PRESENTATION OF THE UNIVERSITY OF
FEDERAL ITAJUBÁ
The Federal University of Itajubá-UNIFEI, founded on 23 November 1913,
under the name of Institute of Mechanical and Electrical engineering
Itajubá-IEMI, personal initiative Theodomiro Carneiro Santiago's lawyer,
was the tenth School of Engineering to settle in the country.
It has two campuses: Itajubá, MG - headquarters and Itabira, MG, advanced
campus.
Campus - Itajubá
Campus - Itabira
PRESENTATION OF THE UNIVERSITY OF
FEDERAL ITAJUBÁ
COURSES OFFERED BY THE GRADUATION IEM –
Campus Itajubá:
• MECHANICAL ENGINEERING;
MECHANICAL ENGINEERING - AIRCRAFT;
ENGINEERING MATERIALS and
ENGINEERING POWER.
PRESENTATION OF THE UNIVERSITY OF
FEDERAL ITAJUBÁ
COURSES OFFERED IN GRADUATE - IEM:
• MASTER IN MECHANICAL ENGINEERING;
• MASTER PROFESSIONAL ENGINEERING OF
MATERIALS and
• PHD IN MECHANICAL ENGINEERING.
SITE: http://www.unifei.edu.br/
JOB TITLE
ACTIVE CONTROL STRUCTURE TYPE
BEAM USING PIEZO ELECTRIC
ACTUATORS IN ANSYS
Author Master : Ribeiro.A.R.B
Co - Author : Phd Junior.L.J.J
DESCRIPTION OF THE PROBLEM
• Consists of performing dynamic
analysis and active control of a beamlike structure using piezoelectric
actuators through the ansys APDL
language.
METHODOLOGY
• Beam: modeled using the cubic element
SOLID45.
Figure 2 - element SOLID45.
METHODOLOGY
• PZT: element SOLID5
Figure 3 - element SOLID5.
METHODOLOGY
• SOLID45 e SOLID5
Table 1. Dimensions and distances
to create the beam, actuator and sensor.
Dimensions of the
structure
type beam (mm)
Dimensions
actuator
(mm)
Distance
actuator
(mm)
Distance
actuator
(mm)
504x25.4x0.7
72x25.4x0.61
12
48
Table 2. Properties of aluminum and pzt.
Modulus of elasticity
of aluminum (GPa)
Poisson's
ratio
Density of
aluminum
(kg/m3)
Density of
PZT (kg/m3)
70
0.32
2800
7500
METHODOLOGY
• Beam clamped free.
Figure 4 – configuration of the beam.
METHODOLOGY
• In this topic we will with the permittivity of the
ceramic, piezoelectric strain matrix and another
matrix as shown in the following table:
Table 4. Permittivity of ceramics.
Permittivity in
direction(x)
Permittivity in
direction(y)
Permittivity in
direction(z)
15.03E-9
15.03E-9
13E-9
METHODOLOGY
Table 5. Matrix deformation piezoelectric [e] .
TBDATA
TBDATA
TBDATA
TBDATA
TBDATA
16,17
14,17
3,-6.5
6,-6.5
9.23.3
Table 6. Matrix elasticity [c] .
TBDATA
TBDATA
1, 126E9, 79.5E9, 84.1E9
7, 126E9, 84.1E9
TBDATA
TBDATA
TBDATA
12, 23.3E9 19, 23E9
21, 23E9
ANSYS APDL
!*** Data of the beam ***!
•
•
•
HEIGHT =.7E-3
WIDTH=25.4E-3
COMPR=504E-3
! direcao Z
! direcao Y
! direcao X
•
•
•
mx=42
my=4
mz=1
! n. blocos na direcao x
! n. blocos na direcao y
! n. blocos na direcao z
•
•
•
DX=COMPR/mx
DY=WIDTH/my
DZ= HEIGHT /mz
ANSYS APDL
!*** Data of the PZT ***!
•
•
•
•
•
•
•
•
DSA=DX
HEIGHT A=.61E-3
WIDTHA=25.4E-3
COMPRA=72E-3
•
•
•
DXA=COMPRA/nx
DYA=WIDTHA/ny
DZA= HEIGHT A/nz
nx=6
ny=4
nz=1
! direção Z
! direção Y
! direção X
! n. blocos na direção z
! n. blocos na direção x
! n. blocos na direção y
ANSYS APDL
!First generate the material 2 and use the
command VATT (piezo).
! Generating ny blocks in y direction.
•
•
•
*DO,i,1,nx
*DO,j,1,ny
*DO,k,1,nz
•
BLOCK,DSA+(i-1)*DXA,DSA+i*DXA,(j-1)*DYA,j*DYA,ALTURA+(k1)*DZA,ALTURA+k*DZA
•
•
•
*ENDDO
*ENDDO
*ENDDO
•
VATT,2,,2
ANSYS APDL
! Automatically be material 1
! Generating ny blocks in y direction (beam)
•
•
•
•
•
•
•
*DO,i,1,mx
*DO,j,1,my
*DO,k,1,mz
BLOCK,(i-1)*DX,i*DX,(j-1)*DY,j*DY,(k-1)*DZ,k*DZ
*ENDDO
*ENDDO
*ENDDO
•
•
•
•
ESIZE,DSA
NUMMERG,ALL
NUMCOMP,ALL
VMESH,ALL
! gera outros blocos de dimensões proporcionais.
! merge pontos duplicados.
! comprime elementos.
! geração da malha.
ANSYS APDL
• ! NODE AT THE BOTTOM OF PZT
•
•
•
•
•
NSEL,S,LOC,Z,,ALTURA
NSEL,R,LOC,X,DSA,DSA+COMPRA
CP,1,VOLT,ALL
! acopla o DOF volt aos nos da superfície inferior e
sup. dos PZT.
CM,AREAUP,NODE
! cria componentes para a superfície inferior.
*GET,N1,NODE,,NUM,MIN
• ! NODE ON TOP OF PZT
•
•
•
•
NSEL,S,LOC,Z,ALTURA+ALTURAA
CP,2,VOLT,ALL
CM,INTRFC,NODE
*GET,N2,NODE,,NUM,MIN
ANSYS APDL
! Restrictions DOF STRUCTURE
•
•
•
•
•
•
•
NSEL,S,LOC,X,0
D,ALL,UZ
DSYM,SYMM,X
DSYM,SYMM,Y
NSEL,ALL
FINISH
/SOLU
! Modal Analysis
•
•
•
•
•
•
•
ANTYPE,MODAL
MODOPT,LANB,3
MXPAND,3
TOTAL,100
SAVE
SOLVE
FINISH
METHODOLOGY
• Beam and PZT sensor.
Figure 4 Beam, actuator and sensor.
METHODOLOGY
• Modal Analysis.
Figure 5, first mode of vibration.
METHODOLOGY
• Modal Analysis.
Figure 6, second mode of vibration.
METHODOLOGY
• Modal Analysis.
Figure 7, third mode of vibration.
METHODOLOGY
• Results of natural frequencies (Hz) obtained
analytically and by Ansys.
Table 8. Experimental Analysis.
Case
First
Second
Third
1
2.25
13.63
37.13
Table 9. Ansys Results.
Case
First
Second
Third
1
2.77
15.95
40.20
METHODOLOGY
• We will make a transient analysis where a
force is applied against time at the end of
the beam, this system will suffer the
influence of a proportional controller with
the objective of reducing the vibrations
that occur in the structure.
METHODOLOGY
• Controlling structure using a proportional
controller, with the gain Kc = 2.
Figure 8, proportional control.
METHODOLOGY
• Controlling structure using a proportional
controller, with the gain Kc = 3.3
Figure 9, proportional control.
METHODOLOGY
• Controlling structure using a proportional
controller, with the gain Kc = 5.
Figure 10, proportional control.
CONCLUSION
• A computer simulation using Ansys
proved very effective in comparison with
the analytical results in the analysis of
natural frequencies and vibration active
control using a proportional controller.
FUTURE WORK
• For future work we intend to implement
other types of controllers such as PID
controller and fuzzy.
• And conduct a new analysis to know
which of the two will be more evetivo
controllers for active control of vibrations.
REFERENCES
• H KARAGÜLLE, L MALGACA AND H F ÖKTEM.
Analysis of active vibration control in smart
structures by ANSYS, Smart Mater. Struct.
p.661–667, 18 May 2004.
• RAO, SINGIRESU S. Vibrações Mecânicas.
Editora Pearson Prentice Hall, 2008.
• OGATA KATSUHIKO. Engenharia de Controle
Moderno. Editora Pearson Prentice Hall, 2003.