i was wondering if somebody could help me solving the following two coupled differential equations...
$$\Delta u_{xx}(x)=dw_{xxx}(x)+\frac{K}{EA}\Delta u(x) \\$$ $$-EI_\infty w_{xxxx}(x)+2d\,EA\;\Delta u_{xxx}(x)+q(x)=0$$
where $q(x)$ is a given function e.g. $q(x)=q_0\sin(\frac{\pi x}{l})$
I tried the following step in Mathematica
DSolve[{-EIinf w''''[x] + 2 d EA du'''[x] + q[x] == 0, du''[x] == d w'''[x] +
K/EA du[x]}, {du, w}, x]
i also tried adding the boundary conditions to the DSolve function but it did not work either. The evaluation is going on "forever" that i have to abort it after some time.
FYI: i have following boundary conditions:
w[0]==0 | w[l]==0 | w''[0]==0 | w''[l]==0 | w''''[0]==q[0]/(EI0) | w''''[l]==q[l]/(EI0) | du'[0]==0 | du'[l]==0
If i transfer the two differential equations to one DE 6th order i get a analytical solution. Why isn't that the case if i solve both equations simultaneously? Thank you in advance!
NDSolve
to get a numerical solution. (And of course, you have then to include you initial and boundary conditions in the call toNDSolve
.) $\endgroup$q
is a known function. I voted to reopen because this question seems clear enough. $\endgroup$