AbstractThis paper investigates the effect of flexibly attached secondary systems (FSS) on the dynamic behavior of primary structures (PS) under harmonic and seismic ground excitations. An FSS affects the main structure during ground excitation differently than a secondary system that is rigidly attached to it. Small displacements in the FSS are used to derive the equations of motion that define the behavior of the PS and FSS. The analytical formulation presented is validated by a finite element (FE) study conducted in SAP2000. The influence of mass ratio, tuning frequency ratio, and excitation frequency ratio on the dynamic behavior of the PS is investigated. The results show that the combined system (PS+FSS) behaves as a modified single degree of freedom (SDOF) structure at higher tuning frequency ratios. The dynamic response of the structure is independent of the mass ratio at low tuning frequency ratio of FSS. Under seismic excitations, the flexible structure’s response reduces considerably as the mass ratio increases, compared to a stiff structure at a higher tuning frequency ratio. When the tuning frequency ratio is equal to one, smaller mass ratios of FSS increase the seismic performance of the stiff structure. A design methodology is proposed to measure the spectral acceleration of the primary structure by incorporating the effect of FSS in the design response spectrum. An analysis of the tuning frequency ratio and mass ratio on the modified design spectrum is also presented. Finally, the proposed design methodology is validated with an existing study.