DSolve[c^2 D[p {r, \[Theta], z} e^(I\[Omega]t) , {t, 2}] ==
D[p {r, \[Theta], z} e^(I\[Omega]t), {r, 2}] +
D[p {r, \[Theta], z} e^(I\[Omega]t), {\[Theta], 2}] +
D[p {r, \[Theta], z} e^(I\[Omega]t), {z, 2}],
r == a + b Cos[n\[Theta]] Cos[\[Omega]t] +
c Cos[Subscript[k, x] x] Cos[n\[Theta]] +
dCos[Subscript[k, x] x] Cos[n\[Theta]] Cos[\[Omega]t],
D[r (\[Theta], z, t) {t, 1}] ==
Integrate[D[p {r, \[Theta], z} e^(I\[Omega]t), {r, 1}],
t], p, r, \[Theta], z, t]
D[p {r, \[Theta], z} e^(I\[Omega]t), {r, 2}] +
D[p {r, \[Theta], z} e^(I\[Omega]t), {\[Theta], 2}] +
D[p {r, \[Theta], z} e^(I\[Omega]t), {z, 2}],
r == a + b Cos[n\[Theta]] Cos[\[Omega]t] +
c Cos[Subscript[k, x] x] Cos[n\[Theta]] +
dCos[Subscript[k, x] x] Cos[n\[Theta]] Cos[\[Omega]t],
D[r (\[Theta], z, t) {t, 1}] ==
Integrate[D[p {r, \[Theta], z} e^(I\[Omega]t), {r, 1}],
t], p, r, \[Theta], z, t]