ssc-367 - Ship Structure Committee

deflection and stability parameters are known. The deflected form of
this equivalent structure is a cantilever, while typical structure
members and appurtenancesdeflect as a simply supported beam. Hence,
the equivalent structure has a mode shape given by:
y’(x) =
a- a cos(~)
while the real structure has a mode shape given by:
y(x) =
a sin(~)
Substituting into the effective mass formulation,we obtain:
m=
f~[m][a sin ~]2dx
J: [a - a cos ~]2dx
where:
a = maximum modal amplitude
Integration of the above equation leads to the relationship:
i= 2.205 m for simple supported span
i= 1.654 m for fixed supports
ii=
m for cantilever span
Damping Ratio
Welded marine structures exhibit very low values of structural
damping. Vibratory energy is typically dissipated by material and
aerodynamic (radiation) damping. Individual members subjected to
large vibratory motions dissipate energy through the connections to
the main structure largely as dispersive bending and compression
D-4