## 2 Experimental Program
### Test Setup and Procedure  
The pulsation method was applied to measure the dynamic characteristics of the specimen. Vibration pickup sensors (China Orient Institute of Noise & Vibration, Beijing, China) were installed on the center of each floor, which took the earth pulse as the vibromotive source as shown in Figure 5. The vibration pickup sensors and signal acquisition system were shown in Figure 5d; two measurements were taken for accurate results. The sensors were applicable for structures with low natural frequency at the range of 2 Hz to 100 Hz. Due to the symmetry of the cross section, vibration modes in only one horizontal direction were measured. As shown in Figure 6, data collected from the sensors indicated a resonance phenomenon at \(f_{0}\) = 5.942 Hz, which showed the primary frequency. Figure 4: (**a**) Shear wall with an opening; (**b**) details of Shear wall (unit: mm). Figure 3: (**a**) Beam cross-section; (**b**) beam-column connection (unit: mm). Figure 2: (**a**) Column section and dimension; (**b**) dimension of steel skeleton (unit: mm). Furthermore, modal analyses of higher order frequencies based on the measured datas were conducted by the Data Acquisition and Signal Processing (DASP) program. The principle and procedure are shown as the follows [31; 32]. Dynamic characteristics for structure can be expressed by the dynamic equation. Figure 5: (**a**) Arrangement of vibration pick-up instruments; (**b**) the steel skeleton; (**c**) measurement instrument; (**d**) details of the instrument. Figure 6: Natural frequency. \[\dot{M}\ddot{x}+\dot{C}\dot{x}+\dot{K}x=\mathbf{f}(t) \tag{1}\]  
where \(\mathbf{M}\), \(\mathbf{C}\) and \(\mathbf{K}\) are matrices of mass, damping and stiffness, respectively; \(x\), \(\dot{x}\) and \(\ddot{x}\) are the response vectors of displacement, velocity and acceleration, respectively; \(\mathbf{f}(t)\) is the vector of exciting force. Laplace transform method is applied on Equation (1). \[\Big{[}\mathbf{M}s^{2}+\mathbf{C}s+\mathbf{K}\Big{]}\mathbf{X}(s)=\mathbf{F}(s) \tag{2}\]  
where \(s\) is a complex variable. The matrix of generalized impedance \(\mathbf{Z}(s)\) can be expressed as:  
\[\mathbf{Z}(s)=\Big{[}\mathbf{M}s^{2}+\mathbf{C}s+\mathbf{K}\Big{]} \tag{3}\]  
The matrix of frequency response \(\mathbf{H}(s)\) can be expressed as:  
\[\mathbf{H}(s)=\Big{[}\mathbf{M}s^{2}+\mathbf{C}s+\mathbf{K}\Big{]}^{-1} \tag{4}\]  
When \(s=j\mathbf{f}\), \(j\mathbf{f}\) is column matrix of frequency at \(j\)-column. Equation (3) can be expressed as:  
Figure 4:0  
Matrix of vibration mode can be expressed as:  
Figure 4:1  
where \(\phi_{n}\) is the \(n\)-order of vibration mode. A symmetric matrix has weighting orthogonal characteristic, and \(\mathbf{M}\), \(\mathbf{C}\) and \(\mathbf{K}\) are respectively expressed as:  
\[\mathbf{\Phi}^{T}\mathbf{M}\mathbf{\Phi}=\left( \begin{array}{ccc}\ddots&&\\ &m_{r}&\\ &&\ddots\end{array} \right) \tag{7}\]  
\[\mathbf{\Phi}^{T}\mathbf{C}\mathbf{\Phi}=\left( \begin{array}{ccc}\ddots&&\\ &c_{r}&\\ &&\ddots\end{array} \right) \tag{8}\]  
\[\mathbf{\Phi}^{T}\mathbf{K}\mathbf{\Phi}=\left( \begin{array}{ccc}\ddots&&\\ &k_{r}&\\ &&\ddots\end{array} \right) \tag{9}\]  
where \(m_{r}\), \(c_{r}\) and \(k_{r}\) are mass, damping and stiffness at \(r\)-order. According to Equations (7)-(9), Equation (5) can be expressed as:  
\[\mathbf{Z}(f)=\mathbf{\Phi}^{-T}\left( \begin{array}{ccc}\ddots&&\\ &z_{r}&\\ &&\ddots\end{array} \right)\mathbf{\Phi}^{-1} \tag{10}\]  
where \(z_{r}=k_{r}-f^{2}m_{r}+jfc_{r}\), \(j\) is frequency at \(j\)-column.