Transient bending analysis of a functionally graded circular plate with integrated surface piezoelectric layers
International Journal of Mechanical and Materials Engineering
Transient bending analysis of a functionally graded circular plate with integrated surface piezoelectric layers
Ali Asghar Jafari 1
Ali Akbar Jandaghian 0
Omid Rahmani 0
0 Smart Structures and New Advanced Materials Laboratory, Mechanical Engineering Department, University of Zanjan , Zanjan 45371-38791 , Iran
1 Faculty of Mechanical Engineering, K.N.Toosi University of Technology , Pardis St., Tehran 19697 , Iran
Background: Thin and piezoelectric materials are widely used as sensors or actuators in smart structures by embedding or surface-mounted them. Methods: This paper report on the exact, explicit solution for the transient bending of a circular functionally graded (FG) plates integrated with two uniformly distributed actuator layers made of piezoelectric material based on the classical plate theory (CPT). The material properties of the FG 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 form of the electric potential field in the piezoelectric layer is considered such that the Maxwell static electricity equation is satisfied. The governing equations are solved for clamped and simply supported edge boundary condition of the circular plate. The solutions are expressed by elementary Bessel functions and derived via exact inverse Laplace transform. Results and Conclusions: It is seen that the power index (g) and thickness of piezo-layer have significant effect on the deflection amplitude and natural frequency of piezo-FG plate.
Functionally graded material; Piezoelectric; Transient bending; Elasticity solution
Background
The active and controllable mechanical properties of
piezoelectric materials are extensively recognized as one
of the most important resources for the development of
intelligent self-monitoring and self-adaptive lightweight
structures
(Rahmani and Noroozi Moghaddam 2014)
.
Adaptive structures, incorporating piezoelectric patches
for sensing and actuation, are now broadly used in the
field of active and passive vibration and shape control,
in medical instruments, in measuring apparatus, and in
micro-electromechanical systems
(Jandaghian et al.
2013)
. A metal substrate surface bonded or embedded
by a piezoelectric layer has received considerable
attention throughout the last decades for practical designs of
sensors and actuators because of the
electromechanically coupling characteristics
(Jandaghian et al. 2014)
.
Recently, functionally graded (FG) materials which
exhibit smooth variation of material properties
(Rahmani
and Pedram 2014)
have been studied for developing
smart FG structures
(Rahmani et al. 2010)
. By utilizing
piezoelectric materials as actuators or sensors, smart FG
structures have been made with capabilities of
selfcontrolling and self-monitoring. The design of devices
including active piezoelectric materials requires, as an
initial step, an efficient modeling of the electrical,
mechanical, and coupling properties of the host structure, the
piezoelectric elements, and their interactions. In the
following, a review of recent findings and developments in
modeling of smart FG structures will be presented.
Pan
and Han (2005)
presented an exact solution for
multilayered rectangular plate made of functionally graded,
anisotropic, and linear magneto-electro-elastic materials.
In this work, the influence of the exponential factor, the
magneto-electro-elastic properties, and loading types on
induced magneto-electric-elastic fields have been
investigated. Batra
(Batra and Liang 1997; Vel and Batra 2001)
investigated the vibration behavior of a rectangular
laminated elastic plate with embedded piezoelectric
sensors and actuators with a piezoelectric plate subjected
to transient thermal loading. Batra and Geng (2002)
considered a FG viscoelastic layer but a homogeneous PZT
constraining layer and performed the three-dimensional
transient analysis of the problem with the finite element
method (FEM).
He et al. (2001)
suggested a finite element
formulation based on the classical laminated plate (CLP)
theory for the shape and vibration control of the FG
material plates with integrated piezoelectric sensors and
actuators and used a constant velocity feedback control
algorithm for the active control of the dynamic response
of the plate through closed-loop control.
Reddy and
Cheng (2001)
studied the bending of a FG rectangular
plate with an attached piezoelectric actuator. They have
employed the transfer matrix and asymptotic expansion
techniques to obtain a three-dimensional asymptotic
solution.
Bhangale and Ganesan (2006)
studied the static
behavior of functionally graded, anisotropic, and linear
magnetoelectro-elastic plates, using a semi-analytical (...truncated)