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Classes_Absorption_Matrices.cs
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Classes_Absorption_Matrices.cs
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////'Pachyderm-Acoustic: Geometrical Acoustics for Rhinoceros (GPL) by Arthur van der Harten
////'
////'This file is part of Pachyderm-Acoustic.
////'
////'Copyright (c) 2008-2015, Arthur van der Harten
////'Pachyderm-Acoustic is free software; you can redistribute it and/or modify
////'it under the terms of the GNU General Public License as published
////'by the Free Software Foundation; either version 3 of the License, or
////'(at your option) any later version.
////'Pachyderm-Acoustic is distributed in the hope that it will be useful,
////'but WITHOUT ANY WARRANTY; without even the implied warranty of
////'MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
////'GNU General Public License for more details.
////'
////'You should have received a copy of the GNU General Public
////'License along with Pachyderm-Acoustic; if not, write to the Free Software
////'Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
//using System;
//using System.Collections.Generic;
//using System.Text;
//using MathNet.Numerics;
//namespace Pachyderm_Acoustic
//{
// namespace AbsorptionModels
// {
// public static class Explicit_TMM
// {
// //class StateMatrix_Fluid : SparseMatrix
// //{
// // public StateMatrix_Fluid(Complex p, Complex u)
// // : base(2, 1)
// // {
// // this[0, 0] = p;
// // this[0, 1] = u;
// // }
// // public Complex Impedance()
// // {
// // return this[0, 0] / this[0, 1];
// // }
// //}
// //class StateMatrix_Porous : SparseMatrix
// //{
// // public StateMatrix_Porous(Complex V1s, Complex V3s, Complex v3f, Complex sig33s, Complex sig13s, Complex sig33f)
// // : base(6, 1)
// // {
// // this[0, 0] = V1s;
// // this[0, 1] = V3s;
// // this[0, 2] = v3f;
// // this[0, 3] = sig33s;
// // this[0, 4] = sig13s;
// // this[0, 5] = sig33f;
// // }
// //}
// public static SparseMatrix PorousMatrix(bool Rigid, double d, Complex k, Complex sin_theta, double freq, double porosity, double tortuosity, double YoungsModulus, double PoissonRatio, double Viscous_Characteristic_Length, double flow_resistivity, double FrameDensity, double Thermal_Permeability_0, double AmbientMeanPressure)
// {
// double w = Utilities.Numerics.PiX2 * freq;
// double v = Biot_Porous_Absorbers.v();
// double FrameShear = AbsorptionModels.Biot_Porous_Absorbers.Shear_Modulus(YoungsModulus, PoissonRatio);
// double kb = 2 * FrameShear * (PoissonRatio + 1) / (3 * (1 - 2 * PoissonRatio));
// double BulkMod_Frame = AbsorptionModels.Biot_Porous_Absorbers.BulkMod_Solid(YoungsModulus, PoissonRatio);
// Complex Kf = Biot_Porous_Absorbers.BulkMod_Fluid(w, AmbientMeanPressure, porosity, Thermal_Permeability_0);//AmbientMeanPressure / (1 - (gamma - 1) / (gamma * alpha));
// Complex LameL = YoungsModulus * PoissonRatio / ((1 + PoissonRatio) * (1 - 2 * PoissonRatio));
// Complex LameMu = YoungsModulus / (2 * (1 + PoissonRatio));
// Complex delta21 = w * w * FrameDensity;
// Complex delta22 = w * w * FrameDensity;
// Complex delta23 = delta21 / LameMu;
// delta21 /= (LameL + 2 * LameMu);
// delta22 /= (LameL + 2 * LameMu);
// //Taken from Lauriks, et. al., 1990.
// double rho12 = Biot_Porous_Absorbers.rho12(porosity, tortuosity);
// double rhoa = Biot_Porous_Absorbers.rhoA(rho12);
// double Viscous_Permeability = Biot_Porous_Absorbers.Viscous_Permeability(flow_resistivity);
// Complex Gw = Biot_Porous_Absorbers.G_w(tortuosity, porosity, Viscous_Permeability, Viscous_Characteristic_Length, freq, v);
// //Complex rho12eff = Biot_Porous_Absorbers.rho12eff(rhoa, porosity, flow_resistivity, Gw, freq);
// Complex rho22eff = Biot_Porous_Absorbers.rho22eff(rhoa, porosity, flow_resistivity, Gw, freq);
// Complex rho11eff = Biot_Porous_Absorbers.rho11eff(FrameDensity, rhoa, porosity, flow_resistivity, Gw, freq);
// Complex P, Q, R;
// if (!Rigid)
// {
// //Universal (Limp) Frame Case:
// P = ((1 - porosity) * (1 - kb / BulkMod_Frame) * BulkMod_Frame + porosity * BulkMod_Frame * kb / Kf) / (1 - porosity - kb / BulkMod_Frame + porosity * BulkMod_Frame / Kf);
// Q = (1 - porosity - kb / BulkMod_Frame) * porosity * BulkMod_Frame / (1 - porosity - kb / BulkMod_Frame + porosity * BulkMod_Frame / Kf);
// R = porosity * porosity * BulkMod_Frame / (1 - porosity - kb / BulkMod_Frame + porosity * BulkMod_Frame / Kf);
// }
// else
// {
// //Rigid Frame Case:
// P = 4 * FrameShear / 3 + kb + (porosity * porosity) * Kf / porosity;
// R = porosity * Kf;
// Q = Kf * (1 - porosity);
// }
// Complex kt = k * sin_theta;
// Complex k13 = Complex.Sqrt(delta21 - kt * kt);
// Complex k23 = Complex.Sqrt(delta22 - kt * kt);
// Complex k33 = Complex.Sqrt(delta23 - kt * kt);
// Complex Mu1 = Q * delta21 - w * w * rho11eff / (w * w * rho22eff - R * delta21);
// Complex Mu2 = Q * delta22 - w * w * rho11eff / (w * w * rho22eff - R * delta22);
// Complex Mu3 = FrameShear * delta23 - w * w * rho11eff / (w * w * rho22eff);
// SparseMatrix GH = GammaH_P(kt, w, d, FrameShear, P, Q, R, k13, k23, k33, Mu1, Mu2, Mu3);
// SparseMatrix G0T = Gamma0T_P(kt, w, FrameShear, P, Q, R, k13, k23, k33, Mu1, Mu2, Mu3);
// return GH * G0T;
// }
// public static SparseMatrix GammaH_P(Complex kt, double w, double h, double ShearModulus, Complex P, Complex Q, Complex R, Complex k13, Complex k23, Complex k33, Complex Mu1, Complex Mu2, Complex Mu3)
// {
// SparseMatrix M = new SparseMatrix(6,6);
// h *= -1;
// //double w = Utilities.Numerics.PiX2 * freq;
// //Complex LameL = FrameElasticity * PoissonRatio / ((1 + PoissonRatio) * (1 - 2 * PoissonRatio));
// //Complex LameMu = FrameElasticity / (2 * (1 + PoissonRatio));
// //Complex delta21 = w * w * FrameDensity;
// //Complex delta22 = w * w * FrameDensity;
// //Complex delta23 = delta21 / LameMu;
// // delta21 /= (LameL + 2 * LameMu);
// //delta22 /= (LameL + 2 * LameMu);
// ////Complex k1 = k * Complex.Cos(theta);
// ////Complex k3 = k * Complex.Sin(theta);
// //Complex k13 = Complex.Sqrt(delta21 - kt * kt);
// //Complex k23 = Complex.Sqrt(delta22 - kt * kt);
// //Complex k33 = Complex.Sqrt(delta23 - kt * kt);
// ////Complex Damping1 = LameMu * (k13 * k13 - k0 * k0);
// ////Complex Damping2 = 2 * LameMu * k0;
// //double rho12 = Biot_Porous_Absorbers.rho12(porosity, tortuosity);
// //double rhoa = Biot_Porous_Absorbers.rhoA(rho12);
// //double Viscous_Permeability = Biot_Porous_Absorbers.Viscous_Permeability(flow_resistivity);
// //double v = Biot_Porous_Absorbers.v();
// //Complex Gw = Biot_Porous_Absorbers.G_w(tortuosity, porosity, Viscous_Permeability, characteristic_length, freq, v);
// //Complex rho12eff = Biot_Porous_Absorbers.rho12eff(rhoa, porosity, flow_resistivity, Gw, freq);
// //Complex rho22eff = Biot_Porous_Absorbers.rho22eff(rhoa, porosity, flow_resistivity, Gw, freq);
// //Complex rho11eff = Biot_Porous_Absorbers.rho11eff(FrameDensity, rhoa, porosity, flow_resistivity, Gw, freq);
// //Complex Kf = AmbientMeanPressure / (1 - (gamma - 1) / (gamma * alpha));
// //Complex P = 4 * FrameShear / 3 + kb + (phi_1 * phi_1) * Kf / porosity;
// //Complex R = porosity * Kf;
// //Complex Q = Kf * (1 - porosity);
// //Complex Mu1 = Q * delta21 - w * w * rho11eff / (w * w *rho22eff - R *delta21);
// //Complex Mu2 = Q * delta22 - w * w * rho11eff / (w * w * rho22eff - R * delta22);
// //Complex Mu3 = FrameShear * delta23 - w * w * rho11eff / (w * w * rho22eff);
// Complex D1 = (P + Q * Mu1) * (kt * kt + k13 * k13) - 2 * ShearModulus * kt * kt;
// Complex D2 = (P + Q * Mu2) * (kt * kt + k23 * k23) - 2 * ShearModulus * kt * kt;
// Complex E1 = (R * Mu1 + Q) * (kt * kt + k13 * k13);
// Complex E2 = (R * Mu2 + Q) * (kt * kt + k23 * k23);
// //Complex Mu1 =
// //Taken from Lauriks, et. al 1990.
// M[0, 0] = w * kt * Complex.Cos(k13 * h);
// M[0, 1] = -Complex.I * k13 * Complex.Sin(k13 * h);
// M[0, 2] = -Complex.I * k13 * Mu1 * Complex.Sin(k13 * h);
// M[0, 3] = -D1 * Complex.Cos(k13 * h);
// M[0, 4] = 2 * Complex.I * ShearModulus * kt * k13 * Complex.Sin(k13 * h);
// M[0, 5] = -E1 * Complex.Cos(k13 * h);
// M[1, 0] = -Complex.I * w * kt * Complex.Sin(k13 * h);
// M[1, 1] = w * k13 * Complex.Sin(k13 * h);
// M[1, 2] = w * k13 * Mu1 * Complex.Sin(k13 * h);
// M[1, 3] = Complex.I * D1 * Complex.Sin(k13 * h);
// M[1, 4] = -2 * ShearModulus * kt * k13 * Complex.Cos(k13 * h);
// M[1, 5] = Complex.I * E1 * Complex.Sin(k13 * h);
// M[2, 0] = w * kt * Complex.Cos(k23 * h);
// M[2, 1] = -Complex.I * k23 * Complex.Sin(k23 * h);
// M[2, 2] = -Complex.I * k23 * Mu2 * Complex.Sin(k23 * h);
// M[2, 3] = -D2 * Complex.Cos(k23 * h);
// M[2, 4] = 2 * Complex.I * ShearModulus * kt * k23 * Complex.Sin(k23 * h);
// M[2, 5] = -E2 * Complex.Cos(k23 * h);
// M[3, 0] = -Complex.I * w * kt * Complex.Sin(k23 * h);
// M[3, 1] = w * k23 * Complex.Sin(k23 * h);
// M[3, 2] = w * k23 * Mu2 * Complex.Sin(k23 * h);
// M[3, 3] = Complex.I * D1 * Complex.Sin(k23 * h);
// M[3, 4] = -2 * ShearModulus * kt * k23 * Complex.Cos(k23 * h);
// M[3, 5] = Complex.I * E2 * Complex.Sin(k23 * h);
// M[4, 0] = Complex.I * k33 * Complex.Sin(k33 * h);
// M[4, 1] = w * kt * Complex.Cos(k33 * h);
// M[4, 2] = w * kt * Mu3 * Complex.Cos(k33 * h);
// M[4, 3] = 2 * Complex.I * ShearModulus * k33 * kt * Complex.Sin(k33 * h);
// M[4, 4] = ShearModulus * (k33 * k33 - kt * kt) * Complex.Cos(k33 * h);
// M[4, 5] = 0;
// M[5, 0] = -w * k33 * Complex.Cos(k33 * h);
// M[5, 1] = -Complex.I * w * kt * Complex.Sin(k33 * h);
// M[5, 2] = -Complex.I * 2 * kt * Mu3 * Complex.Sin(k33 * h);
// M[5, 3] = -2 * ShearModulus * k33 * kt * Complex.Cos(k33 * h);
// M[5, 4] = -Complex.I * ShearModulus * (k33 * k33 - kt * kt) * Complex.Sin(k33 * h);
// M[5, 5] = 0;
// return M;
// }
// public static SparseMatrix Gamma0T_P(Complex kt, double w, double ShearModulus, Complex P, Complex Q, Complex R, Complex k13, Complex k23, Complex k33, Complex Mu1, Complex Mu2, Complex Mu3)
// {
// SparseMatrix M = new SparseMatrix(6,6);
// Complex A1 = -(P - 2 * ShearModulus + Mu1 * Q) * kt * kt - 2 * ShearModulus * k13 * k13;
// Complex A2 = -(P - 2 * ShearModulus + Mu2 * Q) * kt * kt - 2 * ShearModulus * k23 * k23;
// Complex B1 = -(Q + R * Mu1) * kt * kt;
// Complex B2 = -(Q + R * Mu2) * kt * kt;
// Complex X = B1 * A2 - B2 * A1;
// Complex Y = X - 2 * ShearModulus * w * w * kt * kt * (B1 - B2);
// Complex Mu21 = Mu2 - Mu1;
// Complex Mu31 = Mu3 - Mu1;
// M[0, 0] = -B2 * 2 * ShearModulus * w * kt / (Complex.I * Y);
// //M[0,1] =
// //M[0,2] =
// M[0, 3] = -B2 * (1 / X + 2 * ShearModulus * w * w * kt * kt * (B1 - B2)) / (X * Y);
// //M[0,4] =
// M[0, 5] = 1 + B2 * ((A1 / X) - (1 - A1 * (B1 - B2) / X) * (2 * ShearModulus * w * w * kt * kt) / Y) / B1;
// //M[1,0] =
// M[1, 1] = -((1 + Mu1 / Mu21) - 2 * w * w * kt * kt * (1 - Mu31 / Mu21) / (kt * kt)) / (Complex.I * k13);
// M[1, 2] = 1 / (k13 * Mu21);
// //M[1,3] =
// M[1, 4] = -w * kt * (1 - (Mu31 / Mu21)) / (k13 * ShearModulus * kt * kt);
// //M[1,5] =
// M[2, 0] = (B1 * 2 * ShearModulus * w * kt) / (Complex.I * Y);
// //M[2,1] =
// //M[2,2] =
// M[2, 3] = B1 * (1 / X + (B1 - B2) * (2 * ShearModulus * w * w * kt * kt) / (X * Y));
// //M[2,4] =
// M[2, 5] = -(A1 / X - 2 * ShearModulus * w * w * kt * kt * (1 - A1 * (B1 - B2) / X) / Y);
// //M[3,0] =
// M[3, 1] = (Mu1 / Mu21 + 2 * (w * w * kt * kt * Mu31) / (kt * kt * Mu21)) / (Complex.I * k23); ///Shown in paper as simply alpha... alpha2 = k23 in Atalla's work...
// M[3, 2] = -1 / (Complex.I * k23 * Mu21);
// //M[3,3] =
// M[3, 4] = -(w * w * kt * kt * Mu31) / (k23 * ShearModulus * kt * kt * Mu21);
// //M[3,5] = M[0,0] =
// //M[0,4] =
// M[4, 1] = -(2 * w * w * kt * kt) / (Complex.I * kt * kt);
// //M[4,2] =
// //M[4,3] =
// M[4, 4] = 1 / (ShearModulus * kt * kt);
// //M[4,5] =
// M[5, 0] = X / (Complex.I * k33 * Y);
// //M[5,1] =
// //M[5,2] =
// M[5, 3] = w * kt * (B1 - B2) / (k33 * Y);
// //M[5,4] =
// M[5, 5] = w * kt * (1 - A1 * (B1 - B2) / X) / (k33 * Y * B1);
// return M;
// }
// public static SparseMatrix FluidMatrix(double h, Complex kz, double freq, double rho)
// {
// SparseMatrix M = new SparseMatrix(2,2);
// Complex kzh = kz * h;
// Complex sinkzh = Complex.Sin(kzh);
// Complex coskzh = Complex.Cos(kzh);
// double pr2 = Utilities.Numerics.PiX2 * freq * rho;
// M[0, 0] = coskzh;
// M[0, 1] = (Complex.I * kz / pr2) * sinkzh;
// M[1, 0] = (Complex.I * pr2 / kz) * sinkzh;
// M[1, 1] = coskzh;
// return M;
// }
// public static SparseMatrix Solid_Matrix(Complex ksolid, Complex kprev, Complex SinTheta, double h, double freq, double density, double PoissonRatio, double ModulusElasticity)
// {
// h *= -1;
// //Complex k_inc_x = kfluid * SinTheta;
// //Complex k_inc_x =
// double w = Utilities.Numerics.PiX2 * freq;
// Complex LameL = ModulusElasticity * PoissonRatio / ((1 + PoissonRatio) * (1 - 2 * PoissonRatio));
// Complex LameMu = ModulusElasticity / (2 * (1 + PoissonRatio));
// Complex delta21 = w * w * density;
// Complex delta23 = delta21 / LameMu;
// delta21 /= (LameL + 2 * LameMu);
// Complex k1 = ksolid * SinTheta;
// //Complex k3 = Complex.Sqrt( - k1 * k1);
// Complex k13 = Complex.Sqrt(delta21 - k1 * k1);
// Complex k33 = Complex.Sqrt(delta23 - k1 * k1);
// Complex D1 = LameMu * (k13 * k13 - kprev * kprev); //ksolid could also be k_air, or k of the previous layer (not clear).
// Complex D2 = 2 * LameMu * ksolid;
// Complex cosk13h = Complex.Cos(k13 * h);
// Complex sink13h = Complex.Sin(k13 * h);
// Complex cosk33h = Complex.Cos(k33 * h);
// Complex sink33h = Complex.Sin(k33 * h);
// Complex wk1 = w * k1;
// Complex wk13 = w * k13;
// Complex wk33 = w * k33;
// Complex D1k13 = D1 * k13;
// Complex D1k33 = D1 * k33;
// Complex D2k13 = D2 * k13;
// Complex D2k33 = D2 * k33;
// SparseMatrix MH = new SparseMatrix(4, 4);
// MH[0, 0] = wk1 * cosk13h;
// MH[0, 1] = -Complex.I * wk13 * cosk13h;
// MH[0, 2] = -D1 * cosk13h;
// MH[0, 3] = Complex.I * D2k13 * sink13h;
// MH[1, 0] = -Complex.I * wk1 * sink13h;
// MH[1, 1] = wk13 * cosk13h;
// MH[1, 2] = Complex.I * D1 * sink13h;
// MH[1, 3] = -D2k13 * cosk13h;
// MH[2, 0] = Complex.I * wk33 * sink33h;
// MH[2, 1] = wk1 * cosk33h;
// MH[2, 2] = Complex.I * D2k33 * sink33h;
// MH[2, 3] = D1 * cosk33h;
// MH[3, 0] = -wk33 * cosk33h;
// MH[3, 1] = -Complex.I * wk1 * sink33h;
// MH[3, 2] = -D2k33 * cosk33h;
// MH[3, 3] = -Complex.I * D1 * sink33h;
// SparseMatrix M0 = new SparseMatrix(4, 4);
// M0[0, 0] = 2 * k1 / (w * delta23);
// M0[0, 3] = (k33 * k33 - k1 * k1) / (w * k33 * delta23);
// M0[1, 1] = (k33 * k33 - k1 * k1) / (w * k13 * delta23);
// M0[1, 2] = (k1) / (w * delta23);
// M0[2, 0] = -1 / (LameMu * delta23);
// M0[2, 3] = -k1 / (LameMu * k33 * delta23);
// M0[3, 1] = -k1 / (LameMu * k13 * delta23);
// M0[3, 2] = 1 / (LameMu * delta23);
// return MH * M0;
// }
// public static SparseMatrix InterfacePP(double porosity_of_1, double porosity_of_2)
// // : base(6, 6)
// {
// SparseMatrix M = new SparseMatrix(6, 6);
// double phi2_1 = porosity_of_2 / porosity_of_1;
// double phi1_2 = porosity_of_1 / porosity_of_2;
// M[0, 0] = 1;
// M[1, 1] = 1;
// M[2, 1] = 1 - phi2_1;
// M[2, 2] = phi2_1;
// M[3, 3] = 1;
// M[3, 5] = 1 - phi1_2;
// M[4, 4] = 1;
// M[5, 5] = phi1_2;
// return M;
// }
// public static SparseMatrix InterfaceSF_Solid()
// //: base(3, 4)
// {
// SparseMatrix M = new SparseMatrix(3, 4);
// M[0, 1] = 1;
// M[1, 2] = 1;
// M[2, 3] = 1;
// return M;
// }
// public static SparseMatrix InterfaceSF_Fluid()
// //: base(3, 2)
// {
// SparseMatrix M = new SparseMatrix(3,2);
// M[0, 1] = -1;
// M[1, 0] = 1;
// return M;
// }
// public static SparseMatrix Interfacepf_Porous(double porosity)
// //: base(4, 6)
// {
// SparseMatrix M = new SparseMatrix(4, 6);
// M[0, 1] = 1 - porosity;
// M[0, 2] = porosity;
// M[1, 3] = 1;
// M[2, 4] = 1;
// M[3, 5] = 1;
// return M;
// }
// public static SparseMatrix Interfacepf_Fluid(double porosity)
// //: base(4, 2)
// {
// SparseMatrix M = new SparseMatrix(4, 2);
// M[0, 1] = -1;
// M[1, 0] = 1 - porosity;
// M[3, 0] = porosity;
// return M;
// }
// public static SparseMatrix Interfacesp_Solid()
// //: base(5, 4)
// {
// SparseMatrix M = new SparseMatrix(5, 4);
// M[0, 0] = 1;
// M[1, 1] = 1;
// M[2, 1] = 1;
// M[3, 2] = 1;
// M[4, 3] = 1;
// return M;
// }
// public static SparseMatrix Interfacesp_Porous()
// {
// SparseMatrix M = new SparseMatrix(5,6);
// M[0, 0] = 1;
// M[1, 1] = 1;
// M[2, 2] = 1;
// M[3, 3] = 1;
// M[3, 5] = 1;
// M[4, 4] = 1;
// return M;
// }
// public static SparseMatrix Interfacepi_Porous()
// //: base(4, 6)
// {
// SparseMatrix M = new SparseMatrix(4, 6);
// M[0, 1] = 1;
// M[1, 2] = 1;
// M[2, 3] = 1;
// M[2, 5] = 1;
// M[3, 4] = 1;
// return M;
// }
// public static SparseMatrix Interfacepi_Thinplate()
// {
// SparseMatrix M = new SparseMatrix(4,2);
// M[0, 1] = -1;
// M[1, 1] = -1;
// M[2, 0] = 1;
// return M;
// }
// public static SparseMatrix RigidTerminationP()
// {
// SparseMatrix M = new SparseMatrix(3, 6);
// M[0, 0] = 1;
// M[1, 1] = 1;
// M[2, 2] = 1;
// return M;
// }
// public static SparseMatrix RigidTerminationF()
// {
// SparseMatrix M = new SparseMatrix(1, 2);
// M[0, 1] = 1;
// return M;
// }
// public static SparseMatrix RigidTerminationS()
// {
// SparseMatrix M = new SparseMatrix(2, 4);
// M[0, 0] = 1;
// M[1, 1] = 1;
// return M;
// }
// //public static SparseMatrix GlobalTransfer()
// //{
// // MathNet.Numerics.LinearAlgebra.Matrix<SparseMatrix> D0 = new
// //}
// }
// }
//}