*HEADING EC288AFAT: AC2D8 ELEMENTS Tube with nonreflective end-condition and *TIE constraint. Part of the air in the tube is modelled with continuum elements with air properties. ************************************************ *NODE, Nset=ODB_NSET 1,0.0, 41,0.5, 101,0.0,0.0125 141,0.5,0.0125 201,0.0,0.025 241,0.5,0.025 *NGEN,NSET=NALL 1,41 101,141 201,241 *NCOPY,OLDSET=NALL,NEWSET=NSOL,CHANGENUMBER=1000,SHIFT 0.0,0.0,0.0 1.0,0.0,0.0,0.0,1.0,0.0 *NSET,NSET=SAMPLE,GENERATE 1,41 *NSET,NSET=LOAD1 1,201 *NSET,NSET=LOAD2 101, ** First 5 elements are acoustic *ELEMENT,TYPE=AC2D8 1,1,3,203,201,2,103,202,101 *ELGEN,ELSET=ACOU 1,5,2,1 ** Then 5 continuum elements *ELEMENT,TYPE=CPS8 6,1011,1013,1213,1211,1012,1113,1212,1111 *ELGEN,ELSET=STRUCT 6,5,2,1 ** Next 10 elements are acoustic *ELEMENT,TYPE=AC2D8 11,21,23,223,221,22,123,222,121 *ELGEN,ELSET=ACOU 11,10,2,1 *ELSET,ELSET=NONREF 20, ************************************************ *SURFACE,TYPE=ELEMENT,NAME=ACR 5,S2 *SURFACE,TYPE=ELEMENT,NAME=SOL 6,S4 *SURFACE,TYPE=ELEMENT,NAME=SOR 10,S2 *SURFACE,TYPE=ELEMENT,NAME=ACL 11,S4 *TIE,NAME=CRAVAT SOL,ACR ACL,SOR ************************************************ ** ** Acoustic Element Properties ** *SOLID SECTION,MATERIAL=AIR,ELSET=ACOU 40., *MATERIAL,NAME=AIR *DENSITY 1.21, *ACOUSTIC MEDIUM,BULK MODULUS 0.1424E6, ************************************************ ** ** Continuum Element Properties ** *SOLID SECTION,MATERIAL=AIRSOLID,ELSET=STRUCT 40., *MATERIAL,NAME=AIRSOLID *DENSITY 1.21, *ELASTIC 0.1424E6, ************************************************ ** ** ANALYTIC SOLUTION ** ** ** at freq=100, ** Impedance: Z = root( K_f rho ) ** = 415.095 ** Propagation constant ** b = i (omega/K_f) Z ** = 1.8315 i ** ** Solution: with nonreflective end, ** Complex pressure ** p(x) = Z v(0) exp( - b x) ** i.e. |p(x)| = |Z v(0)| exp ( - Re(b) x) ** = 415.09 ** ** Arg(p) = Arg(Z) - Im(b) x ** ppor = - 104.94 x ** ************************************************ *Elset,Elset=ODB_ESET ACOU, STRUCT *Nset, Nset=ODB_NSET ODB_NSET, NALL, SAMPLE, LOAD1 LOAD2, ************************************************ *STEP *STEADY STATE DYNAMIC,DIRECT 100, ** For reference, these IMPEDANCE PROPERTY ** constants could be used to specify the nonreflecting ** condition at the given frequency: ** 1/k1= 0, 1/c1= 2.40908E-03 ** 0, 1/Z ** *IMPEDANCE NONREF,I2 ** Conditions at x=0 : Define the source inward accel ** to be a = A_tributary * omega * i, so v (inward) = 1. ** The loaded nodes have tributary areas of 1/3 & 4/3. ** The angular frequency omega = 2 * pi * f ** *CLOAD,LOAD CASE=2 LOAD1, 8, 104.7197551 LOAD2, 8, 418.8790204 ** simulation of uniaxial condition *BOUNDARY NSOL,2,2 *NODE PRINT, NSET=SAMPLE COORD,POR,PPOR *OUTPUT,FIELD,OP=ADD,FREQUENCY=9999 *ELEMENT OUTPUT,ELSET=STRUCT S *NODE OUTPUT,NSET=SAMPLE POR, *OUTPUT,HISTORY,OP=ADD,FREQUENCY=9999 *NODE OUTPUT,NSET=SAMPLE POR, *ELEMENT OUTPUT,ELSET=STRUCT COORD,S11 *END STEP