For the plate in Problem 9.4, assume a loading in the form of a concentrated force P(t) applied at..

For the plate in Problem 9.4, assume a loading in the form
of a concentrated force P(t) applied at (x = ξ, y = η). Find: a. The
frequency response function of the deflection b. The deflection caused by P(t)
= P0 cos ωt (P0 = constant) c. The deflection caused by P(t) = P0δ(t)
( P0 = constant)

Problem 9.4

Given a thin elastic plate with arbitrary boundary
conditions, assume the natural frequencies ωmn and natural modes Wmn are
known (Wmn form an orthogonal set). For a uniform loading p(x, y, t) = p(t),
determine: a. The frequency response functions of the deflection. b. The
deflection caused by p(t) = P0 cos ωt (P0 = constant) c. The deflection
caused by p(t) = P0δ(t) (P0 = constant) and w x( , y w , ) 0 0 = = ( , x
y, ) 0