Factors influencing equipment response in linear and nonlinear structures

Recent parameter studies involving floor response spectra (FRS) in nonlinear single degree-of-freedom (SDOF) structures, have consistently shown structure nonlinearity to lessen the floor spectra values in comparison to those seen for linear structural behavior, at floor spectra frequencies greater than the structure’s natural frequency ( Lin & Mahin, 1985 ). Some studies performed for linear and nonlinear multiple degree-of-freedom (MDOF) structures ( Newmark & Kennedy, 1979 ; Kennedy et al., 1981 , 1984 ; Wesley & Hashimoto, 1981 ; and Bumpus, 1981 ), however, have shown occasional increases as well as decreases in floor spectra at high frequencies (i.e., frequencies greater than the structure’s fundamental mode frequency) for nonlinear as compared to linear structural behavior. These MDOF structure studies, though, have typically emphasized behavior of the structure (forces, deformations, etc.) rather than the character of floor motions that affect equipment response. For some cases, the occasional increases in floor spectra for MDOF structures were quite substantial, where maximum floor response spectra values 2 to 3 times the corresponding linear-structure values were observed. The reasons for these floor spectra increases in nonlinear MDOF structures as opposed to the decreases always seen in SDOF structures have been mostly unexplained, and such increases have been difficult to predict qualitatively or quantitatively.