## 3 Experimental Investigation and Results
### Modal Test and Model Validation  
This section describes the experiments required to perform a modal analysis on the CBF. Non-parametric system identification is applied to the input and output spectra to obtain a set of FRFs. The first step in the procedure is to measure the impulse response of a system, by means of an impact test. This is performed using an impact hammer and tri-axial acceleration sensors. A data acquisition module is utilized to measure the input and output signals between each excitation point and measured output. Analog signals are converted into discrete time signals by the module, which are then communicated to the computer at fixed time intervals specified by the sampling frequency. These input and output signals are transformed to the frequency domain by means of the Discrete Fourier Transform. These transformed signals are used to calculate the FRFs. The following equipment is required to perform an impact test:  
1. The free boundary condition is subject to limitations imposed by the natural frequencies of the rigid body modes. To investigate the dynamic behavior of a CBF, it is suspended from a chain hoist, creating one or more rigid body modes based on the stiffness of the supporting materials and the total mass of the structure. If the natural frequencies of these rigid body modes are significantly different from the first natural frequency of the structure, the measured FRF data should not be affected by this boundary condition. 2. The 3D motion at each test point is desired in the resulting mode shapes. A roving triaxial accelerometer is used and the CBF is impacted at a fixed DOF with the hammer. The locations in the structural testing refer to the 3D wireframe model (208 points) of CBF, shown in Figure 3. The tri-axial accelerometer must be simultaneously sampled together with the force data; a four-channel FFT analyzer is required instead of a two-channel analyzer. 3. The data-acquisition device DT9837B is used with the IPE signal conditioning unit. This device is a high-accuracy dynamic signal acquisition module that is ideal for vibration measurements. It contains four synchronized 24-bit sensor inputs that provide a data stream that is matched in time, which can be used for signal analysis. During the tests, only one SIMO transfer is measured, using one impulse force hammer (type 9722A500) and one tri-axial accelerometer (type 8763B100) from KISTLER. 4. Sampling frequency, also known as sampling rate, refers to the number of samples taken per unit of time during the process of digitizing an analog signal. It represents the rate at which the continuous analog signal is discretized into discrete samples. The choice of an appropriate sampling frequency depends on the characteristics of the signal being sampled and the specific requirements of the application. Higher sampling frequencies capture more detail and allow for the accurate representation of high-frequency components, but they also require more storage and computational resources. Let us define the sampling frequency for our testing based on the number of samples and frequency span in the FRF setup as 4096 lines and 1024 Hz. According to [PERSON]'s theorem, we can only accurately measure frequencies up to half of the sampling rate. Therefore, the sampling frequency should be set at least twice the maximum frequency component present in the signal. So, our spectral line resolution is calculated as half of the sample rate divided by the number of lines, resulting in 0.5 Hz. The window calculation time is 2 s. Each experiment is repeated at least three times, and the best three measurements are used to determine the averaged FRF for the corresponding SIMO transfer. Setting up the signal processing: During the measurement, choose the frequency domain and select the FRF (transfer function) for calculation. Use the linear method for averaging and set the number of repetitions to three times. Regarding sampling, set the number of samples to 2048 in the time domain. In the frequency domain, set the maximum frequency to 1280 Hz.