# Design and Experiment of a Passive Vibration Isolator for Small Unmanned Aerial Vehicles
## 4 Vibration Shaker Experiment: Analysis of Damping Characteristic  
### Random Vibration Test  
The random vibration test simulates the wide-bandwidth spectrum of the vibrations generated by a drone using a shaker. This system allows the production of vibrations by generating signals that vary randomly within the frequency range. In this study, one end was fixed, while the other end was attached to the shaker to generate random signals at frequencies below 500 Hz. Since the operational frequency band of the drone's motor was 40-85 Hz, the vibration characteristics by stiffness were compared and analyzed within the 100 Hz band in the random vibration test. Figure 14: FEM analysis results: (**a**) Mode 1: bending frequency 9.10 Hz (hardness 30); (**b**) Mode 2: bending frequency 49.47 Hz (hardness 30); (**c**) Mode 3: bending frequency 71.99 Hz (hardness 30); (**d**) Mode 1: bending frequency 10.21 Hz (hardness 50); (**e**) Mode 2: bending frequency 57.54 Hz (hardness 50); (**f**) Mode 3: bending frequency 79.85 Hz (hardness 50); (**g**) Mode 1: bending frequency 11.07 Hz (hardness 70); (**h**) Mode 2: bending frequency 64.81 Hz (hardness 70); (**i**) Mode 3: bending frequency 85.24 Hz (hardness 70). Figure 15a illustrates the utilized equipment diagram, and Figure 15b depicts the test environment. The random vibration signal caused by the shaker was measured by the S3 accelerometer. The S1 accelerometer represents the vibration signal of a fixed-fixed beam. Additionally, the S2 acceleration sensor represents the vibration signal that is directly transmitted to the optical equipment through the vibration isolator from the fixed-fixed beam. Figure 16 depicts the natural frequencies of vibration isolators based on hardness level from a random vibration test. In the random vibration test, the first natural frequencies of the fixed-fixed beam were 9.2 Hz, 10.4 Hz, and 11.2 Hz. The FEM analysis (Figure 14) confirmed these frequencies to be 9.1 Hz, 10.21 Hz, and 11.0 Hz, with the error rates in the first natural frequency determined to be 1.0%, 1.8%, and 1.1%, respectively. The second natural frequency is represented by the red dotted line in Section 1, while the third natural frequency is indicated by the black dotted line in Section 2. Figure 17 depicts the natural frequencies of vibration isolators based on hardness level from a random vibration test. In the random vibration test, the first natural frequencies of the fixed-fixed beam were 9.2 Hz, 10.4 Hz, and 11.2 Hz. The FEM analysis (Figure 14) confirmed these frequencies to be 9.1 Hz, 10.21 Hz, and 11.0 Hz, with the error rates in the first natural frequency determined to be 1.0%, 1.8%, and 1.1%, respectively. The second natural frequency is represented by the red dotted line in Section 1, while the third natural frequency is indicated by the black dotted line in Section 2. The graph depicts that the amplitude of the damping data at the first natural frequency is greater than the amplitude of the non-damped data. To verify the attenuation of vibrations, the magnitudes of the sensor data from S1 and S2 were compared. Figure 16: Accelerance FRF of the random vibration test (1.7 kg): (**a**) hardness of 30; (**b**) hardness of 50; (**c**) hardness of 70 (unit = mm/s\({}^{2}\)/N). Figure 15: Random vibration test: (**a**) schematic diagram; (**b**) test setup. Figure 18 represents the vibration signal in the time domain for a weight of 1.7 kg with a hardness of 70. S1 denotes the signal from the accelerometer attached to the fixed-fixed beam, S2 denotes the signal from the accelerometer attached to the vibration isolator, and S3 denotes the signal from the accelerometer attached to the shaker. The vibration attenuation of the vibration isolator was verified through cross-validation between the frequency domain and the time domain. Figure 19 represents the transmissibility calculated from the input and output signals of the random vibration test.