Abstract: Analytical investigation of the free vibration behavior
of circular functionally graded (FG) plates integrated with two
uniformly distributed actuator layers made of piezoelectric (PZT4)
material on the top and bottom surfaces of the circular FG plate
based on the classical plate theory (CPT) is presented in this paper.
The material properties of the functionally graded substrate plate are
assumed to be graded in the thickness direction according to the
power-law distribution in terms of the volume fractions of the
constituents and the distribution of electric potential field along the
thickness direction of piezoelectric layers is simulated by a quadratic
function. The differential equations of motion are solved analytically
for clamped edge boundary condition of the plate. The detailed
mathematical derivations are presented and Numerical investigations
are performed for FG plates with two surface-bonded piezoelectric
layers. Emphasis is placed on investigating the effect of varying the
gradient index of FG plate on the free vibration characteristics of the
structure. The results are verified by those obtained from threedimensional
finite element analyses.
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 this paper, an analytical approach for free vibration
analysis of rectangular and circular membranes is presented. The
method is based on wave approach. From wave standpoint vibration
propagate, reflect and transmit in a structure. Firstly, the propagation
and reflection matrices for rectangular and circular membranes are
derived. Then, these matrices are combined to provide a concise and
systematic approach to free vibration analysis of membranes.
Subsequently, the eigenvalue problem for free vibration of membrane
is formulated and the equation of membrane natural frequencies is
constructed. Finally, the effectiveness of the approach is shown by
comparison of the results with existing classical solution.
Abstract: Analytical solution of the first-order and third-order
shear deformation theories are developed to study the free vibration
behavior of simply supported functionally graded plates. The
material properties of plate are assumed to be graded in the thickness
direction as a power law distribution of volume fraction of the
constituents. The governing equations of functionally graded plates
are established by applying the Hamilton's principle and are solved
by using the Navier solution method. The influence of side-tothickness
ratio and constituent of volume fraction on the natural
frequencies are studied. The results are validated with the known
data in the literature.
Abstract: In the present paper, an improved initial value
numerical technique is presented to analyze the free vibration of
symmetrically laminated rectangular plate. A combination of the
initial value method (IV) and the finite differences (FD) devices is
utilized to develop the present (IVFD) technique. The achieved
technique is applied to the equation of motion of vibrating laminated
rectangular plate under various types of boundary conditions. Three
common types of laminated symmetrically cross-ply, orthotropic and
isotropic plates are analyzed here. The convergence and accuracy of
the presented Initial Value-Finite Differences (IVFD) technique have
been examined. Also, the merits and validity of improved technique
are satisfied via comparing the obtained results with those available
in literature indicating good agreements.
Abstract: In this paper, an analytical approach for free vibration
analysis of four edges simply supported rectangular Kirchhoff plates
is presented. The method is based on wave approach. From wave
standpoint vibration propagate, reflect and transmit in a structure.
Firstly, the propagation and reflection matrices for plate with simply
supported boundary condition are derived. Then, these matrices are
combined to provide a concise and systematic approach to free
vibration analysis of a simply supported rectangular Kirchhoff plate.
Subsequently, the eigenvalue problem for free vibration of plates is
formulated and the equation of plate natural frequencies is
constructed. Finally, the effectiveness of the approach is shown by
comparison of the results with existing classical solution.
Abstract: This paper describes a study of geometrically
nonlinear free vibration of thin circular functionally graded (CFGP)
plates resting on Winkler elastic foundations. The material properties
of the functionally graded composites examined here are assumed to
be graded smoothly and continuously through the direction of the
plate thickness according to a power law and are estimated using the
rule of mixture. The theoretical model is based on the classical Plate
theory and the Von-Kármán geometrical nonlinearity assumptions.
An homogenization procedure (HP) is developed to reduce the
problem considered here to that of isotropic homogeneous circular
plates resting on Winkler foundation. Hamilton-s principle is applied
and a multimode approach is derived to calculate the fundamental
nonlinear frequency parameters which are found to be in a good
agreement with the published results. On the other hand, the
influence of the foundation parameters on the nonlinear fundamental
frequency has also been analysed.
Abstract: This work presents the highly accurate numerical calculation
of the natural frequencies for functionally graded beams with
simply supported boundary conditions. The Timoshenko first order
shear deformation beam theory and the higher order shear deformation
beam theory of Reddy have been applied to the functionally
graded beams analysis. The material property gradient is assumed
to be in the thickness direction. The Hamilton-s principle is utilized
to obtain the dynamic equations of functionally graded beams. The
influences of the volume fraction index and thickness-to-length ratio
on the fundamental frequencies are discussed. Comparison of the
numerical results for the homogeneous beam with Euler-Bernoulli
beam theory results show that the derived model is satisfactory.