
11.5. Fourth-Order Stationary Equations 1011
4
◦
. Boundary conditions are prescribed:
w = 0 at r = 1, ∂
rr
w +
ν
r
∂
r
w = 0 at r = 1.
These boundary conditions correspond to a hinged circular plate. (The deflection w and the
bending torque vanish on the support contour; ν is the Poisson ratio.)
Green’s function:
G(r, ϕ, ξ, η) = G
0
(r, ϕ, ξ, η) +
ξ(ξ
2
− 1)(r
2
− 1)
8π(ν + 1)
F
1,
ν + 1
2
;
ν + 3
2
; ξre
−i(ϕ−η)
+ F
1,
ν + 1
2
;
ν + 3
2
; ξre
i(ϕ−η)
− 1
,
where G
0
(r, ϕ, ξ, η) is the Green’s function in Item 2
◦
and F (a, b; c; z) is the hypergeo-
metric function.
5
◦
. Boundary conditions are prescribed:
w = 0 at r = 1, ∂
rr
w +
ν
r
+ γ
∂
r
w = 0 at r = 1.
These boundary conditions correspond ...