Effect of Base-Level Inerters on the Higher Mode Response of Uplifting Structures

Performance-based seismic design and assessment of rocking timber buildings equipped with inerters

“…Moreover, previous analytical studies have demonstrated that higher vibration modes can be coupled with the rocking motion and excited by the forces generated during impact, regardless of the frequency of the excitation [26]. This behaviour has been experimentally observed in steel rocking structures [27], it has been predicted to occur also in rocking timber structures, albeit with lower amplitudes due to their typically softer set down [28] and was speculated to lie behind some of the large peak acceleration amplifications anticipated in multi-storey panellized timber buildings with rocking motion components [29]. Wiebe and Christopolous examined the alternative of using multiple rocking sections over the height of a base-rocking system, thus allowing the designer to control the higher mode amplification of moments above the base of the wall [25].…”

Uniform risk spectra for rocking structures

“…Prestressing the restrainers would also change the uplifting force (Figure 1B). 15–32 A more stable system can also be achieved without changing the uplifting force by extending the block ends in a curved shape (Figure 1C) 33,34 or by adding damping or inerter devices 35–39 …”

“…[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] A more stable system can also be achieved without changing the uplifting force by extending the block ends in a curved shape (Figure 1C) 33,34 or by adding damping or inerter devices. [35][36][37][38][39] Among other reasons, rocking isolation has not been widely adopted in practice because of its high nonlinearity. 40 Small changes in the excitation or any imperfection in the system can lead to a completely different response.…”

Response of seismic isolated structures with supplemental rotational inertia

“…Following the pioneering work in Japan and the subsequent theoretical and experimental studies by Smith and coworkers 1,8,9 who established, within the context of linear networks, the analogy of the inerter to the electric capacitor; a growing number of publications have proposed the use of inerters for the response modification of buildings by installing them at all floor levels 10–13 ; at selected levels 14–18 or at the ground level, either within the context of protecting a first soft‐story, 3,19,20 or within the context of enhancing a seismic isolation system 21–24 . More recently, the use of inerters has been proposed to control the higher modes of uplifting structures 25 …”

“…[21][22][23][24] More recently, the use of inerters has been proposed to control the higher modes of uplifting structures. 25 F I G U R E 1 Classical two-degree-of-freedom seismic isolation structure 26,27 with supplemental rotational inertia at the isolation system This study was partly motivated from the ability of inerters to control the response of flexible and yielding structures 3,19,20 and partly from their known property to eliminate the participation of higher modes. 10,24 Our study shows that while a small amount of supplemental rotational inertia is needed to eliminate the participation of the second mode of the two-degree-of-freedom isolated structure shown in Figure 1, the effect of this elimination is marginal on the structural response, since the participation of the second mode is invariably small even when isolation systems without inerters are used.…”