modelCoaxialDirichlet

Coaxial Dirichlet Boundary-Value Problem
Diagram of CoaxialDirichletOpen the diagram
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Extends from Modelica.Icons.UnderConstruction (Icon for classes that are still under construction).

Information


Unm(r,phi,z) = Rn(kr) Z(kz) ei*m*phi .

Rn(kr) = An Jn(kr) + Bn Yn(kr) .

Rn(xni) = An Jn(xni) + Bn Yn(xni) = 0  -->  Rn(x) = Yn(xn0) Jn(x) - Jn(xn0) Yn(x) ...
Rn(xnj) = Yn(xn0) Jn(xnj) - Jn(xn0) Yn(xnj) = 0 .

xnj - xn0 = kj (b - a) ; or rather, xn0 (xnj/xn0 - 1) = kj a (b/a - 1) .

So for each mode (n,j), xn0 needs to be adjusted until xnj/xn0 = b/a ; then kj = xn0/a = xnj/b .

Rn(kr) = Cn In(kr) + Dn Kn(kr) .

Rn(xn0) = Cn In(xn0) + Dn Kn(xn0) = 0  -->  Rn(x) = Kn(xn0) In(x) - In(xn0) Kn(x) .

Parameters

TypeNameDefaultDescription
Realx11
Realx220

Components

TypeNameDefaultDescription
Modelica.Blocks.Sources.Rampx_ramp
GNU_ScientificLibrary.Blocks.specfunc.Bessel_Inbessel_In
GNU_ScientificLibrary.Blocks.specfunc.Bessel_Knbessel_Kn
Blocks.specfunc.Bessel_Jnbessel_Jn
GNU_ScientificLibrary.Blocks.specfunc.Bessel_Ynbessel_Yn