## 2 Development of Novel Piezolectric Bricks  
A novel piezoelectric brick model made of a pair of LPCBs, a force amplifier, and a case, were designed and fabricated as displayed in Figure 1. The LPCB shown as Figure 1a includes a PCS with a length of \(l_{p}\), a fixed end, and a force arm segment (\(L\)) with a length of \(l\) and two adjustable length of \(a\). The PCS of the LPCB is a substrate bonded with one/two square piezoelectric patches. The substrate has a thickness of \(t_{1}\) and a width of \(l_{p}\), the piezoelectric patch has a side length of \(l_{p}\) and a thickness of \(t_{p}\). The fixed end and the force arm segment have a same thickness of \(t_{2}\) which is evidently bigger than \(t_{1}\) to make the strain of the LPCB focus on the PCS. Two LPCBs are connected by the force amplifier through the shaft which can be seen from Figure 1b. The piezoelectric brick can be formed by putting the structure shown in Figure 1b in the brick case and embedding two fixed ends tightly in the slots on the side wall, as displayed in Figure 1c. The force amplifier is connected to two covers by a shaft and the covers are hinged to the side wall of the case. The experimental specimen of this piezoelectric brick is revealed in Figure 1d.  
The force amplifier can amplify the vertical force of \(F(t)\) from footstep by a pair of boards inclining close to horizontal shown in Figure 2a in which the initial angle is satisfied to tan\(\theta=1/3\). According to the moment balance principle: \(F_{h}(t)L_{p}(t)=F_{v}(t)L_{h}(t)\)  
Figure 1: 1# piezoelectric brick made of a pair of LPCBs with one PCS. (**a**) A section view of an LPCB; (**b**) An assembly diagram; (**c**) A section view of 1# piezoelectric brick; (**d**) An experiment specimen of a piezoelectric brick.  
when \(L_{h}(t)>2\,L_{o}(t)\), the excitation force (\(F_{h}(t)\)) exerted on the force arm of the L-shaped beam can be amplified, namely, \(F_{h}(t)>F(t)\). The force amplification factor \(\mu\) (\(\mu=F_{h}/F\)) corresponding to different excited force is computed and listed in Figure 2b. It indicates that the force amplification factor \(\mu\) increases from 1.632 to 1.804 with the increase of the footstep excitation amplitude from 250 N to 500 N.  
Figure 3 depicts a piezoelectric brick similar to the one shown in Figure 1 except its LPCB includes two PCSs. As revealed in Figure 3a, the LPCB with two PCSs includes fixed end with a thickness of \(t_{2}\), PCSs with a substrate thickness of \(t_{1}\) and a PZT4 patch with a thickness of \(t_{p}\), a connecting segment with a thickness of \(t_{3}\), and a force arm segment with a thickness of \(t_{2}\). Similar to the preceding reason, the thicknesses of \(t_{2}\) and \(t_{3}\) are notably bigger than \(t_{1}\) to make the strain focus on the PCSs. Obviously, the PCS has a uniform bending moment which leads to the uniform surface strain of the PZT4 patches in the vibration process when the force exerts on the force arm of the LPCB. The PCS and the force arm segment shown in Figure 3a have a same size as those of the LPCB shown in Figure 1a. The corresponding experimental specimen of this piezoelectric brick is displayed in Figure 3b, which is similar to that shown in Figure 1d.  
Figure 3: 2# piezoelectric brick made of a pair of LPCBs with two PCSs. (**a**) A section view of an LPCB with two PCSs; (**b**) An experiment specimen of 2# piezoelectric brick.  
Figure 2: Physical simplified model of the force amplifier and the force amplification factor versus the footstep excitation amplitude. (**a**) Simplified model of force amplifier; (**b**) Force amplification factor (\(L=33.5\) mm).