ABSTRACT
Many practical structures are composed of bodies of revolution containing bulkheads. These structures have complicated mass distribution due to machinery and internal equipment. However, each normal component of a natural mode of the structure can be approximated by (r → p, q):
q s q z A q B q p z
rn rn pq pq( ) ( , ) ( cos sin )sin≡ = +ϕ ϕ ϕ pi
(12.1)
Expression 12.1 is a half-range Fourier expansion in the longitudinal direction (which is chosen as the distance along the surface of the structure) between bulkheads, which are distance ℓ apart, and a full-range Fourier expansion in the peripheral (φ) direction. The boundary conditions at the bulkheads will not be satis˜ed exactly by the sin (ppiz/ℓ) term, but Arnold and Warburton1 have demonstrated that if an equivalent length is used, sin (ppiz/ℓ) can be used to approximate the mode shapes.
