Analytical Simulation of Dynamically Equivalent Components

Abstract

The inertia concept of modal mass was developed to provide a consistent methodology for establishing an analytically equivalent dynamic model of any discrete section within a complex piping network. The multidegree of freedom system is reduced to several multiple excitation single degree of freedom (SDOF) systems representing its modal masses and modal stiffnesses. The multiple excitation residual mass and residual stiffness matrices were also formulated. The combination of modal mass-modal stiffness SDOF systems and residual mass-residual stiffness matrices can simulate the complete dynamic characteristic of any desired portion of the piping network. This technique was extended to cover substructuring applications, and was proved mathematically to be equivalent to the conventional modal synthesis formulation.