/// <summary>
/// Computes the eigenfrequencies.
/// Formula 2.91
/// </summary>
/// <returns>The eigenfrequencies.</returns>
/// <param name="plate">Plate.</param>
/// <param name="P">P.</param>
/// <param name="Q">Q.</param>
public static Complex[][] ComputeSimplySupportedPlateEigenfrequencies(Plate plate, int P, int Q)
{
Complex[][] wp = ComplexMatrix.Create2D(P, Q);
for (int p = 1; p <= P; p++)
{
for (int q = 1; q <= Q; q++)
{
double multiplier = Math.Sqrt((Math.Pow(Math.PI, 4) * plate.B) / (plate.H * plate.Rho));
wp[p - 1][q - 1] = multiplier * (Math.Pow(Math.Pow(p / plate.L_x, 2) + Math.Pow(q / plate.L_y, 2), 2));
}
}
return(wp);
}
/// <summary>
/// Computes the acoustic wave expansion.
/// Formula 2.36
/// </summary>
/// <returns>The acoustic wave expansion.</returns>
/// <param name="room">Room.</param>
/// <param name="f">F.</param>
/// <param name="c">C.</param>
/// <param name="M">M.</param>
/// <param name="N">N.</param>
public static Complex[][] ComputeAcousticWaveExpansion(Room room, double f, double c, int M, int N)
{
Complex ka = ComputeAcousticWaveNumber(room, f, c);
Complex[][] kz = ComplexMatrix.Create2D(M, N);
for (int m = 0; m < M; m++)
{
for (int n = 0; n < N; n++)
{
kz[m][n] = Complex.Sqrt(Complex.Pow(ka, 2.0)
- Complex.Pow(m * Math.PI / room.L_x, 2.0)
- Complex.Pow(n * Math.PI / room.L_y, 2.0));
}
}
return(kz);
}
/// <summary>
/// Computes the norms of room wave functions.
/// Formula 2.86
/// </summary>
/// <returns>The norms of room wave functions.</returns>
/// <param name="room">Room.</param>
/// <param name="M">M.</param>
/// <param name="N">N.</param>
public static Complex[][] ComputeNormsOfRoomWaveFunctions(Room room, int M, int N)
{
var result = ComplexMatrix.Create2D(M, N);
for (int m = 0; m < M; m++)
{
for (int n = 0; n < N; n++)
{
result[m][n] = GaussLegendreRule.Integrate((x, y) =>
{
return(Math.Pow(ComputePhiRoom(room, m, n, x, y), 2.0));
}, 0.0, room.L_x, 0.0, room.L_y, 5);
}
}
return(result);
}
// Helper
private static Complex[][] ComputeC1OrC2(Room room, double f, double c, int M, int N, double sign)
{
var result = ComplexMatrix.Create2D(M, N);
var kz = ComputeAcousticWaveExpansion(room, f, c, M, N);
for (int m = 0; m < M; m++)
{
for (int n = 0; n < N; n++)
{
Complex t = sign * kz[m][n] * room.L_z;
result[m][n] = Complex.Cos(t)
+ Complex.ImaginaryOne * Complex.Sin(t);
}
}
return(result);
}
/// <summary>
/// Computes the norms of the plate modes.
/// Formula 2.102
/// </summary>
/// <returns>The norms of the plate modes.</returns>
/// <param name="room">Room.</param>
/// <param name="M">M.</param>
/// <param name="N">N.</param>
public static Complex[][] ComputeNormsOfThePlateModes(Plate plate, int P, int Q,
Func <Plate, int, int, double, double, double> func)
{
var result = ComplexMatrix.Create2D(P, Q);
for (int p = 1; p <= P; p++)
{
for (int q = 1; q <= Q; q++)
{
result[p - 1][q - 1] = GaussLegendreRule.Integrate((x, y) =>
{
return(Math.Pow(func(plate, p, q, x, y), 2.0));
}, 0.0, plate.L_x, 0.0, plate.L_y, 5);
}
}
return(result);
}
/// <summary>
/// Computes the F.
/// Formula 2.74
/// </summary>
/// <returns>The f.</returns>
/// <param name="room">Room.</param>
/// <param name="M">M.</param>
/// <param name="N">N.</param>
public static Complex[][] ComputeF(Room room, int M, int N)
{
Complex[][] result = ComplexMatrix.Create2D(M, N);
if (room.IsSource)
{
for (int m = 0; m < M; m++)
{
for (int n = 0; n < N; n++)
{
result[m][n] = ComputePhiRoom(room, m, n, room.X_s, room.Y_s);
}
}
}
else
{
throw new Exception("F does not apply to non-source room.");
}
return(result);
}
/// <summary>
/// Computes the C3.
/// Formula 2.96 and 2.98
/// </summary>
/// <returns>The c3.</returns>
/// <param name="room">Room.</param>
/// <param name="f">F.</param>
/// <param name="c">C.</param>
/// <param name="M">M.</param>
/// <param name="N">N.</param>
public static Complex[][] ComputeC3(Room room, double f, double c, double rhoAir, int M, int N)
{
Complex[][] result = ComplexMatrix.Create2D(M, N);
Complex[][] kz = ComputeAcousticWaveExpansion(room, f, c, M, N);
if (room.IsSource)
{
// Formula 2.96
Complex[][] N1 = ComputeNormsOfRoomWaveFunctions(room, M, N);
Complex[][] F = ComputeF(room, M, N);
for (int m = 0; m < M; m++)
{
for (int n = 0; n < N; n++)
{
Complex t = kz[m][n] * Math.Abs(room.Z_s - room.L_z);
Complex firstTerm = Complex.Cos(t) + Complex.ImaginaryOne * Complex.Sin(t);
Complex secondTerm = 2 * Math.PI * f * rhoAir / (kz[m][n] * N1[m][n]);
result[m][n] = 0.5 * firstTerm * secondTerm * F[m][n];
}
}
}
else if (room.IsReceiving)
{
throw new Exception("Receiving room does not need C3");
}
else
{
// Formula 2.98
Complex[][] Ni = ComputeNormsOfRoomWaveFunctions(room, M, N);
for (int m = 0; m < M; m++)
{
for (int n = 0; n < N; n++)
{
Complex firstTerm = -1.0 * Complex.Pow(2 * Math.PI * f, 2.0) / (kz[m][n] * Ni[m][n]);
Complex secondTerm = 1.0 / Complex.Sin(kz[m][n] * room.L_z);
result[m][n] = firstTerm * secondTerm;
}
}
}
return(result);
}
/// <summary>
/// Computes the plate room projection coefficients.
/// Formula 2.87
/// </summary>
/// <returns>The plate room projection coefficients.</returns>
/// <param name="plate">Plate.</param>
/// <param name="room">Room.</param>
/// <param name="M">M.</param>
/// <param name="N">N.</param>
/// <param name="P">P.</param>
/// <param name="Q">Q.</param>
public static Complex[][][][] ComputePlateRoomProjectionCoefficients(Plate plate, Room room, int M, int N, int P, int Q)
{
var result = ComplexMatrix.Create4D(M, N, P, Q);
for (int m = 0; m < M; m++)
{
for (int n = 0; n < N; n++)
{
for (int p = 1; p <= P; p++)
{
for (int q = 1; q <= Q; q++)
{
result[m][n][p - 1][q - 1] = GaussLegendreRule.Integrate((x, y) =>
{
return(ComputePhiRoom(room, m, n, x + plate.DeltaX, y + plate.DeltaY)
* ComputePhiPlateSimplySupported(plate, p, q, x, y));
}, 0.0, plate.L_x, 0.0, plate.L_y, 5);
}
}
}
}
return(result);
}