Two piezoelectric bending actuators of a novel design are presented and analysed in the paper. Numerical modelling and experimental study of the piezoelectric bending actuators were performed to verify operating principle and to investigate dynamic characteristics of the actuators. Numerical calculations are performed by using finite element method. Results of experimental study of piezoelectric actuators are compared with the results of finite element simulations. Results of the numerical and experimental research are analysed and discussed

D. Mažeika

J. Navickas

R. Bansevičius

R. Lučinskis

S. Navickaitė

V. Jūrėnas

English

Journal of Vibroengineering

1064  VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 2013. VOLUME 15, ISSUE 2. ISSN 1392-8716  
1022. Investigation of novel design piezoelectric bending 
actuators 
R. Bansevičius, S. Navickaitė, V. Jūrėnas, D. Mažeika, R. Lučinskis, J. Navickas 
1022. INVESTIGATION OF NOVEL DESIGN PIEZOELECTRIC BENDING ACTUATORS.  
R. BANSEVIČIUS, S. NAVICKAITĖ, V. JŪRĖNAS, D. MAŽEIKA, R. LUČINSKIS, J. NAVICKAS 
R. Bansevičius1, S. Navickaitė2, V. Jūrėnas3, D. Mažeika4, R. Lučinskis5, J. Navickas6 
1, 2, 3, 6Kaunas University of Technology, Donelaicio str. 73, LT-44029 Kaunas, Lithuania 
4, 5Vilnius Gediminas Technical University, Sauletekio av. 11, LT-10223 Vilnius, Lithuania  
E-mail: 1ramutis.bansevicius@ktu.lt, 2sigita.navickaite@ktu.lt, 3vytautas.jurenas@ktu.lt, 
4dalius.mazeika@vgtu.lt, 5raimundas.lucinskis@vgtu.lt, 6jonas.navickas@stud.ktu.lt 
(Received 22 April 2013; accepted 3 June 2013)  
Abstract. Two piezoelectric bending actuators of a novel design are presented and analysed in 
the paper. Numerical modelling and experimental study of the piezoelectric bending actuators 
were performed to verify operating principle and to investigate dynamic characteristics of the 
actuators. Numerical calculations are performed by using finite element method. Results of 
experimental study of piezoelectric actuators are compared with the results of finite element 
simulations. Results of the numerical and experimental research are analysed and discussed. 
Keywords: piezoelectric bimorph, amplitude-frequency response, dynamic characteristics. 
1. Introduction 
Piezoelectric cantilever bending actuators are widely used in many micromanipulation and 
microrobotic applications due to high resolution and fast response time [1]. Classical examples of 
piezoelectric cantilever bending actuators have unimorph, bimorph and multimorph 
configurations. Such actuators with a simple design are capable of producing large stroke under 
low electric voltage and provide high mechanical force/load sensitivity as sensory devices [2].  
A bimorph bender consists of two piezoelectric thin plates with polarization perpendicular to 
the interface plane (Fig. 1a). One plate is expanding while another is contracting when electric 
field is applied on the electrodes of the actuator. Since there is constraint at the interface of these 
two plates, bending deformation occurs in the whole structure. Similarly, bending can be produced 
in the unimorph actuator, where the transverse deformation of the piezoelectric plate is constrained 
by the passive elastic plate (Fig. 1b). Therefore, bimorph and unimorph structures can be used as 
actuation elements. Triple layer benders, which consist of two piezoelectric layers and a 
sandwiched central elastic layer (Fig. 1c) can be used to improve the mechanical reliability. 
However, in any case, the interfaces in the bimorph, unimorph or triple layer benders are 
mechanically weak locations. Delamination may occur after being driven for a period of time 
under periodic excitations due to the relaxation and debonding of the adhesive materials [1-3].  
  
Fig. 1. The schemes of piezoelectric bending actuators: a) piezoelectric bimorph,  
b) piezoelectric unimorph, c) piezoelectric triple layer bender [1-3] 
1022. INVESTIGATION OF NOVEL DESIGN PIEZOELECTRIC BENDING ACTUATORS.  
R. BANSEVIČIUS, S. NAVICKAITĖ, V. JŪRĖNAS, D. MAŽEIKA, R. LUČINSKIS, J. NAVICKAS 
  VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 2013. VOLUME 15, ISSUE 2. ISSN 1392-8716 1065 
Seeking to bond all layers of piezoelectric benders, adhesives are used. For instance, the 
adhesives used for bonding the piezoelectric patch have a finite service life, usually shorter than 
the host structure’s life-span [4, 5].  
Two novel design piezoelectric bending actuators are presented in this paper. These actuators 
consist of one piezoelectric plate and electrodes with the special design. Comparing them to the 
classic piezoelectric bending actuators, they have no bonding layer between piezoelectric plates, 
so influence of the bonding layer is avoided. Modelling based on finite element method was 
performed to make modal and harmonic response analysis of the actuators. Experimental 
investigations were made to define the dynamic characteristics of the actuator. 
2. Design of novel piezoelectric benders  
Investigated piezoelectric bending actuators consist of piezoelectric plate and electrodes 
(Fig. 2a). Silver electrodes are placed on top and bottom of actuator, and are used apply driving 
voltage (Fig. 2b). Two different types of platinum electrodes are placed in the middle plane of 
piezoelectric plate during the sintering process of ceramics and are used for polarizing of 
piezoelectric plate as it is showed in Fig. 2d and Fig. 2e. In one case perforated foil platinum 
electrode is used as middle electrode (Fig. 2c). In other construction wire electrodes are placed 
along the length of actuator, in middle plane of it, and they are positioned as it can be seen in 
Fig. 2f. Parameters of piezoelectric material and geometric parameters of actuators are given in 
Table 1 and Table 2. 
 
Fig. 2. Structure of novel design piezoelectric bending actuators: a) isometric view of novel design 
piezoelectric actuator, where 𝐿, 𝐵, ℎ – geometric parameters of cantilever, 𝐹 and 𝑀 – bending force and 
moment; b) polarization of piezoelectric plate, where 𝑃 – direction of polarization; c) shape of perforated 
foil electrode placed in middle plane, where 𝐿, 𝐴, 𝐷, 𝐸, 𝑡 – geometric parameters of foil-type electrode; 
d) polarization scheme of piezoelectric bender with inner foil-type electrode; e) polarization scheme of 
piezoelectric bender with inner wire-type electrodes; f) cross section of piezoelectric bender with inner 
wire-type electrodes, where 𝑑 and 𝐶 – geometric parameters of wire-type electrode 
3. Modelling of bimorph actuators 
Finite element software ANSYS v.13 was used to perform numerical modelling of the two 
bimorph actuators – classic design and novel with wire-type electrodes. The aim of the modelling 
1022. INVESTIGATION OF NOVEL DESIGN PIEZOELECTRIC BENDING ACTUATORS.  
R. BANSEVIČIUS, S. NAVICKAITĖ, V. JŪRĖNAS, D. MAŽEIKA, R. LUČINSKIS, J. NAVICKAS 
1066  VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 2013. VOLUME 15, ISSUE 2. ISSN 1392-8716  
was to perform modal-frequency and harmonic response analysis of the actuators. Finite element 
model was made of SOLID5 and SOLID45 finite elements [6, 7]. It was assumed that polarization 
direction of the piezoceramic is constant within the finite element pale and is organized as shown 
Fig. 2e. The dimensions and material properties of the finite element models are given in Table 1 
and Table 2. One end of the bimorph actuator was clamped so all mechanical degree of freedom 
of corresponding nodes was set to zero. The electrodes layers on the top and bottom of the actuator 
were not considered in the FEM model because their mechanical behaviour can be neglected due 
to their thickness. Electrodes were created by grouping surface nodes of the FEM model and 
harmonic voltage of excitation 𝑈 = 145 V were applied. 
The modal shapes and the resonant frequencies of the actuators were calculated and harmonic 
response analysis was performed. The first bending mode out of plane is the object of interest and 
natural frequency of this mode was found at 275 Hz for classic actuator (two piezoelectric plates 
glued together) and at 300 Hz for the second actuator with wire-type electrodes (Fig. 2f).  
Peaks in the graphs (Fig. 3) indicate the resonant vibrations at first bending mode. Resonance 
amplitudes are 37 µm and 35 µm accordingly for classic and second actuator with wire-type 
electrodes. 
Table 1. Parameters of piezoelectric material 
Material Pz 26 
Piezoelectric constants,  
(m/V×10-12) 
d31 -130 
d33 360 
Coupling factor, 𝑘𝑝 0,57 
Density 𝜌, kg/cm3 7700 
Dielectric constant 𝐾3
𝑇 1300 
Mechanical constant 𝑄𝑚 1000 
Young’s modulus 𝐸, GPa 63 
Relative dielectric constant 𝜀𝑇/𝜀𝑜 1000 
Table 2. Geometric parameters of the piezoelectric benders 
Length L, m 0,045 
Width B, m 0,0042 
Height h, m 0,0017 
Distance between wires C, m 0,00035 
Wire electrode diameter d, m 0,0001 
Distance between the holes in foil electrode A, m 0,0003 
Distance between the holes in foil electrode E, m 0,0003 
Diameter of holes in foil electrode D, m 0,0004 
Thickness of foil electrode t, m 0,0001 
 
 
a) 
 
b) 
Fig. 3. Harmonic analysis: a) FEM model, b) amplitude-frequency response of piezoelectric actuator with 
wire electrodes (numerical simulation). Here 1 – novel design bender, 2 – classic piezoelectric bimorph 
1022. INVESTIGATION OF NOVEL DESIGN PIEZOELECTRIC BENDING ACTUATORS.  
R. BANSEVIČIUS, S. NAVICKAITĖ, V. JŪRĖNAS, D. MAŽEIKA, R. LUČINSKIS, J. NAVICKAS 
  VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 2013. VOLUME 15, ISSUE 2. ISSN 1392-8716 1067 
4. Experimental results 
Prototype actuator with wire-type middle electrode (Fig. 2f) was made for experimental 
investigation (Fig. 4b). During experiments there were investigated two characteristics of bimorph 
actuators: rigidity of piezoelectric cantilever actuator with wire-type electrodes and 
amplitude-frequency response. The aims of experiment were to verify results of numerical 
modelling. 
The experimental setup is shown in Fig. 4a. It consists of: 1 – signal generator Agilent 33220A, 
2 – power amplifier EPA-104, 3 – laser sensor controller LK-G3001PV, 4 – computer, 
5 – multimeter MS8218, 6 – analog digital converter (ADC) “PicoScope-3424”, 7 – laser 
displacement sensor LK-G82, 8 – piezoelectric bending actuator, 9 – holder of piezoelectric 
bender. 
 
a) 
 
b) 
Fig. 4. Experimental investigation: a) setup and b) piezoelectric actuator used in experiments  
As a result of experiments we have amplitude-frequency responses that are shown in Fig. 5. 
Experimental results confirm the results of numerical modelling of piezoelectric bender with wire-
type electrodes. 
 
a) 
 
b) 
Fig. 5. Experimental results: a) rigidity of piezoelectric cantilever actuator with wire-type electrodes and 
b) amplitude-frequency responses. Here 1 – novel design bender, 2 – classic piezoelectric bimorph 
The experimental results have confirmed harmonic analysis of piezoelectric actuator wire-type 
electrodes. Comparing amplitude-frequency responses of novel bender and classic bimorph it can 
be seen, that resonance frequency increases from 305 Hz till 312 Hz, for novel design benders, 
but amplitude decreases by 7 % (Fig. 5b).  
Novel design piezoelectric benders have very wide area of applications, such as sensor systems, 
1022. INVESTIGATION OF NOVEL DESIGN PIEZOELECTRIC BENDING ACTUATORS.  
R. BANSEVIČIUS, S. NAVICKAITĖ, V. JŪRĖNAS, D. MAŽEIKA, R. LUČINSKIS, J. NAVICKAS 
1068  VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 2013. VOLUME 15, ISSUE 2. ISSN 1392-8716  
printing technologies, positioning transducers, viscosity measurement systems, flow measurement 
systems, energy harvesting, laser beam controlling systems, pneumatic valves for industrial and 
automotive applications, valves in medical applications, insulin pumps, braille keys for the blind, 
textile machinery, optical switches, oil exploration, machine and equipment monitoring, 
automotive engines, feedback sensors, high temperature accelerometers, gyroscope sensors, 
intrusion alarms and many other devices. So development and investigations of such types of 
piezoelectric actuators are very important. 
5. Conclusions 
Novel design piezoelectric benders have very wide area of applications. Comparing amplitude-
frequency responses of novel bender and classic bimorph it can be seen, that resonance frequency 
increases from 305 till 312 Hz, for novel design benders, but amplitude decreases by 7 %. 
Comparing them to classic piezoelectric bending actuators, they have no bonding layer between 
piezoelectric plates, so absence of bonding layer improves the performance and reliability of the 
actuator. Comparing numerical and experimental results it can be seen small difference between 
them (numerical values are different for classic actuator for 9 % and for novel – 4 %). These 
differences can be explained in many different factors during theoretical investigation and real 
experiments, such as: material properties, bounding conditions, damping, temperature of 
environment and other. 
Acknowledgement 
This research is funded by the European Social Fund under Project “Microsensors, 
Microactuators and Controllers for Mechatronic Systems (Go-Smart)” (Agreement 
No. VP1-3.1-ŠMM-08-K-01-015). 
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Investigation of novel design piezoelectric bending actuators

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