Learning Forum

[jesusepp]

Greetings,

I'm currently working on a simulation that studies the PSD of a voltage response coming from a piezoelectric bimorph beam connected to a host structure that is excited with a band-limited displacement (known PSD). After trying multiple alternatives, I noticed the following aspects:

1- The "Random Vibration" module is the only one capable of performing this type of analysis

2- Piezoelectric voltage responses can be studied via a coupled field analysis for harmonic excitations (as shown in Piezoelectric Flexure simulation using Ansys Mechanical) or by using the extension "PiezoAndMEMS" (as showcased in Harmonic Analysis and Voltage Response of Piezoelectric Energy Harvester using Ansys Workbench)

3- The "PiezoAndMEMS" extension does not work with the "Random Vibration" module, i.e., no voltage PSD can be extracted from such analysis

With that said, I am wondering how I can obtain the voltage PSD for a random vibration analysis that includes piezoelectric and non-piezoelectric components.

Additionally, I also want to know if there is a way to "connect" the voltage degrees of freedom of a piezoelectric component at different locations via a resistance (that is, if I am trying to emulate a parallel or in series connection for the bimorph plate, e.g., Erturk, A., & Inman, D. J. (2009). An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations. Smart materials and structures, 18(2), 025009).

[dlooman]

It's not supported by the Workbench gui and not documented or tested with APDL commands, but it isn't obvious why it wouldn't just work.  I ran the test below and it isn't blocked at least.  

/title, Complex Voltage example using model from Example 2.3.7 of Coupled Physics Guide

!! Material constants for Quartz
! - Stiffness coefficients, N/m**2 
c11= 86.74e9   $ c12= 6.99e9    $ c13= 11.91e9   $  c14= -17.91e9 
c33= 107.2e9    
c44= 57.94e9   
c66= 39.88e9

! - Viscosity coefficients, N/m**2 s
eta11= 1.37e-3 $ eta12= 0.73e-3 $ eta13= 0.72e-3 $ eta14= 0.01e-3 
eta33= 0.97e-3    
eta44= 0.36e-3   
eta66= 0.32e-3

! - Piezoelectric stress constants, C/m**2
e11= 0.171
e14=-0.0406

! - Permittivity constants at constant strain, F/m
ep11=39.21e-12
ep33=41.03e-12

! - Dielectric loss tangent
tand11=1.6e-4
tand33=1.8e-4

! - Density, kg/m**3
rho = 2649

! - Material matrices [c],[e],[PER] in IEEE format
!
!   [c11  c12 c13  c14   0  0 ]   [ e11  0  0]   [ep11  0    0  ]
!   [c12  c11 c13 -c14   0  0 ]   [-e11  0  0]   [  0  ep11  0  ]
!   [c13  c13 c33   0    0  0 ]   [  0   0  0]   [  0   0   ep33]
!   [c14 -c14  0   c44   0  0 ]   [ e14  0  0]
!   [ 0    0   0    0  c44 c14]   [  0 -e14 0]
!   [ 0    0   0    0  c14 c66]   [  0 -e11 0]
!
! - Material matrices [c],[e],[PER] in ANSYS format
!
!   [c11  c12 c13   0  c14  0 ]   [ e11  0  0]    [ep11  0    0  ]
!   [c12  c11 c13   0 -c14  0 ]   [-e11  0  0]    [  0  ep11  0  ]
!   [c13  c13 c33   0   0   0 ]   [  0   0  0]    [  0   0   ep33]
!   [ 0    0   0   c66  0  c14]   [  0 -e11 0]
!   [c14 -c14  0    0  c44  0 ]   [ e14  0  0]
!   [ 0    0   0   c14  0  c44]   [  0 -e14 0]

!  Plate dimensions
l=2e-2                    ! m
w=0.6e-2
t=0.1e-2

!  Voltage load
V=1                       ! V
 
/PREP7
tb,ANEL,1,,,0             ! Anisotropic elasticity table
tbda,1,c11,c12,c13,,c14
tbda,7,c11,c13,,-c14
tbda,12,c33
tbda,16,c66,,c14
tbda,19,c44
tbda,21,c44

tb,AVIS,1,,,0             ! Anisotropic viscosity table
tbda,1,eta11,eta12,eta13,,eta14
tbda,7,eta11,eta13,,-eta14
tbda,12,eta33
tbda,16,eta66,,eta14
tbda,19,eta44
tbda,21,eta44

tb,PIEZ,1,,,0             ! Piezoelectric coefficient table
tbda,1,e11
tbda,4,-e11
tbda,7
tbda,10,,-e11
tbda,13,e14
tbda,16,,-e14

eps0=8.854e-12
emunit,epzro,eps0
tb,DPER,1,,,0             ! Permittivity table
tbda,1,ep11/eps0,ep11/eps0,ep33/eps0

tb,DLST,1,,,0             ! Dielectric loss tangent
tbda,1,tand11,tand11,tand33

mp,DENS,1,rho             ! Density

local,11

!  Element coordinate system for AT-cut rotation
local,12,,,,,,-35.25

block,0,l,0,t,0,w
et,1,226,1001             ! Piezoelectric analysis option
esize,t/4
csys,11
mat,1  $ type,1 $ esys,12
vmesh,1

! Mechanical boundary conditions
nsel,s,loc,x,0
! nsel,r,loc,y,0
! nsel,r,loc,z,0
d,all,ux,0,,,,uy,uz
nsel,all

! Electrodes
nsel,s,loc,y,0
cp,1,volt,all
ng=ndnext(0)     
nsel,s,loc,y,t
cp,2,volt,all
nd=ndnext(0)
nsel,all

d,ng,volt,0       

eplot
fini

/solve
antype,modal
modop,lanb,6
mxpand,6

dmpstr,.05        ! .05 structural damping

outres,all,all

solve
fini

/solu

antype,spectrum
dmprat,0.25
spopt,psd,,yes
outres,all,1

psdunit,1,acel
psdfrq,1,,1000,10000
psdval,1,100.0,100.0
nsel,s,loc,x,0
d,all,uy,1.0
nsel,all

pfact,1,base
psdcom
solve
fini

/post1
set,3,1
/view,1,3,2,1
/show,png
plns,uy
plns,volt