The uncoupling criteria for subsystem seismic analysis

Abstract

This paper discusses the uncoupling effects of a subsystem from the system based on frequency, mode shape and response variations. The two-mass system is first used to study the problem, and a closed form solution of the frequency variation is derived for the two resonant masses with different mass ratios. Since the coupled and uncoupled analyses have a different number of modes, proper selection of modes for frequency variation check is also discussed. The resonance effect of a coupled analysis is shown in the mode shapes. Thus, the closed form solution of mode shapes for two resonant masses is also derived as a function of mass ratio. Since the response variation is a function of input, the response variation of a two-mass system subjected to white noise input is discussed. Since multiple degree of freedom systems are used in the majority of cases, the results of the two-mass system are extended to the multiple degree of freedom systems by the concept of normal modes. Each normal mode can be represented by a single degree of freedom system with equivalent modal mass and equivalent modal spring. Different equations were used in the past to define the equivalent modal masses depending on the objective of the analysis. The method of defining the equivalent modal mass which takes into account the location of a subsystem, is recommended. Once the equivalent two-mass system of the multiple degree of freedom systems and subsystems is derived, the frequency, mode shape, and response variations of the multiple degree of freedom system and subsystem can be assessed. The above coupling/uncoupling analysis is applied to two different situations. The first one is the building-equipment interaction usually with small mass ratios. The second one is the equipment-equipment interaction where the mass ratio can be large. Here, the equipment includes piping systems, pressure vessels, pumps, etc. The uncoupling analysis of the first case is required because the equipment information is not available during the building analysis. The uncoupling analysis of the second case is required due to practical need to reduce the size of the model. The recommendations of the uncoupling analysis of both cases are presented.