Mohd Hafiz Abdul Satar and Ahmad Zhafran Ahmad Mazlan*
School of Mechanical Engineering, Malaysia
*Corresponding author: Ahmad Zhafran Ahmad Mazlan, The Vibration Lab, School of Mechanical Engineering, 14300 Nibong Tebal, Pulau Pinang,
Malaysia
Submission: January 4, 2019; Published: February 15, 2019
Piezoelectric Material Non-Linear Characteristics,
Compensation Methods and Application
Introduction
Piezoelectric material has been widely used as sensor and
actuator in many applications such as in structural vibration
reduction [1-3], control of flexible structures [4,5], positioning
control [6,7] and energy harvesting [8]. This is due to the
piezoelectric effects which converted the mechanical energy to the
electrical energy (i.e., sensing ability) and conversely from electrical
energy to the mechanical energy (i.e., actuating ability). These
piezoelectric effects were firstly discovered but only been used in
1940 (Figure 1a & 1b). Show both of the piezoelectricity working
principle of sensing and actuating abilities, respectively. From these
Figure 1a & 1b, the first effect is due to the mechanical stress which
transfers the energy to the electrical charge across the material and
the second effect is conversely due to the applied electrical charge
to the material resulting in mechanical stress [9].
The detail of piezoelectric constitutive equations in the stress-
charge form are given by:
c S e E
E p e
σ = −
(1)
T
D e S E
e p s e
= +∈
(2)
Where S is the strain, σ is the stress, D
e
is the electric
displacement, E
e
is the electric field strength, e
p
is the piezoelectric
coupling coecient in the stress-charge form, c
E
contains stiffness
coecients under constant electric field and ϵ
S
is the electric
permittivity matrix under constant strain. Subscripts E indicates
zero or constant electric field and σ is the zero or constant
stress field, while superscript T denotes matrix transposition.
Piezoelectric actuators are known for their various shapes,
flexibility, high frequency response and high stiffness but very
limited on displacement [10-12]. Thus, they are suitable for the
vibration isolation of stiff structures. For example, piezoelectric
actuator has been used to control the vibration in automotive
[13,14], aerospace [1,15], robotic [7] and civil structures [16].
Figure 1: Sensing and actuating abilities from piezoelectric
effect [10].
Non-linear hysteresis and creep are the inherent characteristic
of the piezoelectric actuator, which affect their performance and
these characteristics will be described in the next section. In
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Abstract
Piezoelectric materials are capable of converting the mechanical stress to the electrical charge and vice versa. These piezoelectric effects made
them useful for sensors and actuators in many applications, such as in the control of structural vibration. Nonlinear hysteresis is one of the inherent
characteristics of the piezoelectric material, which affect their performance. This characteristic has been widely studied and can be compensated using
operator-based or differential-based models. Another important characteristic to be considered is creep. It has caused slow drift in the actuation process.
In general, the compensated method can be divided into two group; open and closed loop methods. The non-linear characteristics of the piezoelectric
material is important to be characterized and compensated, in particular for used in the Active Vibration Control (AVC) system.
Keywords: Piezoelectric materials; Hysteresis; Creep; Structural vibration
ISSN: 2640-9690