# A Multiple and Multi-Level Substructure Method for the Dynamics of Complex Structures
## 4 Analysis of Dynamic Characteristics Based on Substructure
### Modal Experiment of Combustion Rotor and Verification of Substructure Method
#### 4.3.2. Experiment System  
Experimental modal analysis methods can be divided into a frequency response function method and environmental excitation method. The so-called force measurement method is a method that needs to measure the excitation force and response at the same time during the experiment. The classic force measurement method uses the frequency response function (FRF) in the frequency domain or the impulse response function (IRF) in the time domain to estimate the modal parameters. The frequency response function is the ratio of the Fourier transform of the response and the force, and the impulse response function must be measured first and then obtained by the inverse Fourier transform. Therefore, the force measurement method must use a vibrator or a hammer with a dynamometer to apply a measurable excitation force. The force measurement method can estimate all  
Figure 10: Combustion rotor.  
Figure 9: Comparison of MAC between finite element model and the substructure model.  
modal parameters, including natural frequency, modal shape, damping or damping ratio, modal mass and modal stiffness; furthermore, the accuracy is high.  
Boundary conditions  
This experiment is a free-mode experiment of the combustion rotor. In order to avoid other structures or excitation sources from affecting the test results, the installation method selected this time is the free suspension method. This installation method can eliminate external interference to the greatest extent and ensure the accuracy of the test results. The suspension mode is shown in Figure 11.  
Incentive method and acquisition system  
Modal test experiments can be divided into a hammering method and a vibration exciter method [32]. The hammering method is generally suitable for cases where the mass and the volume of the test piece is small, and its characteristic is that the test is convenient; the vibration exciter method is generally suitable for the case of the large mass and volume of the test object, and its advantage is that a larger excitation can be generated by the vibration exciter to stimulate the inherent characteristics of the test object. The research object of this experiment is the combustion-engine rotor. According to the above description, the free modal experiments are carried out by the hammering method of multi-point excitation and a single-point vibration pickup. The modal experiment equipment used in this experiment is the Donghua DHDAS dynamic signal acquisition and analysis system shown in Figure 12. The model is DH5922D, which is used to collect force signals and acceleration signals. Channel 1 is connected to the force hammer, and channel 2 is connected to the acceleration sensor. The head of the force hammer is rubber, the sensitivity of the force sensor is 3.65 mV/N; the acceleration sensor can convert the acceleration of mechanical vibration into an electric charge to output, whose sensitivity is 2.86 mV/m/s\({}^{2}\). The starting point of tapping is the No. 1 measuring point, tapping in the order of the number of the measuring points, tapping twice for each measuring point, and linearly averaging the results collected by tapping, and then obtaining the tapping data of the measuring point. In the process of percussion, you need to pay attention to the intensity of the percussion. If the intensity is too large, it is easy to cause an overload. If the intensity is too small, the data cannot be collected. In addition, it is necessary to be quick and accurate in the process of percussion to prevent the occurrence of combos, which will affect the results.  
Figure 11: The way of suspension.