1. Design and realization of piezoelectric
mobiles for cooperative use (piezoelectric
mini-robots)
Dr. Hassan Hariri
Pr. Yves Bernard & Pr. Adel Razek
GeePs: Génie électrique et électronique de Paris
http://www.geeps.centralesupelec.fr/
Email: haririhas@gmail.com

2. Copyright Hassan Hariri 2016
Introduction
 Inspired by the stingray fish, we think that a
locomotion in various environments (soil, air,
liquid) using piezoelectric patches bonded on a
thin structure is possible.
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3. Copyright Hassan Hariri 2016
Introduction
 A schematic of thin structure with piezoelectric
patches
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4. Copyright Hassan Hariri 2016
A two dimensions modeling of non-
collocated piezoelectric patches
bonded on thin structure
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5. Copyright Hassan Hariri 2016
 Under the assumption of linear elastic materials
and plane stress formulation, we can write
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A two dimensions modeling of non-
collocated piezoelectric patches
bonded on thin structure

6. Copyright Hassan Hariri 2016
 Under the assumption of linear elastic materials
and plane stress formulation, we can write
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A two dimensions modeling of non-
collocated piezoelectric patches
bonded on thin structure

7. Copyright Hassan Hariri 2016
 Applying Hamilton principle, we obtain the
variational equation that represents the
mechanical and piezoelectric system
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A two dimensions modeling of non-
collocated piezoelectric patches
bonded on thin structure

8. Copyright Hassan Hariri 2016
 Numerically integrating the variational equation
over the entire volume of the system and taking
the boundary conditions into account in the
assembly of matrices, the numerical equation is
then written taking into account the damping
matrix as follows
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A two dimensions modeling of non-
collocated piezoelectric patches
bonded on thin structure

9. Copyright Hassan Hariri 2016
A Traveling Wave Piezoelectric Beam
Robot
 Geometric parameters, coordinate system, and
description of the neutral axis
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10. Copyright Hassan Hariri 2016
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A Traveling Wave Piezoelectric Beam
Robot
vibrator–absorber:1ME
vibrator–vibrator:2ME

11. Copyright Hassan Hariri 2016
A Traveling Wave Piezoelectric Plate
Robot
 Still under publication
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12. Copyright Hassan Hariri 2016
Mobile Piezoelectric Device (patent)
 The present invention relates to a piezoelectric
device (1) comprising: a flexible plate (2), at least
three unaligned piezoelectric transducers (3)
attached onto a single surface of the plate (2), and
a sinusoidal voltage generator (4) that generates
sinusoidal voltage and is connected to at least one
piezoelectric transducer (3) such as to generate a
traveling wave in the flexible plate (2). The
piezoelectric device (1) is characterized in that the
flexible plate (2) supporting the at least three
piezoelectric transducers (3) is mobile, the
generated traveling wave being capable of moving
the flexible plate (2)
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13. Copyright Hassan Hariri 2016
Mobile Piezoelectric Device (patent)
 Different configurations
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3
3
3
3
2
1
4
4 4
4
0
+λ/4
2
33
0
3
1

14. Copyright Hassan Hariri 2016
Mobile Piezoelectric Device (patent)
 Two Modes Excitation method (2ME)
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0 +λ/4
0 +λ/4
2
3
3 33
x
y
1
1 2
34
1
0 +λ/4
-λ/4 +λ/4
2
3
3 33
2
34
x
y
0 +λ/4
0 -λ/4
2
3
3 33
1 2
34
x
y

15. Copyright Hassan Hariri 2016
Mobile Piezoelectric Device (patent)
 One Mode Excitation method (1ME)
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2
3
3
3
34
4
5
51
51
52
521 2
34
2
3
3
3
3 4
4 51
52
52
51 1 2
34

16. Copyright Hassan Hariri 2016
References
 [1] http://animals.desktopnexus.com/wallpaper/209676/
 [2] http://picinpic.blogspot.fr/2011/07/manta-ray-fish.html
 [3] H. Hariri, Y. Bernard, A. Razek, ‘’A two dimensions modeling of
non-collocated piezoelectric patches bonded on thin structure’’,
Journal of curved and layered structures, 2015.
 [4] H. Hariri, Y. Bernard, A. Razek, ‘’ Finite element model of a
beam structure with piezoelectric patches using RL shunt circuits’’,
Proceedings of Adaptronic congress 2011, pp. 124-131.
 [5] H. Hariri, Y. Bernard, A. Razek, ‘’Travelling wave piezoelectric
beam robot’’, Journal of smart materials and structures, 2013, pp. 1-
9.
 [6] H. Hariri, Y. Bernard, A. Razek, ‘’Dual piezoelectric beam robot:
The effect of piezoelectric patches’ positions’’, Journal of Intelligent
Material Systems and Structures, 2015.
 [7] Yves Bernard, Hassan Hariri, Adel Razek. Mobile piezoelectric
device. Patent n° : WO 2015/059283. 2015.
http://www.google.com/patents/WO2015059283A1?cl=en
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