a算 の実行
猛員サイズのずれ 骨11をタイムステップのず⇒1 計算が続了Lた時点での音圧.違匿デ→ を別配列に=ピー」ておく
}1髄而留bPだ1†齢算憲違める
魏 鵠 叫 〜 膠 階 蕩器 醇難 委識 瀦 解 鑛 徽̀れ を一つ
時期がモるった音圧と逗屋のデータをMlxdatoに楳存する
1
各 入 カ ファイル ポ イン ト解 説 一pe̲array2.ftxinp① 一
■モデルの 拡張;
SS叩1の 翼方向 については、最小座標 変数がx1.最 大座標変 致ゐ{浦.これ苦前後に拡 張し、罵〔駆6を 定義するx7‑x5 は素子部の 形状を特微付 ける吏数なので、st叩2では用 いない{素子aoが あ筍ところには水を割り当ててしまう)。同 様 にY方向もyD,ySjlestまで頴壊を笛張 する.
■要索サ イズの 設定;SpeetralFlexでは、要素分 割数1ま3‑41wavoで 十分な場舎が 多い
:騨 細̀轡 伽 姻 ..帥』瞬峠繍'≒ 僻圃.
■メッシュ生歳=gt6p2で は、生体組鍾 の邸分 はtoolkitの1mportM3torid棲能を使って材 料叡り当てフ7イル 老作成す るので.この 薗分についてはモデルを特微 付ける寸法変数 を般 定しない。寸法 喪数はモデル の領 域端のみ に設定。
.器緯 講 躍 繊 蹄.:・ 脚 戴・… 轍 鴨
命 繭 卿 ・P嶺嘱 出...:...S騨 ・a・同・・を用・覗 合1・嵐 鰍 砿 致としてー隣・峰 翻
■座標 魔数と拓 点盗数の 対応付 け=各方向について、最小 愛数と最 大変数とだけを対応 付けさせ る。
層$購 輝..
..巽吋.靭o鱒醐'.
"...
}一 一 一 一 一
各 入 カプァイル ポ イント解 説 一pe̲array2.flxinp③ 一
■材料定義と割り当て 幡..
肺o曲w博pon'..・ 、
ヒ.'
.proplap1100ニ1590.0.propDonn1050.14W:0:
proppom900:1300.0..・..1.蕊.
脚PM山 雪㎝0.1500.0.
醐
申価 嫌 塾鵜 監.字・...『'、.∵..1 叩P瑚 冨‑=甲:霞:...・.∵.・llこ 鱒.'....'b‑:..
噸w帥F'、.:
想 ㎞丁翻hM岨 由t器4面 睾岬 .樋 扁
B!Aの 設定方訟1コマンドリファレンス2‑300ベ ージ〕
く記述倒 》 pr叩wstriOOO.isw.a・
5.0‑S.e6S.Oe6 副A一 尺 一一一￣1V10肝音圧
モデル内椎定量夫量圧(負の儲を入力, ih:IB夙以降 は2行 目に賓 く
Importmaterialtoolを 用 」、て 作成 した材斜 割 り昌て77イル を読 み 込む.恩 鳥眠y5h眠 で 原貞位assわ せ る.?5.40ぜ 唯 鑑大 串.
■境界染件の 股定:SpecvalFlex'Cは 吸収境界 条件の 代わりにPM」(pertectlymatchedIgアer}を用いる◎
脚 .
劇bg埆.uo.旭 ..部由 亀,mしro5此
Bide2側 」・'{as■晦.
.鼎3酬 「03曜晦 蝉由4P耐'10獅 剛
弓O=填 界に掻 するiD蚕 素 をマ ッチン グ層 とす る。
・a旺Ol濠誕 串'1纂 素
各 入 カ フ ァ イ ル ポ イ ン ト解 説 一pe̲array2.flxinp④ 一
■ファイル出 力処理:
的 仙 酬1¶.}1回 繍:諏 蔚1.L丸 蘇...L 可繭 轍{ロ 」2i㎞ φ 、勢2.釣2.'エ1.‑・
.:鋼b 、勧f即 β}岬 雛 解L:
師b琳'1.晦4}由 聰5舖 細...
.r轡騨 『『1『畔 『『}塑『慈' 1榊 璽1歯。. 糾 艸 細r。r判騨
舳 ゆ 岬
.な.慨.コ 卵b蟹̀》}出 馳 痢i .、.「
.魏 撫 寄紳 η+:1'ξ:.淺い 卿b紬.S剛1
伽 輪 璃 幅..'...1:.
.ヒ.軸瀬b噛暉癬Froゆ冒.獅d::..ナ...:...15.....11"
dawopt.li.Sinod
印油.例̀漁 ゾη.『岬5胡 陣 」
罷騒 黛曜1.一 隠.
.噌 燐脚 覧ヒ. ..
瞬L=..・....‑:...1.國
・.ミ1..端1触r謄鰹 璽 塁∵＼.
各産橿直の鮪貞醤号を域得くモデル内に緊子位覆や黒点粒霞芒示す瓢壱引 くために用いa;
レ坤 ・で鰍 した・血 ・酬,7孤 を蟻み淋 }錦 。で龍 を印mrるx加 朗 の願欝号を鵬 }螂 で音匡・印加する点の… 柚 期位置・を脳 }S融1万 仙 を報
試咽 で音圧髪印加する点の敗とxR向位aとを出力
崩 βでの音圧印加位置壱S即oldファイルに出力
即p3での膏圧印加位置の音圧辿形をllKhstファイルに出力
各 入 カファイル ポ イント解 説 一pe̲array2.flxi叩 ⑤ 一 国モデル 駆動のための般 定:
圃.
wndoSkSi5311'Sj5 剛6P㌧ 岬,軸 加 網
steelで 得た9xdaloデータ壱黄 色粋内 に与 えることでモデ ルを駆 動する。
5.﹂50t
各 入 カ ファイルポ イン ト解 説 一pe̲array3.revinp① 一
■駆動音 圧テキストファイルの出 力:step2で得られた指定 した各位置 での圧力渡形 データをテキ λト7アイルに出 力 する
・婦"議 噸 唖t＼ ・. ...凝.}・ ス・・一・・禰 膝細
・諦 融1曲 』
.1融 κ:..1:...}ヒ ストリー・・イ澗 データ敷を聞
闘由.
町・1'.伽 卵」.・..:・、....ぐ こ::'1.
QO100DII1.5哺 隊 ・.へ こ.:1.
1醐 鯉 辱「
:'..'・...11'
・贈.b磁 ゆ.圃 戯 興
輔d5b中,.、.、 ....
、●nd..'・.・.、'...'・..q・....■、'㌔、1・..・'..
獅
ヒス トリーファイル の各 デー タを一つ ず つテキxト ファイ1LIC
各 入 カ ファイル ポイ ント解 説 一pe ̲array4.flxinp① 一
■駆動音圧7ア イルの読み込 みと駆 動設定:畳 信部モデルを駆動す るために.step2で 保 群した各位置 での音圧波形 ファイルを読み 込み、対応 する位置 に印加する。
筆 簾嗣謬 瓢 …
留.ll.剛 ぎ1、.1...・1.L凝 淵 響 轡 畔1些
窒… 一 一 …
軸 轡 騨}鱒 噸 搾.融r' :' ..ズ ト励 ・闘 圏 ・対応す欄 嗣 ・・得 蜘 軸 臨 醐 鱒 幽
鱒 ・『鱒」.試:卜...'i,.・ ..∴ ・.呂 函d...'
由繍 醗 い1.1∵'
雨 醜 ㈱4.㌦..・.1=...ド 叛ゆ 隔 ロ隅旨.至,、:∫、....:.気・
.'』 』 誰 繍 『州 塾鞭 卵 咋
り曙d .」:」
旺力印加位置Aの 苛貫詮定(ただL境界に迅ずピると 二うから音圧壱印加す巻とよくない,
2
c mem 100 c C c c
/* allocate 100 megawords of memory, 400 MegaBytes /* NOTES Not needed for Windows versions
/* MEM command must be first command in file. if used
***#*k******** **~ *** 4* x ********4q.14***### yaw **********#*,Px********4*************
*#*****
c c c
FLEX INPUT FILE TEMPLATE
c
c 'Bare Bones' Example File
c Contains basic commands that are essential, and those almost always used c
c DESIGNER : Robbie Banks. Weidlinger Associates Inc.
c MODEL DESCRIPTION : Phased array model for computing pressure wave. The pressure output c: of which is stored and use to calculate the propagating in the corresponding c: SpectralFlex model. Beam can be steered in this example
c DATE CREATED : 26/07/05
c VERSION : 1.0
c c
********
c
c Essential commands are: GRID. GEOM. MATR. SITE. BOUN, PRCS. EXEC c at least one of PLOD or PIEZ
c at least one of FUNC or DATA c
c Common commands are CALC, POUT c
c Note the use 'a' at the start of a line means that line will be read as a comment c
c Set job identity names that will be 'tagged' with output files using TITL command.
c The first is an 8 character dentifier, then up to a 60 character description
*4444#
titl pe arrayl• Phased Array transmission model for target
*#******* ************************************k*4*****4********4****4*4*** ***Adak***************,pk**
c c c
MODEL PARAMETERS
***4**** k*- *****l ***##dal*******#****4**********4k#k44****4k******************
***** *
c Setup symbol variables for later use. Typical values include thickness etc c e.g.
c symb pztthick = 2.e-3 /* PZT thickness
c symb pztradius = 20.e-3 /* PZT width
c
c Note that units are arbitrary, but must be consistent throughout model
*******
c
cINSERT YOUR MODEL PARAMETER VARIABLES BELOW
c c
!** k*#tk###************ ****
1
symb #get { chkfile I findfile function.dat if ( $chkfile eq notfound ) then symb #msg 2
Input drive function file funtion.dat file not found Please run 'makecurv.revinp' with Review first symb #exit
endif
rest no/* no restart files saved
c Model parameters symb #get { jobname Ijobname
symb bcklthck = 0.4e-3 /* backing thickness symb blckthok = 02e-3 /* pzt thickness symb frntthck = 0.02e-3 /* matching layer symb devdpth = 15.e-3 /* device depth symb focus = 7.5e-3/* focal depth symb yoffset = 0.0e-3 /* Focus offset from centre
symb watlside = 0.45e-3 symb blckwdth = 0.04e-3 symb blcksep = 0.02e-3 symb numpzt = 64
symb wat2thck = $focus * 0.25 symb simtime = 1.1e-6 symb freqint = 12.0e6 symb numelem = 15 symb velmin = 1500.
symb velwat = 1500.
symb txpres = 10000.
symb pi=4,*atan( 1.) symb nloops = 20 c symb numpzt2 = symb wgtedge = 0.25
)zt /* always 1.
/* water width at edge /* width of PZT element /* separation of elements
/* number of PZT pillars (should be even no.) /* thickness of water on front face /* simulation runtime
/* frequency of interest
/* Number of elements per wavelength at highest frequency of interest /* Minimum velocity in materials
/* velocity in water
/* Output Scaling Pressure for transducer in Pascals /* value of PI
/* number of pressure images to plot during runtime
/* number of PZT elements in symmetrical half of model weighting of drive function for edge elements
or centre elements and varies with a cosine from max to min.
symb ycentre = (nint ( $numpzt / 2) ) * ( $blckwdth + $blcksep ) + $watt side /* Y centre for focus symb yfocus = $ycentre + $yoffset /* Determine focul point on y axis
symb tfoeus = $focus / $velwat/* Time to focus from front of transducer c
c C c c
X-Y-Z CO-ORDINATE SYSTEM
**lee**
c
c Define x, y (and z for 3D) co-ordinates as symbol variables
c Creating these as a function of previously defined variables, and relative to c previous x, y position allows for simple altering of model,
c
c For 3D. also specify z-coordinates
2
cINSERT YOUR XYZ VARIABLES BELOW
c Set x and y points symb xl = 0.
symb x2 = $xl + $bcklthck/4 backing/pzt boundary symb x3 = 5x2 + $blckthck 7* Front of PZT symb x4 = $x3 + $frntthck /4 Top of Matching Layer symb x5 = $x4 + $wat2thck/* Water Load symb y1 = 0.
symb y2 = $yl + $watl side
symb y3 = $y2 + ( $blcksep / 2.) 7* inital kerf symb #msg 2
xl = $xl x2 = $x2 x3 = $n3 x4= $x4 x5= $x5 y1 = $y1 y2 = $y2 y3 = $y3
c Set up 'do' loop to create an appropriate number of 'y' positions c for a given number of PZT elements
symb jtmpl = 3 do loopi 1 1 $numpzt
symb jtmp2 = $jtmpl + 1 symb jtmp3 = $jtmp2 + 1
symb y$jtmp2 = $y$jtmpl + $blckwdth symb y$jtmp3 = $y$jtmp2 + $blcksep symb jtmpl = Sjtmpl + 2 c Calculate distance from focal point
symb ycent = $yfocus - ( ( $y$jlmp2 + $y$jtmp3 ) / 2. ) symb dist = sqrt ( ( $focus * $focus ) + ( Sycent * Sycent) ) symb tsep$I = $dist / $velwat
end$ loopi symb fend = $jtmp 1
symb y$jend = $y$jtmp3 + ( $blcksep / 2.) symb jend2 $fend + 1
symb y$jend2 = $y$jend+ $watlside
cDEFINE MESHING
c Set variable for approximate element size for model c Must be sufficient to represent wavelengths of interest c Recommended that at least 15 elements per wavelength are used c May be specified explicitly, e.g. symb box = 1.e-6
c or calculated based upon frequency of interest. and material velocities, e.g.
c Note this is only setting a variable for later use in IJK index calculation
3
symb freqmax = 2.0 * $fregint/* Maximum frequency of interest symb freqdamp = $freqintJ* Set damping frequency
symb wavemin = $velmin / $fregmax/* Calculate minimum wavelength symb box = $wavemin / $numelem/* Calculate typical element size
c I-J-K CO-ORDINATE SYSTEM
***#**
c Calculate I, J. and K (for 3D) indices
c As for x. y. z positions, set relative to previous index to allow simple alterations c e.g.
c symb it = I/* index for centre of PZT
c symb i2 = $i1 + nint (( $x2 - $xl ) 7 $box ) /* set i-index for edge of PZT
c/* based on x positions and
c/* approximate element size
c symb indgrd = $i2/* maximum i-index
c etc...
c For 3D, also specify k-indices
*******
cINSERT YOUR IJK VARIABLES BELOW
*****************************************************************************************************
c Set I indices symb il=1
symb i2 = $i1 + max (1 . Hint ( ( $x2 - $xl ) / $box) ) symb i3 = $i2 + max (1 , Hint ( ( $x3 - $x2 ) / Sbox) ) symb i4 = $i3 + max (1 , Hint ( ( $x4 - $x3 ) / $box) ) symb i5 = $i4 + max (1 , nint ( ( 5x5 - $x4 ) / $box ) ) symb ila = nint ( ( Si] + $i2 ) / 2. )/* midpoint of backing symb indgrd = $i5
c Set j indices symb j1 = 1
symb j2 = $jl + max (1 . nint ( ( $y2 symb j3 = $j2 + max (1 , Hint ( ( $y3 c As with y locations, j indices set up symb jtmpl = 3
do loopi I 1 $numpzt symb jtmp2 = $jtmpl + 1 symb jtmp3 = $jtmp2 + 1 symb j$jtmp2 = $j$jtmpl + max (1 ,
- $y1 ) / $box ) ) -$y2)/$box))
in 'do' loop
nint ( ( $y$jtmp2 - $y$jtmpl ) / $box ) )
4
symb j$jtmp3 = $j$jtmp2 + max (1 , nint ( ( $y$jtmp3 - $y$jtmp2 ) / Shea ) ) symb jtmpl = $jtrnpl + 2
end$ loopi symb fend = $jtmp l
symb j$jend = $j$jtmp3 + max (1 , Hint ( ( $y$jend - $y$jtmp3 ) / $boa) ) symb jend2 = $jend + 1
symb j$jend2 = $j$jend + max (1 , nint ( ( $y$jend2 - $y$jend ) / Sbox ) ) symb jndgrd = $j$jend2
cGRID DEFINITION
*#***#************************#****************************************#**************************
*******
c •Set size and type of finite element grid c Specified as number of nodes in each direction
c There are always one less elements in each direction than nodes c •Can be explicitly stated as a number, or as a previously calculated c •Options are any one (and only one) of:
c grid Sindgrd $jndgrd/* 20 (plane strain) -c grid Sindgrd $jndgrd axixi* 2D (axisymmetric)
c grid Sindgrd $jndgrd $kndgrd/* 3D
variable.
(or axiyi
c
c INSERT YOUR GRID COMMANDS BELOW
grid Sindgrd $jndgrd
* ** ****
cGEOM DEFINITION
**_*****
c •Asscoiate ijk grid with xyz co-ordinates
c Specify each axis and the regions within (xcrd and ycrd for 2D. also zcrd for 3d) c Entire grid must be specified
c Skewed partitions and external build files read in here c e.g.
c geom
c xcrd Sal $x2 $11 $i2 c xcrd $x2 $x3 $i2 $i3 c ycrd Syl $y2 $jl $j2
c zcrd $zl $z2 Ski $k2 %* only needed for 3D
5
******
cINSERT YOUR GEOM COMMANDS BELOW
******
geom
xcrd Sal $x2 $i1 $i2 xcrd $x2 $x3 $i2 Si3 scrd $x3 $x4 $i3 $i4 xcrd $x4 $x5 $i4 $i5 ycrd Syl $y2 $j1 5j2
do loopi 12 $jend2-1
symb J = $I+ 1 ycrd $y$I Sy$J $j$I $j$J
endS loopi end
*****
cMATERIAL PROPERTIES
•
#
c •While Material names and Properties can be specified within the Flex input file c it is usually good practice to maintain a separate 'materials file' that is then c read into the Flex input file. This is the method used here. The materials file c basictemplatematr' details the method for specifiying material properties.
c •e.g.
c symb dread basicternplate.matr/* read in material properties c •Materials used must have been specified already with the MATR command c or read in from a materials file.
c •Only VOID exists by default which has no density. stiffness or velocity c and is used to represent vacuum. It does not by default have dielectric c properties specified.
c •Materials can be placed by nodal (ijk) ranges (areas or volumes) with REGN c or by co-ordinates (xyz) with BLOK
c •Specified ranges can be a small as a single element or as large as the whole model c If no indices are specified. then the entire model is set to that material
c •Any element may have a particular material set an unlimited number of times c but only the last material specification will be applied.
***#
c c c
READ IN OR DEFINE YOUR MATERIALS BELOW
symb #read phased.matr site
regn poly
regn back $i1 Si2 $j1 regn watt $i4 $i5 $j1 symb jtmpl = 3
$jndgrd
$jndgrd
6
end$ loopi
end grph
nvcw 1 ttl 1
Phased Array Simulation c Change colour of certain materials
map watr 3
map poly 6
c Create lines around PZT pillars and material section boundaries symb jtmpl = 3
do loopi I 1 $numpzt
symb jtmp2 = $jtmpl + 1 draw node $12 $i2 $j$jtmpl $j$jtmp2
draw node $13 $i3 $j$jtmpl $j$jtmp2
draw node $12 $i3 $j$jtmp1 $j$jtmpl draw node $32 $13 $J$JtmP2 $j$jtmp2 symb jtmpl = $jtmpl + 2 end$ loopi
draw node $i2 $i2 $j1 $jndgrd draw node $i3 $i3 $j1 $jndgrd
draw node $i4 $i4 $j1 $jndgrd
c Create block to plot PZT and limited backing section blot al Sits Si4 $j1 $jndgrd
line off
swap off
revr x off
plot matr
end
*****
cBOUNDARY CONDITIONS
*****
c How the model interacts with the 'rest of the world'
c Commonly used for symmetry (SYMM) and infinite absorbing boundaries (ABSR) c If conditions are not specified. FREE (unconstrained) is assumed
c Can be specified as nodel indicies but more conveniently by model side. e.g.
c SIDE 1/xmin/imin - X-MINIMUM c SIDE 2/xmax/imax - X-MAXIMUM c SIDE 3/ymin/jmin - Y-MINIMUM c SIDE 4/ymax/ymax - Y-MAXIMUM c SIDE 5/zmin/kmin - Z-MINIMUM (3D only) o SIDE 6/zmax/kmax - Z-MAXIMUM (3D only)
****
7
boun
side xmin absr stnd side xmax absr stud
side ymin absr stnd
side ymax absr stnd end
c Zone model for efficiency zone * $11 $i2-1 $j1 Sjndgrd zone *$i2-1 $13++1 $J1 $jndgrd zone *$i3+1 514+1 $j1 $jndgrd zone * $i4+1 $i5 5j1 $jndgrd
*****************************************************************************************************
***
cDRIVING FUNCTION
***
c A number of predefined waveform functions can be accessed in PZFlex.
c The SINE wave option is used below, other examples include wavelets, gaussians, c and step functions. The manual details the function entries
c •e.g.
c func sine $freqint 1. 0, 1./* apply single cycle sinusoid
c/* at frequency of variable 'fregint
c-OR-c
c Data may also be read in from an external file with the DATA HIST command. e.g.
c from an oscilloscope measurement, and set as the function c •e.g.
e data hist drvl * function.dat/* Read contents of file 'function.dat'
c/* into array 'drvl'
c/* File should be in 2 column ASCII format
c/* as Time Amplitude
c func hist drvl/* Set FUNC equal to DRV1
*****************************************************************************************************
***
c SELECT DRIVING FUNCTION AND INSERT BELOW
c Select driving function - use ASCII file output from revinp.makecury data hist drvl * function.dat /* read data from function.dat into 'drvl' func hist drvl/* set func to equal drvl
/* could use drvl instead. but stick to func for consistency symb ascale = $devdpth/* area scaling factor for electrodes, set to model depth
***
8
***
c
c c c c c c c c c
CALCULATED PROPERTIES
•*********MKS************ ****#**********************************************#,k*********************
By default. Flex only calculates the minimum required data set. typically this means only velocities. This is done for memory efficiency.
Should other properites be required (e.g. displacements. stresses. strains. pressure).
then these must be requested by the CALC command The manual lists all these options
e.g.
calc
disp7* calculate displacements
Ares7* calculate pressure (average of stresses in solid) end
CHOOSE PROPERTIES TO CALCULATE AND INSERT BELOW
***
calc Ares disp
c max pres prmn pmlx '* also store pressure min and max at any time in arrays PRMN and PRMX end
*#
c
c
ELECTRICAL FIELD APPLICATION
c •Apply a load with either piezoelectric material or direct pressure application c •To apply load with Piezoelectric material:
c •Load applied as electrical conditions c Piezoelectric converts to mechanical energy
c •Must specify region within which piezoelectric effect occurs (electric window) c i.e. all piezoelectric elements and electrodes must be in the window
c electric window elements more 'expensive' than regular elements — minimise size c all materials inside electric window must have dielectric constant specified c •REMEMBER: Use ascale to scale the model if symmetry is being used c •e.g.
c symb ascale = 2./* ratio of model electrode size to
c/* actual electrode size
c •piez
c wndo $i1 $indgrd $j1 $jndgrd /* specify electric window c defn top $ascale
c node $indgrd $indgrd $j1 $jndgrd /* place active electrode on top of ceramic c •defn bet $ascale
c node $11 $i1 $j1 $jndgrd /* place gmd electrode on base of model c be top volt func 0.5/* apply voltage boundary condition to
c/* electrode 'top'. Signal applied defined by
c/* FUNC. scaled by 0.5 to account for symmetry
9
C c c C C
*****
c c c
bc bot grnd end
/* make bottom electrode ground
IF PIEZOELECTRIC MATERIALS USED. INSERT COMMANDS BELOW
*****
c Specify piezoelectric window and electrodes
c use 'nod2' subcommand to select nodes between 2 materials for electrode c Ensure all materials within electric window have associated permittivity piez
symb jendpz = $jend - 1
wndo $i2 $i3 $j2 $j$jendpz i* set electric window
/* could set around each pillar but gaps are small so no need c Use 'do' loop for active electrodes
symb jtrnpl = 3 do loopi I 1 $numpzt
symb jtmp2 = $jtmpl + 1 defn tp$I $ascale
node $i3 $i3 $j$jtmpl $j$jtmp2 symb jtrnpl = $jtmpl + 2 end$ loopi
c Ground electrode defn bot $ascale
node $i2 $i2 $j2 $j$jendpz c Apply drive function to pillars
c Each needs appropriate time shift for focussing and function weighting. The model c will fire the outer electrodes first and move towards the middle produce the focussing c effect.
symb numpzt2 = Hint ( $numpzt / 2 ) do loopi I 1 $numpzt
symb tshft$I = $tsep$I — $tfocus /* ca lc time shift for focus c Weighting for smooth decay towards edges follows half cosine wave shape
if ($1 le $numpzt2 ) then
symb wgt$I = $txpres * ( $wgtedge + ((1. - $wgtedge ) * ( cos (((1. * $1 / $numpzt2 ) * $pi ) + $pi ) + 1.) ) /2.)
else
symb J = $1- $numpzt2
symb wgt$I = $txpres * ( $wgtedge + ((1. - $wgtedge ) * ( cos ((1. * $J / $numpzt2 ) * $pi ) + 1.)) / 2. ) end if
bc tp$l volt func $wgt$1 $tshft$I /* apply drive to live electrodes on top half of txdr end$ loopi
bc bot gmd/* ground electrodes
end
cPRESSURE LOAD APPLICATION
10