material. Eringen's Nonlocal Elasticity Theory is used in modeling of the system. The effects of nonlocal parameter and stiffness of elastic medium to the non-dimensional frequencies of the system are investigated in detail. Two frequency set are obtained for double carbon nanotube system for a given half wave number. It is also shown that some mode shapes are anti-phase and some of them are in-phase. The present results can be useful in design of nanoelectromechanical systems like rotary servomotors.
Turkish Journal of Engineering and Environmental Sciences, May 1, 2007
To determine the cardiovascular risk (CVR) in patients with rheumatoid arthritis (RA) and its cor... more To determine the cardiovascular risk (CVR) in patients with rheumatoid arthritis (RA) and its correlation with disease activity and functional ability by using the Framingham risk score (FRS) and to compare the CVR of the RA patients with the control group with the help of the FRS. Materials and methods: Seventy-four RA patients, who were in conformity with the criteria of the American College of Rheumatology, were included in this study at Bezmialem Vakıf University Hospital. A total of 39 subjects without inflammatory arthritis were included as the control group. The FRS was calculated by evaluating age, smoking habits, diabetes, cholesterol and blood pressure measurements. The disease activity score-28 (DAS-28) and the health assessment questionnaire (HAQ-DI) were applied to the RA patients. Results: We could not find any significant difference between the case and control groups in terms of FRS. The means of erythrocyte sedimentation rate (ESR) and blood pressure of participants in the study group were significantly higher than those of the control group. There was not any significant difference in terms of C-reactive protein (CRP) and cholesterol levels between the groups. DAS-28, HAQ-DI, CRP, ESR, and disease duration were not significantly correlated with FRS. Conclusion: For patients who have inflammatory arthritis, new risk score calculation that consists of other disease-specific risk factors, in addition to traditional ones, is needed.
Journal of Reinforced Plastics and Composites, Oct 1, 2006
The free vibrations of angle-ply laminated cylindrical shells are studied numerically and experim... more The free vibrations of angle-ply laminated cylindrical shells are studied numerically and experimentally. The material of the cylindrical shell is a carbon fiber reinforced plastic (CFRP). First, the material properties for the lamina of the cylindrical shell are measured. Secondly, using the measured material properties of the lamina, the natural frequencies and mode shapes of the angle-ply laminated cylindrical shells with clamped edges are computed by the finite element method (FEM). Finally, the vibration tests of the angle-ply laminated cylindrical shells with clamped edges are carried out. By applying the experimental modal analysis technique, natural frequencies and mode shapes of the shells are obtained. From the comparison between experimental and numerical results, one can see the good agreement between these results. Furthermore, the effects of length of the angle-ply laminated cylindrical shells with clamped edges on the natural frequencies and mode shapes are investigated numerically and experimentally. An approximate frequency equation for the shell's length is proposed.
Mechanics of Advanced Materials and Structures, Sep 29, 2015
In this study, vibration of symmetrically laminated composite plates with attached mass is studie... more In this study, vibration of symmetrically laminated composite plates with attached mass is studied. The Ritz method with algebraic polynomial displacement field is used. The plates with at least two adjacent free edges are considered in the formulations. The effect of various parameters (material, number of layers, ratio of attached mass to the plate mass, position of attached mass, fiber orientation) upon the frequencies is investigated.
Dynamic response of a cylindrical tube surrounded by an unbounded elastic medium due to plane har... more Dynamic response of a cylindrical tube surrounded by an unbounded elastic medium due to plane harmonic SH-Waves is studied. A two-dimensional mathematical model is considered. Cylindrical coordinates are used for convenience. The surrounding medium is assumed to be homogeneous, isotropic and linear elastic. The tube is assumed to be made of linear elastic Functionally Graded Materials (FGMs) such that shear modulus and shear wave velocity are assumed to change linearly from inner surface to outer surface. Material properties are constant along circumferential direction. It is assumed that the inner surface of the tube is traction-free and there is a welded contact between the tube and the surrounding medium. Governing equations are slightly different in the tube region and the unbounded region. Both of the governing equations are solved by applying Finite Fourier Transform in circumferential direction. The exact solution series are presented in terms of Fourier-Bessel series in the unbounded region and power series in the tube region. The presented numerical results show that when the incoming wave lengths decrease, shear stresses at the tube increase significantly. It was shown that for the shorter incoming wave lengths, tubes made of FGMs are subjected to smaller shear stresses compared to the tubes homogeneously made of outer surface material of the FG cases.
Abstract In the present study, vibration of rotating composite beams is studied. Different beam t... more Abstract In the present study, vibration of rotating composite beams is studied. Different beam theories are used in the formulation including Euler–Bernoulli, Timoshenko and Reddy beam theories. Ritz method is used in the solution of the problem. Simple polynomials are chosen for the displacement field. The continuity of transverse stresses is satisfied among the layers. Results are obtained for different orthotropy ratios, rotation speed, hub ratio, length to thickness ratio of the rotating composite beam and different boundary conditions.
Mechanics Based Design of Structures and Machines, Jun 18, 2019
Abstract Since the two-directional functionally graded (2D-FG) materials can satisfy the new requ... more Abstract Since the two-directional functionally graded (2D-FG) materials can satisfy the new requirements raised based on the elimination of the stress concentration, delamination and cracking problems accompanying with the low cost and lightweight on the structures without sacrificing the stiffness and strength, the structural analyses of these structures become more important than ever. Moreover, the usage of the micro-electromechanical systems composed of 2D-FG materials has been increasing in automotive, military, space, biomedical, and nuclear energy industries. Within this study, the free vibration and buckling behaviors of 2D-FG porous microbeams are investigated based on the modified couple stress theory by employing a transverse shear-normal deformation beam theory and using finite element method. The effects of the thickness to material length scale parameter (MLSP) accompanying with the micro-porosity volume fraction ratio, boundary condition, aspect ratio, and gradient index on the dimensionless fundamental frequencies and dimensionless critical buckling loads of the 2D-FG porous microbeams are investigated. Moreover, with assumption of the variable material length scale parameters (VMLSP), the computed results are compared with ones obtained by employing constant MLSP. It is found that VMLSP increases the stiffness of the 2D-FG porous microbeams and effects the free vibration and buckling responses of these structures.
This paper is dedicated to study the elastic buckling behavior of isotropic, laminated composite ... more This paper is dedicated to study the elastic buckling behavior of isotropic, laminated composite and sandwich beams subjected to various axially varying in-plane loads and boundary conditions (BCs). The formulation of the problem is derived by using the Ritz method with the displacement field based on a shear and normal deformable beam theory (SNDBT). Polynomial functions are employed to present the displacement field. The convergence studies are performed and then obtained results are compared with those of reported works. Results from extensive analysis are presented for different BCs, aspect ratios, orthotropy ratios, fiber angles and loading conditions. It is observed that the type of the axially variable in-plane load significantly affects the critical buckling loads and mode shapes of the beams depending on the BCs. The normal deformation effect depends on not only the aspect ratio but also BCs and the fiber orientation angles.
This paper presents free vibration of composite beams under axial load using a four-unknown shear... more This paper presents free vibration of composite beams under axial load using a four-unknown shear and normal deformation theory. The constitutive equation is reduced from the 3D stress-strain relations of orthotropic lamina. The governing differential equations of motion are derived using the Hamilton's principle. A two-node C 1 beam element is developed by using a mixed interpolation with linear and Hermite-cubic polynomials for unknown variables. Numerical results are computed and compared with those available in the literature and commercial finite element software (ANSYS and ABAQUS). The comparison study illustrates the effects of normal strain, lay-ups and Poisson's ratio on the natural frequencies and load-frequency curves of composite beams.
In the present study, buckling of eccentrically loaded nanobeams in which the load is not applied... more In the present study, buckling of eccentrically loaded nanobeams in which the load is not applied at the centroid of cross section, has been studied. Eringen’s Nonlocal Elasticity Theory has been used in the formulation of governing equation of motion of the nanobeam. Simply supported and free boundary conditions for nanobeam have been taken consideration. The effect of nonlocal parameter, eccentricity of the load, nanobeam length on the buckling deflection and critical buckling load on nanobeam have been investigated. Present results can be useful in the design of nano-structures.
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Papers by Metin Aydogdu