Abstract: In this study, out-of-plane free vibrations of a circular
rods is investigated theoretically. The governing equations for
naturally twisted and curved spatial rods are obtained using
Timoshenko beam theory and rewritten for circular rods. Effects of
the axial and shear deformations are considered in the formulations.
Ordinary differential equations in scalar form are solved analytically
by using transfer matrix method. The circular rods of the mass matrix
are obtained by using straight rod of consistent mass matrix. Free
vibrations frequencies obtained by solving eigenvalue problem. A
computer program coded in MATHEMATICA language is prepared.
Circular beams are analyzed through various examples for free
vibrations analysis. Results are compared with ANSYS results based
on finite element method and available in the literature.
Abstract: The FOSDT (the First Order Shear Deformation
Theory) is taking into consideration to study the static behavior of a
bimorph beam, with a delamination zone between the upper and the
lower layer. The effect of limit conditions and lengths of the
delamination zone are presented in this paper, with a PVDF
piezoelectric material application. A FEM “Finite Element Method”
is used to discretize the beam. In the axial displacement, a
displacement field appears in the debonded zone with inverse effect
between the upper and the lower layer was observed.
Abstract: Effect of aging treatment on microstructural aspects of interfacial layers of the Cu/Al clad sheet produced by differential speed rolling (DSR) process were studied by electron back scattered diffraction (EBSD). Clad sheet of Al/Cu has been fabricated by using DSR, which caused severe shear deformation between Al and Cu plate to easily bond to each other. Rolling was carried out at 100oC with speed ratio of 2, in which the total thickness reduction was 45%. Interface layers of clad sheet were analyzed by EBSD after subsequent annealing at 400oC for 30 to 120min. With increasing annealing time, thickness of interface layer and fraction of high angle grain boundary were increased and average grain size was decreased.
Abstract: In the present investigation, free vibration of functionally graded material (FGM) skew plates under thermal environment is studied. Kinematics equations are based on the Reddy’s higher order shear deformation theory and a nine noded isoparametric Lagrangian element is adopted to mesh the plate geometry. The issue of C1 continuity requirement related to the assumed displacement field has been circumvented effectively to develop C0 finite element formulation. Effective mechanical properties of the constituents of the plate are considered to be as position and temperature dependent and assumed to vary in the thickness direction according to a simple power law distribution. The displacement components of a rectangular plate are mapped into skew plate geometry by means of suitable transformation rule. One dimensional Fourier heat conduction equation is used to ascertain the temperature profile of the plate along thickness direction. Influence of different parameters such as volume fraction index, boundary condition, aspect ratio, thickness ratio and temperature field on frequency parameter of the FGM skew plate is demonstrated by performing various examples and the related findings are discussed briefly. New results are generated for vibration of the FGM skew plate under thermal environment, for the first time, which may be implemented in the future research involving similar kind of problems.
Abstract: Al/Cu clad sheet has been fabricated by using differential speed rolling (DSR) process, which caused severe shear deformation between Al and Cu plate to easily bond to each other. Rolling was carried out at 100 and 150oC with speed ratios from 1.4 to 2.2, in which the total thickness reduction was in the range between 14 and 46%. Interfacial microstructure and mechanical properties of Al/Cu clad were investigated by scanning electron microscope equipped with energy dispersive X-ray detector, and tension tests. The DSR process was very effective to provide a good interface for atoms diffusion during subsequent annealing. The strength of bonding was higher with the increasing speed ratio. Post heat treatment enhanced the mechanical properties of clad sheet by forming intermetallic compounds in the interface area.
Abstract: A trigonometric shear deformation theory for flexure of thick beams, taking into account transverse shear deformation effects, is developed. The number of variables in the present theory is same as that in the first order shear deformation theory. The sinusoidal function is used in displacement field in terms of thickness coordinate to represent the shear deformation effects. The noteworthy feature of this theory is that the transverse shear stresses can be obtained directly from the use of constitutive relations with excellent accuracy, satisfying the shear stress free conditions on the top and bottom surfaces of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions are obtained by using the principle of virtual work. The thick cantilever isotropic beams are considered for the numerical studies to demonstrate the efficiency of the. Results obtained are discussed critically with those of other theories.
Abstract: A trigonometric shear deformation theory for flexure of thick beams, taking into account transverse shear deformation effects, is developed. The number of variables in the present theory is same as that in the first order shear deformation theory. The sinusoidal function is used in displacement field in terms of thickness coordinate to represent the shear deformation effects. The noteworthy feature of this theory is that the transverse shear stresses can be obtained directly from the use of constitutive relations with excellent accuracy, satisfying the shear stress free conditions on the top and bottom surfaces of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions are obtained by using the principle of virtual work. The thick simply supported isotropic beams are considered for the numerical studies to demonstrate the efficiency of the results obtained is discussed critically with those of other theories.
Abstract: In this paper a study on the vibration of thin
cylindrical shells with ring supports and made of functionally
graded materials (FGMs) composed of stainless steel and
nickel is presented. Material properties vary along the
thickness direction of the shell according to volume fraction
power law. The cylindrical shells have ring supports which are
arbitrarily placed along the shell and impose zero lateral
deflections. The study is carried out based on third order shear
deformation shell theory (T.S.D.T). The analysis is carried out
using Hamilton-s principle. The governing equations of motion of
FGM cylindrical shells are derived based on shear deformation
theory. Results are presented on the frequency characteristics,
influence of ring support position and the influence of boundary
conditions. The present analysis is validated by comparing results
with those available in the literature.
Abstract: In the present work, study of the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. Material properties are graded in the thickness direction of the shell according to volume fraction power law distribution. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of boundary conditions on the natural frequencies of the FG cylindrical shell. The study is carried out using third order shear deformation shell theory. The governing equations of motion of FG cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of constituent volume fractions and the effects of free-free boundary conditions.
Abstract: Two geometrically nonlinear plate theories, based either on first- or third-order transverse shear deformation theory are used for finite element modeling and simulation of the transient response of smart structures incorporating piezoelectric layers. In particular the time histories of nonlinear vibrations and sensor voltage output of a thin beam with a piezoelectric patch bonded to the surface due to an applied step force are studied.
Abstract: Aluminum/Copper clad sheet has been fabricated using
asymmetric extrusion method, which caused severe shear deformation
between Al and Cu plate to easily bond to each other. Interfacial
microstructure and mechanical properties of Al/Cu clad were studied
by scanning electron microscope equipped with energy dispersive
X-ray detector, micro-hardness, and tension tests. The asymmetric
extrusion bonding was very effective to provide a good interface for
atoms diffusion during subsequent annealing. The strength of bonding
was higher with the increasing extrusion ratio.
Abstract: In the present work, study of the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. Material properties are graded in the thickness direction of the shell according to volume fraction power law distribution. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of boundary conditions on the natural frequencies of the FG cylindrical shell. The study is carried out using third order shear deformation shell theory. The analysis is carried out using Hamilton's principle. The governing equations of motion of FG cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of constituent volume fractions and the effects of free-free and clamped-clamped boundary conditions.
Abstract: The governing differential equations of laminated
plate utilizing trigonometric shear deformation theory are derived
using energy approach. The governing differential equations
discretized by different radial basis functions are used to predict the
free vibration behavior of symmetric laminated composite plates.
Effect of orthotropy and span to thickness ratio on frequency
parameter of simply supported laminated plate is presented.
Numerical results show the accuracy and good convergence of radial
basis functions.
Abstract: In this study, it is investigated the stability boundary of
Functionally Graded (FG) panel under the heats and supersonic
airflows. Material properties are assumed to be temperature
dependent, and a simple power law distribution is taken. First-order
shear deformation theory (FSDT) of plate is applied to model the
panel, and the von-Karman strain- displacement relations are
adopted to consider the geometric nonlinearity due to large
deformation. Further, the first-order piston theory is used to model the
supersonic aerodynamic load acting on a panel and Rayleigh damping
coefficient is used to present the structural damping. In order to find a
critical value of the speed, linear flutter analysis of FG panels is
performed. Numerical results are compared with the previous works,
and present results for the temperature dependent material are
discussed in detail for stability boundary of the panel with various
volume fractions, and aerodynamic pressures.
Abstract: In this paper, an analytical approach is used to study the coupled lateral-torsional vibrations of laminated composite beam. It is known that in such structures due to the fibers orientation in various layers, any lateral displacement will produce a twisting moment. This phenomenon is modeled by the bending-twisting material coupling rigidity and its main feature is the coupling of lateral and torsional vibrations. In addition to the material coupling, the effects of shear deformation and rotary inertia are taken into account in the definition of the potential and kinetic energies. Then, the governing differential equations are derived using the Hamilton-s principle and the mathematical model matches the Timoshenko beam model when neglecting the effect of bending-twisting rigidity. The equations of motion which form a system of three coupled PDEs are solved analytically to study the free vibrations of the beam in lateral and rotational modes due to the bending, as well as the torsional mode caused by twisting. The analytic solution is carried out in three steps: 1) assuming synchronous motion for the kinematic variables which are the lateral, rotational and torsional displacements, 2) solving the ensuing eigenvalue problem which contains three coupled second order ODEs and 3) imposing different boundary conditions related to combinations of simply, clamped and free end conditions. The resulting natural frequencies and mode shapes are compared with similar results in the literature and good agreement is achieved.
Abstract: In the traditional buckling analysis of rectangular
plates the classical thin plate theory is generally applied, so
neglecting the plating shear deformation. It seems quite clear that this
method is not totally appropriate for the analysis of thick plates, so
that in the following the two variable refined plate theory proposed
by Shimpi (2006), that permits to take into account the transverse
shear effects, is applied for the buckling analysis of simply supported
isotropic rectangular plates, compressed in one and two orthogonal
directions.
The relevant results are compared with the classical ones and, for
rectangular plates under uniaxial compression, a new direct
expression, similar to the classical Bryan-s formula, is proposed for
the Euler buckling stress.
As the buckling analysis is a widely diffused topic for a variety of
structures, such as ship ones, some applications for plates uniformly
compressed in one and two orthogonal directions are presented and
the relevant theoretical results are compared with those ones obtained
by a FEM analysis, carried out by ANSYS, to show the feasibility of
the presented method.
Abstract: Study of the vibration cylindrical shells made of
a functionally gradient material (FGM) composed of stainless
steel and nickel is important. Material properties are graded in
the thickness direction of the shell according to volume
fraction power law distribution. The objective is to study the
natural frequencies, the influence of constituent volume
fractions and the effects of boundary conditions on the natural
frequencies of the FG cylindrical shell. The study is carried
out using third order shear deformation shell theory. The
governing equations of motion of FG cylindrical shells are
derived based on shear deformation theory. Results are
presented on the frequency characteristics, influence of
constituent volume fractions and the effects of clampedclamped
boundary conditions.
Abstract: In the present work, study of the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. Material properties are graded in the thickness direction of the shell according to volume fraction power law distribution. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of boundary conditions on the natural frequencies of the FG cylindrical shell. The study is carried out using third order shear deformation shell theory. The analysis is carried out using Hamilton's principle. The governing equations of motion of FG cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of constituent volume fractions and the effects of clamped-free boundary conditions
Abstract: This article considers the positional buckling of
composite thick plates under thermal loading . For this purpose , the
complex finite strip method is used . In analysis of complex finite
strip, harmonic complex function in longitudinal direction , cubic
functions in transversal direction and parabola distribution of
transverse shear strain in thickness of thick plate based on higherorder
shear deformation theory are used . In given examples , the
effect of angles of stratification , number of layers , dimensions ratio
and length – to – thick ratio across critical temperature are
considered.
Abstract: In this paper the Differential Quadrature Method (DQM) is employed to study the coupled lateral-torsional free vibration behavior of the laminated composite beams. In such structures due to the fiber orientations in various layers, the lateral displacement leads to a twisting moment. The coupling of lateral and torsional vibrations is modeled by the bending-twisting material coupling rigidity. In the present study, in addition to the material coupling, the effects of shear deformation and rotary inertia are taken into account in the definition of the potential and kinetic energies of the beam. The governing differential equations of motion which form a system of three coupled PDEs are solved numerically using DQ procedure under different boundary conditions consist of the combinations of simply, clamped, free and other end conditions. The resulting natural frequencies and mode shapes for cantilever beam are compared with similar results in the literature and good agreement is achieved.