5.2.4. Effects of the Time Delay

The time delay induced by the dynamics of the shake table is a significant factor when conducting SSTT. According to previous studies [39], the time delay can be regarded as having a negative damping effect because it introduces additional energy into the SSTT system. GCR algorithms with *κ*1 = 1/2, *κ*2 = 1/4 and a time step of Δ*t* = 0.01 s are used to solve the EOM. Four time delays (*τ* = 0.01 s, 0.02 s, 0.05s, 0.1 s) are considered. Figure 15 presents the lateral displacements of the controlled structure with a mass ratio of 1% for different levels of time delay. The errors are calculated and listed in Table 6.

Figure 15 and Table 6 show that the time delay has a negative influence on the structural responses. Essentially, the errors increase with the increase in time delay. For *τ* = 0.01 s, 0.02 s, 0.05 s, the PD cases have the largest errors. The TMD case has relatively large errors close to 20% when *τ* = 0.1 s. The errors of the TLD and PTMD cases are less than 7% for all time delays. This means that the influence of the time delay on SSTT of the frame structure with the TLD and PTMD is less significant. However, if the time delay continues to increase, the negative impact will undoubtedly be enhanced and delay compensation techniques [40–42] will be required to eliminate any adverse effects.

**Figure 15.** Effects of the time delay on structural responses. (**a**) TMD; (**b**) TLD; (**c**) PD; (**d**) PTMD.


**Table 6.** Error indices of top lateral displacements with different time delays (unit: %).
