I'd like to as a question that might be very simple, but the thing is that I am completely new to Maple, and I have some homework I need to solve all of a sudden... I tried watching some tutorials and did a lot of search, but I just can't make this one work.
Briefly - my task is to derive the vibrational modal shapes of an annular disk (a circular disk with the center "missing"). So far what I know for sure is, that the radial term of the vibrational deflection is given as a linear combination of 4 types of bessel functions (Jn, Yn, In and Kn) - bessel functions of the 1st and second kind, and modified bessel functions of the 1st and second kind. Something like this:
Rmn(r) = A*Jn(kr) + B*Yn(kr) + C*In(kr) + D*Kn(kr).
Now, I need to find the values for k (the wavenumber), and the coeffitients B, C and D. I don't need coeffitient A, because I'll jus fix that to be 1. To do this, I have the following 4 boundary conditions:
1) Rmn(b) = Jn(kb) + B*Yn(kb) + C*In(kb) + D*Kn(kb) = 0
2) R'mn(b) = k(Jn'(kb) + B*Yn'(kb) + C*In'(kb) + D*Kn'(kb)) = 0
3) R''mn(a) = k2(Jn''(ka) + B*Yn''(ka) + C*In''(ka) + D*Kn''(ka)) = 0
4) R'''mn(a) = k3(Jn'''(ka) + B*Yn'''(ka) + C*In'''(ka) + D*Kn'''(ka)) = 0
So, four equations in four unknowns (k, B, C and D) - and I can't get it to work.
I did the following, and it gives me some totally wrong values (complex wavenumbers and such). Again, I am completely new to Maple, so I might have done something completely silly without even noticing...
b := 0.17e-1;
a := 0.8e-1;
n := 1;
R(r) := BesselJ(n,k r) + B BesselY(n, k r) + C BesselI(n, k r) + D BesselK(n, k r) ;
eq1 := R(b) = 0;
eq2 := eval(diff(R(x), x), x = b) = 0;
eq3 := eval(diff(R(x), x, x), x = a) = 0;
eq4 := eval(diff(R(x), x, x, x), x = a) = 0;
solve([eq1, eq2, eq3, eq4], [k, B, C, D])
What is it, that I am not doing right?
Thank you very very much for the help in advance!