I'm trying to plot it but I cannot, where it keeps running without giving any plots for more than 40 mins, and I'm quite sure about code...
The issue that I don't know to how to debug the code at all, so please debug it for me if u can or fix my code if it has an issue for u
(*Geometrical data*)
d = 2*10^-6; h = 2*10^-6; b = 2*10^-6; l = 200*10^-6; EE = 1.66*10^11; Eps = 8.854*10^-12; ρ = 2332;
(*Numerical problem data*)
Subscript[α, 2] = (6*Eps*l^4)/(EE*h^3*
d^3); Subscript[V, pull] = Sqrt[1.72/Subscript[α, 2]]; Subscript[V, dc] = (Range[100] - 1)*Subscript[V, pull]/100;
Solut = {};
(*Number of modes*)
n = 3;
(*Normalized frequencies*)
Subscript[ω, 1] = 3.51602; Subscript[ω, 2] = 22.0345; \Subscript[ω, 3] = 61.6972; Subscript[σ, 1] = 0.7341; \Subscript[σ, 2] = 1.0185; Subscript[σ, 3] = 0.9992;
(*Modeshapes*)
Subscript[ϕ, 1][x_] = Cosh[Sqrt[Subscript[ω, 1]] x] - Cos[Sqrt[Subscript[ω, 1]] x] - Subscript[σ,
1]*(Sinh[Sqrt[Subscript[ω, 1]] x] -
Sin[Sqrt[Subscript[ω, 1]] x]);
Subscript[ϕ, 2][x_] = Cosh[Sqrt[Subscript[ω, 2]] x] - Cos[Sqrt[Subscript[ω, 2]] x] - Subscript[σ,
2]*(Sinh[Sqrt[Subscript[ω, 2]] x] -
Sin[Sqrt[Subscript[ω, 2]] x]);
Subscript[ϕ, 3][x_] = Cosh[Sqrt[Subscript[ω, 3]] x] - Cos[Sqrt[Subscript[ω, 3]] x] - Subscript[σ,
3]*(Sinh[Sqrt[Subscript[ω, 3]] x] -
Sin[Sqrt[Subscript[ω, 3]] x]);
(*The derived eq for Cantilver beam *)
SysEq1 = (\!\(\*SubsuperscriptBox[\(∫\), \(0\), \(1\)]\(\(\*SubscriptBox[\(ϕ\), \(j\)]\)[x] \*SuperscriptBox[\((1 - \*UnderoverscriptBox[\(∑\), \(l = 1\), \(n\)]\*SubscriptBox[\(u\), \(l\)] \(\*SubscriptBox[\(ϕ\), \(l\)]\)[x])\), \(2\)] \((\*UnderoverscriptBox[\(∑\), \(i = 1\), \(n\)]\*SubscriptBox[\(u\), \(i\)] \*SuperscriptBox[SubscriptBox[\(ω\), \(i\)], \(2\)] \(\*SubscriptBox[\(ϕ\), \(i\)]\)[x])\) \[DifferentialD]x\)\) -
Subscript[α, 2] Subscript[V, DC]^2 \!\(\*SubsuperscriptBox[\(∫\), \(0\), \(1\)]\(\(\*SubscriptBox[\(ϕ\), \(j\)]\)[x] \[DifferentialD]x\)\)) /. j -> 1 ;
SysEq2 = (\!\(\*SubsuperscriptBox[\(∫\), \(0\), \(1\)]\(\(\*SubscriptBox[\(ϕ\), \(j\)]\)[x] \*SuperscriptBox[\((1 - \*UnderoverscriptBox[\(∑\), \(l = 1\), \(n\)]\*SubscriptBox[\(u\), \(l\)] \(\*SubscriptBox[\(ϕ\), \(l\)]\)[x])\), \(2\)] \((\*UnderoverscriptBox[\(∑\), \(i = 1\), \(n\)]\*SubscriptBox[\(u\), \(i\)] \*SuperscriptBox[SubscriptBox[\(ω\), \(i\)], \(2\)] \(\*SubscriptBox[\(ϕ\), \(i\)]\)[x])\) \[DifferentialD]x\)\) -
Subscript[α, 2] Subscript[V, DC]^2 \!\(\*SubsuperscriptBox[\(∫\), \(0\), \(1\)]\(\(\*SubscriptBox[\(ϕ\), \(j\)]\)[x] \[DifferentialD]x\)\)) /. j -> 2 ;
SysEq3 = (\!\(\*SubsuperscriptBox[\(∫\), \(0\), \(1\)]\(\(\*SubscriptBox[\(ϕ\), \(j\)]\)[x] \*SuperscriptBox[\((1 - \*UnderoverscriptBox[\(∑\), \(l = 1\), \(n\)]\*SubscriptBox[\(u\), \(l\)] \(\*SubscriptBox[\(ϕ\), \(l\)]\)[x])\), \(2\)] \((\*UnderoverscriptBox[\(∑\), \(i = 1\), \(n\)]\*SubscriptBox[\(u\), \(i\)] \*SuperscriptBox[SubscriptBox[\(ω\), \(i\)], \(2\)] \(\*SubscriptBox[\(ϕ\), \(i\)]\)[x])\) \[DifferentialD]x\)\) -
Subscript[α, 2] Subscript[V, DC]^2 \!\(\*SubsuperscriptBox[\(∫\), \(0\), \(1\)]\(\(\*SubscriptBox[\(ϕ\), \(j\)]\)[x] \[DifferentialD]x\)\)) /. j -> 3 ;
For[k = 2, k <= 100, k++,
Subscript[V, DC] = Subscript[V, dc][[k]]
Sol = Solve[{SysEq1 == 0, SysEq2 == 0, SysEq3 == 0}, {Subscript[u, 1],
Subscript[u, 2], Subscript[u, 3]} ];
W = 0;
For[m = 1, m <= n, m++,
W = W + Subscript[u, m] *Subscript[ϕ, m][1] /. Sol[[1, m]];
];
W = Re[W ];
AppendTo[Solut, {Subscript[V, DC], W}];
];
Subscript[graphic, 1] = ListPlot[Solut, PlotStyle -> PointSize[0.02], PlotRange -> All, AxesLabel -> {"\!\(\*SubscriptBox[\(V\), \(DC\)]\)",
"\!\(\*SubscriptBox[\(W\), \(Max\)]\)"}]
k
- you could write a singleSysEqn[k_]:= ...
and a singleϕ[k_,x_]:=
. Also please don't use subscripts. $\endgroup$Subscript[V, dc] = (Range[100] - 1)*Subscript[V, pull]/100;
- why is $V_{DC}$ a range and yet you're squaring it later ? $\endgroup$NIntegrate
and make theu[i]
parameters, but it's still too slow with theSolve
later on to find the right u[1],u[2],u[3]. An NSolve doesn't work either - and an approach I tried with NMinimize is too slow and has too much error. I can't do much more. $\endgroup$