Optimal inertia lumping from modal mass matrices for structural dynamics Original Research Article

An optimal inertia lumping formulation using modal mass matrices obtained from structural analysis is presented, enabling recovery of lumped inertia information even when substructuring has been employed. The method is implemented with a commercial optimization program and uses reduced mass and stiffness formulations employed in commercial finite element analysis programs. The result is lumped inertia models of complex flexible bodies for use in structural dynamics, including flexible multibody dynamic simulation. A method for dealing with nondifferentiability of repeated eigenvalues that arise in the optimization process is derived and implemented in the proposed formulation. Numerical examples are presented to validate the method, relative to conventional mass lumping approaches.