I have a list of plot in a list called modes. I am interested in knowing whether this list is unique or not, meaning all the plots are different from one another. how to do this?
ClearAll["Global`*"]
Clear[b]
SetDirectory[NotebookDirectory[]];
se1 = 1;
L = 4;
z[1] = L/4;
z[2] = (2*L)/4;
z[3] = (3*L)/4;
Y = 2*10^11;(*Youngs modulus *)
Iyy = 8.333*10^-6;(*area moment of inertia*)
A = 0.1^2;(*cross sectional area*)
\[Rho] = 7850;
kb = (Y*Iyy)/L^3;
n = 3; (* number of springs *)
W[1] = a[1]*Sin[b*x] + a[2]*Cos[b*x] + a[3]*Sinh[b*x] + a[4]*Cosh[b*x];
W[2] = a[5]*Sin[b*(x - z[1])] + a[6]*Cos[b*(x - z[1])] +
a[7]*Sinh[b*(x - z[1])] + a[8]*Cosh[b*(x - z[1])];
W[3] = a[9]*Sin[b*(x - z[2])] + a[10]*Cos[b*(x - z[2])] +
a[11]*Sinh[b*(x - z[2])] + a[12]*Cosh[b*(x - z[2])];
W[4] = a[13]*Sin[b*(x - z[3])] + a[14]*Cos[b*(x - z[3])] +
a[15]*Sinh[b*(x - z[3])] + a[16]*Cosh[b*(x - z[3])];
w = Piecewise[{{W[1], x <= z[1]}, {W[2], z[1] <= x <= z[2]}, {W[3],
z[2] <= x <= z[3]}, {W[4], x >= z[3]}}];
(CANTILEVER BC)
boundary[i_, j_] :=
Module[ {bc},
bc1 = {W[i] /. {x -> 0}, (D[W[i], {x, 1}]) /. {x -> 0}, (D[
W[j], {x, 2}]) /. {x -> L}, ((D[W[j], {x, 3}]) /. {x -> L})};
bc = bc1]
countinuity[i_, j_] :=
Module[{eq},
eq1 = {((W[i] /. x -> z[i]) - (W[j] /.
x -> z[i])), (((D[W[i], {x}]) /.
x -> z[i]) - ((D[W[j], {x}]) /.
x -> z[i])), (((D[W[i], {x, 2}]) /.
x -> z[i]) - ((D[W[j], {x, 2}]) /.
x -> z[i])), (((D[W[i], {x, 3}]) /.
x -> z[i]) - ((D[W[j], {x, 3}]) /. x -> z[i])) +(K[i]*
W[i] /. x -> z[i])}; eq = eq1 ]
e1 = boundary[1, 4];
e2 = countinuity[1, 2];
e3 = countinuity[2, 3];
e4 = countinuity[3, 4];
comb = Tuples[{0, 1*^12}, 3];
eq = Flatten[{e1, e2, e3, e4}];
var = Table[a[i], {i, 1, Length[eq]}];
R = Normal@CoefficientArrays[eq, var][[2]];
R = R /. {K[1] -> K1, K[2] -> K2, K[3] -> K3};
P = 4 b^15 (32 b^9 + 4 b^3 K1 K2 Cosh[2 b] - 4 b^3 K1 K3 Cosh[2 b] -
4 b^3 K2 K3 Cosh[2 b] + 2 b^3 K1 K2 Cosh[4 b] +
2 b^3 K1 K3 Cosh[4 b] + 2 b^3 K2 K3 Cosh[4 b] +
2 Sin[3 b] (-2 K1 K2 K3 Cosh[
b] + (8 b^6 (K1 - K3) + K1 K2 K3) Cosh[3 b] +
4 b^3 K2 (K1 + (3 K1 - K3) Cosh[2 b]) Sinh[b]) -
3 K1 K2 K3 Sinh[2 b] +
2 Cos[b] (-4 b^3 K1 K2 Cosh[
3 b] + (8 b^6 (K1 - K3) + K1 K2 K3) Sinh[b] -
2 K1 K2 K3 Sinh[3 b]) +
2 Cos[3 b] (4 b^3 K1 K2 Cosh[b] +
2 K1 K2 K3 Sinh[b] + (K1 K2 K3 + 8 b^6 (-K1 + K3)) Sinh[
3 b]) + 2 Sin[
b] ((K1 K2 K3 + 8 b^6 (-K1 + K3)) Cosh[b] +
2 K2 (K1 K3 Cosh[3 b] +
b^3 (3 (K1 + K3) Sinh[b] + (-K1 + K3) Sinh[3 b]))) +
8 b^6 K2 Sinh[4 b] + 2 K1 K2 K3 Sinh[4 b] +
Sin[2 b] (-3 K1 K2 K3 + 2 K1 K2 K3 Cosh[2 b] -
3 K1 K2 K3 Cosh[4 b] +
8 b^3 (-K1 K2 + 2 K1 K3 + K2 K3) Sinh[2 b] -
2 b^3 (K1 K2 + 2 K1 K3 + K2 K3) Sinh[4 b]) +
Cos[2 b] (4 b^3 (-K1 K2 + (K1 + K2) K3) +
4 b^3 (K2 K3 + K1 (K2 + K3)) Cosh[4 b] +
2 K1 K2 K3 Sinh[2 b] + (K1 K2 K3 + 8 b^6 (K1 + K3)) Sinh[
4 b]) + Sin[
4 b] (-8 b^6 K2 +
2 K1 K2 K3 + (K1 K2 K3 - 8 b^6 (K1 + K3)) Cosh[
2 b] - (K1 K2 K3 + 8 b^6 (K1 + K2 + K3)) Cosh[4 b] -
2 b^3 (K2 K3 + K1 (K2 + 2 K3)) Sinh[2 b] -
4 b^3 (K2 K3 + K1 (K2 + K3)) Sinh[4 b]) +
Cos[4 b] (-2 b^3 (K2 K3 + K1 (K2 + K3)) -
4 b^3 (K2 K3 + K1 (K2 + K3)) Cosh[2 b] + 32 b^9 Cosh[4 b] -
3 K1 K2 K3 Sinh[
2 b] + (-K1 K2 K3 + 8 b^6 (K1 + K2 + K3)) Sinh[4 b]));
f[k1_, k2_, k3_, beta_] :=
Module[{m}, K1 = k1; K2 = k2; K3 = k3; r = beta; s1 = P;
s2 = NSolve[s1 == 0 && 0 < b < 30]; s3 = N[b /. s2];
s4 = s3[[r]]; {uu, ww, vv} =
SingularValueDecomposition[R /. b -> s4];
NN = Last[Transpose[vv]]; sub1 = Flatten[{var, b}];
sub2 = Flatten[{NN, s4}];
m = w /. Table[sub1[[i]] -> sub2[[i]], {i, 1, Length[sub1]}];
Return[m]];
comb = Tuples[{0, 1*^12}, 3]
g[i_, r_] :=
Module[{s5}, spring = comb[[i]]; a1 = spring[[1]]; a2 = spring[[2]];
a3 = spring[[3]]; a4 = r; s5 = f[a1, a2, a3, a4]]
mode1 = Table[g[i, 1], {i, 1, 2^n}];
mode2 = Table[g[i, 2], {i, 1, 2^n}];
mode3 = Table[g[i, 3], {i, 1, 2^n}];
modes = Flatten[{mode1, mode2, mode3}];
Table[Plot[modes[[i]], {x, 0, L}, PlotRange -> All], {i, 1,
Length[modes]}]
