Spatial structures are also used as evacuation facilities in the event of a disaster, so social demands for human life protection and function maintenance are high. Therefore, there are many studies on applications of response reduction mechanisms to spatial structures.
 TMD is cited as one of the vibration control methods for spatial structures. There are many examples of applications of TMD. A high-rise building and a floor slab with large span in architecture field, a cable stayed bridge and a suspension bridge in civil engineering, for example. The response reduction effects in these examples are verified.
 TMD has the advantage that the damping effect can be obtained by the mass of 1 to 3% of structure. In addition, TMD is fit for the vibration control of spatial structures because it is possible to install TMDs by a single supporting point. Therefore, there are many studies on spatial structures with TMDs. The authors have verified the influences of number and position of installed TMDs, the period and phase characteristics of earthquake motions, input directions of input waves and free vibration characteristics of spatial structures on seismic response reduction effects. However, when TMD is actually applied to structures, construction error of target structures, calculation error of natural periods, manufacturing error of TMDs and the like may also affect the response reduction effects by TMD. In addition, there is no study in which the influence of change of design parameters for TMD installed on spatial structures is investigated systematically. From these backgrounds, the purpose of this study is investigation of the influences of the change of designed values of TMDs on seismic response reduction effects by plural TMDs for cylindrical lattice shell roofs.
 From the numerical results, it is concluded as follows.
 1) The effects of change of mass ratio on response reduction effects are small regardless of half open angle, magnification of out-of-plane stiffness of roof and input wave. The robustness of response reduction effect by TMD with respect to the change in mass ratio is high.
 2) The response reduction effect decreases due to the change in the damping ratio. In addition, the influence of increase and decrease of damping ratio on the response reduction effect varies depending on half open angles, magnification of out-of-plane stiffness of roof and input waves.
 3) As the damping ratio becomes smaller than the optimum value, the stronger asymmetry appears in the shapes of maximum response distributions. Therefore, the nodes in which the maximum vertical responses become larger than those in non-vibration control appear.
 4) The effects of the change of frequency ratio on response reduction effects are large regardless of half open angle, magnification of out-of-plane stiffness of roof and input wave. As the frequency ratio becomes smaller than the optimum value, the response reduction effect decreases in comparison with the frequency ratio becoming larger than that.