## 35

Note that Equation 3.91 is identical to Equation 3.58 when f (or p) approaches zero. The motion equation of a system may be expressed as

where [M] is the mass matrix, [C] is the damping matrix, [K] is the stiffness matrix, and {F(t)} represents the matrix involving externally applied forces or ground motion.

Note that Equation 3.93 is identical to Equation 3.34c of lumped-mass formulation. The major difference is that the mass matrix of the lumped-mass model is mostly a diagonal matrix associated with d.o.f. of side sway (the inertia force due to structural joint rotation is relatively small and thus negligible). However, the mass matrix of the consistent-mass model is a full matrix associated with joint rotations and side sways as shown in Equations 3.92 of a typical constituent member of a system. Thus, the computation effort for the lumped-mass model is much less than that for consistent mass because the dimension of the mass and stiffness matrices of a lumped-mass system can be significantly reduced through matrix condensation by eliminating rotational d.o.f.

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