Pd. Spanos et A. Majed, A RESIDUAL FLEXIBILITY APPROACH FOR DECOUPLED ANALYSIS OF SYSTEMS OF COMBINED COMPONENTS, Journal of vibration and acoustics, 118(4), 1996, pp. 682-686
A residual flexibility approach for the analysis of systems involving
multiple components subjected to dynamic loading is presented. The rea
ctive forces at the junctions of the components are computed directly
without synthesis of component modes or determination of system modes.
This is accomplished by expressing the displacements at the junction
coordinates of the components in terms of the retained component modes
and a first-order account of the residual flexibility of the unretain
ed modes. Once the components are represented in this manner, the requ
irements of displacement compatibility and force equilibrium at the ju
nction coordinates are enforced. This leads to a set of junction-sized
simultaneous algebraic equations for the unknown forces, similar info
rm to that of the flexibility formulation in statics; this is done by
invoking the Newmark integration algorithm. The computed reactive forc
es at a given time point are used to integrate the equations of motion
of the individual components separately far that time point, hence th
e terminology decoupled analysis. The new method compares well with tr
aditional Component-Mode Synthesis approach for a nonclassically dampe
d fixed-fixed beam consisting of two classically damped canilevered be
am components.