Clear["Global`*"]
Clear[Derivative]
Remove[r]
Remove[v]
d = 0.02;
I1 = Pi*d^4/64;
I2 = Pi*d^4/64;
Ip = Pi*d^4/32;
Dn = 1*10^6*Ip;
Dw1 = 7.8*10^6*I1;
Dw2 = 7.8*10^6*I2;
solution =
NDSolve[{Dn*
D[r[s], s,
s] - (Dw1 - Dw2)*(r[s]*(D[v[s], s, s]^2 + D[w[s], s, s]^2) -
D[v[s], s, s]*D[w[s], s, s]) == 0,
D[Dn*D[r[s],
s]*(D[w[s], s, s]*D[v[s], s] -
D[v[s], s, s]*D[w[s], s]) - (Dw1 -
Dw2)*(D[w[s], s]*D[D[v[s], s, s]*r[s], s] +
D[v[s], s]*D[D[w[s], s, s]*r[s], s]) +
Dw1*D[v[s], s, s, s]*D[v[s], s] +
Dw2*D[w[s], s, s, s]*D[w[s], s] + nam[s]*(1 + D[u[s], s]),
s] == 0,
D[ -Dn*D[r[s], s]*
D[w[s], s,
s] + (Dw1 - Dw2)*(D[D[w[s], s, s]*r[s], s] -
D[D[v[s], s, s]*r[s]^2, s] +
D[w[s], s, s, s]*
Integrate[D[v[s], s]*D[w[s], s, s], {s, 0, s}]) -
Dw2*(D[v[s], s, s, s] +
D[v[s], s]*(D[v[s], s, s]^2 + D[w[s], s, s]^2) +
nam[s]*D[v[s], s]), s] == 0,
D[-Dn*D[r[s], s]*
D[v[s], s,
s] + (Dw1 - Dw2)*(D[D[v[s], s, s]*r[s], s] -
D[D[w[s], s, s]*r[s]^2, s] -
D[v[s], s, s, s]*
Integrate[D[w[s], s]*D[v[s], s, s], {s, 0, s}]) -
Dw1*(D[w[s], s, s, s] +
D[w[s], s]*(D[v[s], s, s]^2 + D[w[s], s, s]^2) +
nam[s]*D[w[s], s]), s] == 0,
D[u[s], s] + 0.5*(D[w[s], s]^2 + D[v[s], s]^2) == 0,
v[0] == 0, w[0] == 0, u[0] == 0, Derivative[1][v][0] == 0,
Derivative[1][w][0] == 0, r[0] == 0,
Derivative[1][r][1] ==
0, -Dn*Derivative[1][r][1]*Derivative[1][w][1] -
Dw1*((v^\[Prime]\[Prime])[1] +
Derivative[1][v][
1]*(Derivative[1][v][1]*(v^\[Prime]\[Prime])[1] +
Derivative[1][w][1]*(w^\[Prime]\[Prime])[1])) == 0,
-Dw2*(w^\[Prime]\[Prime])[1] -
Derivative[1][w][
1]*(Dw1*Derivative[1][v][1]*(v^\[Prime]\[Prime])[1] +
Dw2*Derivative[1][w][1]*(w^\[Prime]\[Prime])[1]) == 0,
Dn*Derivative[1][r][1] + Dw1*
\!\(\*SuperscriptBox[\(v\),
TagBox[
RowBox[{"(", "3", ")"}],
Derivative],
MultilineFunction->None]\)[1]*Derivative[1][v][1] + Dw2*
\!\(\*SuperscriptBox[\(w\),
TagBox[
RowBox[{"(", "3", ")"}],
Derivative],
MultilineFunction->None]\)[1]*Derivative[1][w][1] +
nam[1]*(1 + Derivative[1][u][1]) == 0,
-Dn*Derivative[1][r][1]*(w^\[Prime]\[Prime])[1] - Dw1*(
\!\(\*SuperscriptBox[\(v\),
TagBox[
RowBox[{"(", "3", ")"}],
Derivative],
MultilineFunction->None]\)[1] +
Derivative[1][v][
1]*((w^\[Prime]\[Prime])[1]^2 + (v^\[Prime]\[Prime])[
1]^2)) + nam[1]*Derivative[1][v][1] == 0,
Dn*Derivative[1][r][1]*(v^\[Prime]\[Prime])[1] - Dw2*(
\!\(\*SuperscriptBox[\(w\),
TagBox[
RowBox[{"(", "3", ")"}],
Derivative],
MultilineFunction->None]\)[1] +
Derivative[1][w][
1]*((v^\[Prime]\[Prime])[1]^2 + (w^\[Prime]\[Prime])[
1]^2)) + nam[1]*Derivative[1][w][1] == 0}, {v[s], w[s],
r[s], u[s], nam[s]}, {s, 0, 1}];
跪求大佬，可加联系方式细说
