Metin Aydogdu

Semi-inverse Method for Vibration and Buckling of Axially Functionally Graded Beams

In this study, vibration and buckling of axially functionally graded simply supported beams is analyzed by using the semi-inverse method. Euler—Bernoulli beam theory was used in the analysis. By using a pre-specified frequency and buckling loads, variation of the Youngs modulus in the axial direction is obtained in terms of the axial coordinate. It is found that the Youngs modulus changes exponentially between the edges of the beam for the vibration and buckling problem.

Three-Dimensional Vibration Analyses of Functionally Graded Plates under Various Boundary Conditions

Three-dimensional vibration solutions are presented for rectangular functionally graded plates with different boundary conditions, based on the small strain linear elasticity theory. The material properties are assumed to vary as a power form of the thickness coordinate. The Ritz method with Chebyshev displacement functions is used to solve the vibration problem of functionally graded plates. The convergence and comparison studies demonstrate the accuracy and correctness of the present method. The effects of aspect and thickness ratios, and gradient index, on the free vibration frequencies are investigated. Some results are given in the form of tables and figures, which can serve as the benchmark for further research.

Free Vibration Analysis of Angle-ply Laminated Beams with General Boundary Conditions

In this study, vibration analysis of angle-ply laminated beams subjected to different sets of boundary conditions is investigated. The analysis is based on a three-degrees-of-freedom shear deformable beam theory. The governing equations are obtained by means of Hamiltons principle. Six different combinations of free, clamped, and simply supported edge boundary conditions are considered. The free vibration frequencies are obtained by applying the Ritz method where the three displacement components are expressed in a series of simple algebraic polynomials. The numerical results obtained for different lay-ups are presented and compared with that available in the literature.

Comparison of Various Shear Deformation Theories for Bending, Buckling, and Vibration of Rectangular Symmetric Cross-ply Plate with Simply Supported Edges:

In the present study, unified shear deformation theory which was proposed by Soldatos, K.P. and Timarci, T. (1993). A Unified Formulation of Laminated Composite, Shear Deformable Five-degrees-of-freedom Cylindrical Shells on the Basis of a Unified Shear Deformable Shell Theory, Compos. Struct., 25(1–4): 165–171 is used to analyze simply supported symmetric cross-ply rectangular plates for deflections, stresses, natural frequencies, and buckling loads. This theory enables the selection of different in-plane displacement components to represent shear deformation. Exponential shear deformation theory, which is proposed by Karama et al., 40(6) (2003). Mechanical Behavior of Laminated Composite Beam by New Multi-layered Laminated Composite Structures Model with Transverse Shear Stress Continuity, Int J Solids Struct., 40: 1525–1546, is used for the first time to analyze the problem considered. Results which are found by exponential theory are compared with those obtained by using the parabolic shear deformation theory of Reddy, J.N., 51(4) (1984). A Simple Higher-order Theory for Laminated Composite Plates, J Appl Mech., 51: 745–752, the trigonometric shear deformation theory of Touratier, M., 29(8) (1991). An Efficient Standard Plate Theory, Int. Jnl. Engng. Sci., 29(8): 901–916, the hyperbolic shear deformation theory of Soldatos, K.P., 94(3–4) (1992). A Transverse Shear Deformation Theory for Homogeneous Monoclinic Plates, Acta Mech., 94: 1995–220 and with the available three-dimensional elasticity solutions. The study shows that while the transverse displacement and the stresses are best predicted by the exponential shear deformation theory, the parabolic shear deformation and the hyperbolic shear deformation theories yield more accurate predictions for the natural frequencies and the buckling loads.

A nonlocal rod model for axial vibration of double-walled carbon nanotubes including axial van der Waals force effects

In this study, the axial vibration of double-walled carbon nanotubes (DWCNTs) is studied using nonlocal elasticity theory. The nonlocal constitutive equations of Eringen are used in the formulations. The van der Waals forces are considered in the axial direction.An interaction coefficient is obtained in terms of the previously proposed van der Waals coefficient and effective thickness of the single-walled carbon nanotubes. The effect of various parameters like geometry of nanotubes, van der Waals forces and nonlocal parameters on the axial vibration of DWCNTs is discussed. Some mode shapes are also depicted in order to show the relative motion of the nested tubes. The van der Waals forces have strong effects on the axial vibration characteristics of DWCNTs. The present results can be used in the continuum modeling of nanoscale linear motors and oscillators.

Vibration analysis of symmetric laminated composite plates with attached mass

ABSTRACT 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 (number of layers, ratio of attached mass to the plate mass, position of attached mass, fiber orientation) upon the frequencies and mode shapes is investigated. It is found that attachment of a mass has important effects on the vibration characteristics of composite laminated plates.

ANALYSIS OF FREE TORSIONAL VIBRATION IN CARBON NANOTUBES EMBEDDED IN A VISCOELASTIC MEDIUM

Carbon Nanotubes (CNTs) have a great potential in many areas like electromechanical systems, medical application, pharmaceutical industry etc. The surrounding physical environment of CNT is very important on torsional vibration behavior of CNT. Damping and elastic effect of medium to the torsional vibration of CNTs are investigated in the present study. Governing equation of motion of nanotube is obtained using Eringen’s Nonlocal Elasticty Theory. The effects of some parameters like nonlocal parameter, stiffness parameter and nanotube length are studied in detail.

Buckling of Eccentrically Loaded Carbon Nanotubes

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 note on semi-inverse method for buckling of axially functionally graded beams

In a previous paper published in this journal, an attempt was made to study vibration and buckling analysis of axially functionally graded beams. Further studies on this subject show that an additional term needed to be included in the solution of the governing equations that lead to incorrect results. So the aim of the present study is to correct the solution of this problem.

Vibration Analysis of Inclusion Reinforced Composite Square Plates under Various Boundary Conditions

The vibration behavior of E-glass epoxy cross-ply laminated plates containing unidirectionally aligned inclusions was studied under different boundary conditions by using first-order shear deformation theory (FSDT). The effective elastic modulus of composite was expressed by using the Mori—Tanaka mean field approach for unidirectionally aligned inclusions. The governing equations were obtained by means of the Hamiltons principle and solved by using the Navier-type solution and Ritz method. The continuity of transverse shear stress between layers of the symmetric cross-ply laminated plates was satisfied by the use of the shape function incorporated into the theory. The effects of the inclusion volume fraction, the inclusion aspect ratio, and the plate span to thickness ratio on the vibration behavior of the laminated plates were studied. It was found that the dimensionless frequency increases with increasing the aspect ratio of the reinforcements and approaches asymptotically to frequency of the continuous fibers.