Design and Experiment of a Passive Vibration Isolator for Small Unmanned Aerial Vehicles

Abstract

The advancement of sensor, actuator, and flight control technologies has increasingly expanded the possibilities for drone utilization. Among the technologies related to drone applications, the vibration isolator technology for payload has a significant impact on the precision of optical equipment in missions such as detection, reconnaissance, and tracking. However, despite ongoing efforts to develop vibration isolators to mitigate the impact of vibrations transmitted to optical equipment, research on drone-specific natural frequencies and payloads has been lacking. Consequently, there is a need for research on vibration isolators tailored to specific drone types and optical equipment payloads. This study focuses on exploring the correlation between the natural frequencies of drones and the weight of the payload, and proposes methods for developing and testing vibration isolators that consider both factors. To achieve this, the study measured the stiffness of vibration isolator rubbers and conducted cross-validation between random vibration tests and finite element method (FEM) analyses to verify the vibration reduction effects resulting from changes in the dynamic characteristics of vibration isolator rubbers. The rubber with a shore hardness of 70 exhibited relatively high damping and damping performance during random vibration tests. Additionally, it showed relatively high stability with only one resonance point measured within the operational frequency band. Through the findings of this study, a methodology for selecting vibration isolators for drones is proposed, aiming to enhance the stability of optical equipment.

1. Introduction

1.1. Research Background

Uncrewed aerial vehicles (UAVs) refer to uncrewed flying crafts manufactured in the form of fixed-wing or rotary-wing aircraft. In terms of nomenclature, the international civil aviation organization uses the term UAV, whereas the federal aviation administration refers to them as uncrewed aircraft, commonly known as drones. The field of application of UAVs is gradually expanding owing to the sophistication of related sensor-fusion technologies, the development of ultra-high-efficiency motors, and the improved reliability of navigation systems [1]. In the military market, the increasing size and enhanced performance of uncrewed systems are replacing certain mission scopes of manned aircraft. In the civil market, the small-to-medium-sized drone market is rapidly growing owing to the expansion of commercial business model applications [2]. Drones employed in the precision-detection field have demonstrated innovative application in various domains, such as surveillance, reconnaissance, and target coordination [3]. Recently, small to medium-sized drones with enhanced performance have been analyzed based on the development of onboard hyper-spectral camera technology, mapping techniques, and optimal flight technologies [4]. However, while the high efficiency and output of the motor have enabled the attachment of heavier payloads relative to the size of the drone, this also makes it more susceptible to disturbances, significantly affecting the precision of the optical equipment [5,6]. Also, the use of vibration isolation devices to maintain the precision of optical equipment is considered critical for improving the quality of optical devices [7,8]. Therefore, to mitigate the effects of vibrations on optical equipment, the installation of vibration isolators is crucial.

According to a 2022 report by the United States Congressional Research Service [9], optical surveillance equipment such as the electro-optical targeting system (EOTS), electro-optical (EO), and infra-red (IR), which are used in military UAVs, are trending towards weight reduction and high precision owing to the high integration of sensors and actuators.

Figure 1 presents a graph depicting the correlation between the weight of the optical equipment and its precision, based on the catalog information from View-pro (Established in 2005, Shenzhen, China), GSTiR (established in 2013, Wuhan, China), and SPI Corp (established in 1997, Las Vegas, NV, USA). Since optical equipment, which requires high precision, is vulnerable to external vibrations, a vibration isolator must be equipped to enhance their robustness against vibrations. Also, tests must be conducted to select an appropriate vibration isolator for optical equipment.

This study aims to develop a new custom vibration isolator tailored for optical equipment and propose a testing methodology. It achieves this by using a fixed-fixed beam as an equivalent model to replicate the drone’s first natural frequency. Along with the design of the vibration isolator, rubber stiffness tests and finite element method (FEM) analysis were conducted and comparatively analyzed. This led to the classification of rubber based on stiffness, which aided in evaluating the damping characteristics of the vibration isolator. To verify the damping characteristic of the vibration isolator, a testing method simulating the first natural frequency of a drone as a fixed-fixed beam was proposed. Also, the damping characteristic was confirmed based on the results of the random vibration test.

1.2. Research Trends in Vibration Isolation Devices

Vibration reduction in general aviation and mechanical systems closely corresponds to the performance of the system, due to which extensive research is being conducted on vibration reduction across various fields. Vibration isolation devices are categorized into the passive, active, and semi-active types [10], with research focused on active-type devices to improve the vibration damping performance. However, due to the limitations of battery-operated drones, passive-type vibration isolation devices are predominantly employed in the aviation industry. In 2014, a patent by Tian and Jian [11] introduced a passive isolation device developed by integrating rubber processed between metal plates. In 2020, a patent by Zhang et al. [12] presented a passive vibration isolation device for UAVs utilizing steel wire rope and a viscous damper.

Therefore, the basic design of the passive-type vibration isolation device was based on the patents by Tian and Jian [11]. Consequently, research was conducted on the passive-type vibration isolation device by considering the operational environment of the drone (Octocopter type) and the weight of the optical equipment.

2. Design of the Vibration Isolator and Test of Rubber Stiffness

2.1. Design of Vibration Isolator

Based on a survey of technological trends, a basic design for a vibration isolator was developed to protect optical equipment weighing 1.7 kg from vibrations originating from the drone’s rotors and to enhance precision. Figure 2 depicts the initial model of the vibration isolator.

Tension-type vibration isolators were designed in the initial model. However, they are vulnerable to sudden rotations and the effects of gravity during actions such as gusts, collisions, sharp turns, hard landings, and rapid descents, pose risks of detachment and damage to the equipment. Therefore, the design was changed to a compression-type vibration isolator to ensure stable mounting of the optical equipment.

Figure 3a depicts the compression-type vibration isolator designed in this study, and its components are illustrated in Figure 3b.

Table 1. Vibration isolator component detailed description.

Component No.	Designation	Material	Weight
①	Upper plate	AL6061	0.062 kg
②	Vibration isolator Bracket	AL6061	0.022 × 2 kg
③	Damping unit	CR-Rubber	0.0013 × 12 kg
④	Equipment plate	AL6061	0.073 kg
⑤	Lower plate	AL6061	0.1 kg

summarizes detailed information on the materials, weights, and components of the vibration isolator.

2.2. Comparative Verification of Vibration Isolator Stiffness through Experiment and FEM Analysis

To prevent damage to the vibration isolator during operation, AL6061 was chosen because of its high corrosion resistance and yield strength, low weight, design flexibility, machinability, and excellent characteristics in dispersing vibration and shock energy. The vibration isolator is primarily fabricated using rubber. Considering that the mechanical properties of rubber largely depend on temperature, a rubber composite suitable for the operating temperature conditions was selected [13].

Figure 4 presents a graph depicting the non-linearity of rubber stiffness due to temperature and prepressure [14]. In this study, rubber stiffness experiments were conducted in specific areas (temperature: 20 °C), where linearity is maintained under the influence of temperature and prepressure. Meadwell et al. [15] classified rubber into three types by using the Shore A measurement method: soft (Shore A 5~45), semi-rigid (Shore A 50~70), rigid (Shore A 80~95), and plastic (Shore A 100). In this study, to understand the trend of vibration characteristics corresponding to hardness, rubbers with hardness levels of 30, 50, and 70, from the range used in the vibration isolators (30~70), were selected as representative hardness levels for conducting the stiffness measurement experiments.

To measure the stiffness of rubber, the weight of the test mass was set as a variable, which varied from 1 to 4 kg in incremental steps of 1 kg, to measure the displacement of the vibration isolator for each weight increment. Figure 5b depicts the experimental setup, including the test mass, vibration isolator, and laser displacement sensor.

Table 2. Stiffness measurements of rubber by hardness level.

Hardness	Displacement at 1 kg (mm)	Displacement at 2 kg (mm)	Displacement at 3 kg (mm)	Displacement at 4 kg (mm)	Calculated Stiffness (N/m)
30	0.45	0.96	1.41	1.72	1796
50	0.36	0.64	0.92	1.21	2902
70	0.19	0.37	0.54	0.72	4652

is the result of the stiffness measurement experiment according to the hardness. The stiffness values were calculated using a linear function based on the data of the mass’s weight and the displacement of the rubber. The stiffness data derived from the experiment on measuring the stiffness of rubber were validated by comparing it with the stiffness analysis results obtained using Ansys workbench 2019 R3. Figure 6 illustrates the boundary conditions for the static structural analysis.

Figure 6 shows the boundary conditions of the static structural analysis to realize the experimental conditions shown in Figure 5b. The fixed support was applied as shown in Figure 6 [unit C], and a point mass was applied to the inner surface of the top plate where the jig of the weight was contacted, as shown in Figure 6 [unit E]. Additionally, static structural analysis was consistently performed for cases ranging from 0.5 to 2 kg. The top and bottom plates were connected with 12 points of the spring contact as depicted in Figure 6 [unit D].

Before utilizing the rubber stiffness measurement experimental data, a simulation was conducted to verify the reliability of the stiffness measurement data. Static structural analysis was also performed to calculate the displacement due to the load, and the results of the experiment displacement and static structural analysis displacement are organized into

Table 3. Comparison between experiment and static structural analysis.

Load (kg)	Experiment Displacement (mm)	Static Structural Analysis Displacement (mm)	Error (%)
0.5	0.260	0.265	1.8
1	0.476	0.486	2.0
1.5	0.704	0.727	3.1
2	0.942	0.987	4.5

.

In Table 3, the simulation results showed an error rate of less than 4.5%, and the difference from the actual experiment was identified as stemming from the geometric non-linearity of the rubber. As the load increases, the contact area with the metal plate increases, leading to changes in stiffness, which is why there is a discrepancy between the simulation represented by the spring constant and the actual experimental value. However, with a marginal error of less than 4.5%, the data were deemed usable for application.

This study builds upon the earlier work by comparing and validating FEM analysis with experimental environments, thereby ensuring system reliability.

3. Simulation of the Drone’s First Natural Frequency Using a Fixed-Fixed Beam: Numerical and FEM Analysis

3.1. Drone Ground Vibration Test

A drone ground vibration test was conducted to analyze the drone’s natural frequency and its operational frequency band. Through a drone ground vibration test, the drone’s first natural frequency was identified. Subsequently, the effectiveness of the vibration isolators mounted on a fixed-fixed beam, which simulates the first natural frequency of the drone, was assessed in terms of their damping capacity within the drone’s operational frequency band.

Table 4. Drone’s specification.

Category	Value
Frame weight	13.9 kg
Type	Octocopter
Wheelbase	1200 mm
Motor rotation [RPM]	2487–4981
Motor rotation [Hz]	41.45–83.01

lists the specifications of the drone used in the drone ground vibration test to determine its first natural frequency.

Figure 7 depicts the configuration of the drone ground vibration test. Single-axis accelerometers were attached to plates 1 and 2. The acquired data were analyzed using FFT to observe the resonance points of the drone.

Figure 8 presents the FFT graphs of the accelerance data from the drone ground vibration test. In the drone ground vibration test, the rotor rotates at 2487 rpm.

The analysis of the natural frequency in Figure 8 revealed that the first natural frequency of the drone is 10.9 Hz. The natural frequencies in the 40–85 Hz range represent the operational frequency band of the drone’s rotors. By modeling the drone’s first natural frequency at 10.9 Hz as a fixed-fixed beam, the vibration characteristics of the vibration isolator rubbers at different stiffness levels were assessed within the operational frequency band.

3.2. Comparative Analysis between Fixed-Fixed Beam Numerical Analysis and FEM Analysis

As drones are complex structures that often experience harmonic vibrations, an intuitive assessment of the damping effects of a vibration isolator may be challenging owing to the natural frequencies of the complex structure. Vibration experiments based on fixed-fixed beams enable the measurement of the vibrational characteristics of the system, aiding the understanding of the behavior of vibration isolators and providing insights into improving the design.

Numerical analysis and FEM analysis is one of the methods for analyzing the dynamic characteristics of engineering systems. It enables the identification of a system’s natural frequencies and mode shapes, thus allowing for the early detection and prevention of potential issues such as resonance induced at these frequencies. This approach provides an intuitive means for the optimization of design parameters. In this study, a test setup was developed to simulate drone vibrations. According to Verma et al. [16], the vibrations transmitted to the optical equipment affect the Z-axis translational motion more than in the X-Y translational movements. Therefore, only the translational motion along the Z-axis was considered to simulate the drone’s vibration environment.

Figure 9 represents a scheme for depicting the experimental environment through numerical analysis. The numerical analysis, applying the mass conditions of the actual experimental environment, is as follows in Equation (1):

$$f_1=\frac{1}{2\pi }\left[\frac{3EI{(a+b)}^3}{a^3{b}^{3}m}\right]$$

(1)

In Equation (1), a represents the distance from one end to the concentrated mass, and b is that from the other end to the concentrated mass. The parameters for the fixed-fixed beam used here are as follows: $E=78.5 \mathrm{G}\mathrm{P}\mathrm{a}$, $I={6.75\times 10}^{-11} {\mathrm{m}}^4$, $a=0.16 \mathrm{m},$ and $b=0.39 \mathrm{m}$. To ensure the reliability of the numerical analysis results, m was varied across eight cases from 0.5, 1, 1.5, 1.75, 2.0, 2.25, 2.5, and 3 kg comparing numerical and FEM analysis under various mass conditions.

Table 5. Comparison of the first natural frequency between numerical analysis and FEM analysis.

Load (kg)	Numerical Analysis (Hz)	FEM Analysis (Hz)	Error (%)
0.5	20.62	21.50	4.0
1.0	15.57	15.74	1.1
1.5	13.02	13.00	0.1
1.75	12.14	12.08	0.5
2.0	11.42	11.33	0.8
2.25	10.81	10.70	1.0
2.5	10.29	10.17	1.2
3.0	9.44	9.31	1.4

presents the results of a comparative analysis between the numerical and FEM analyses of the first natural frequency, with each concentrated mass case applied in the range of 0.5–3 kg across eight cases. Due to the limitations in the mass of optical equipment cases that can be mounted on the vibration isolator, reliability was ensured by comparing and analyzing FEM analysis with numerical analysis. An observed trend is the decrease in the first natural frequency as the mass increases. The discrepancy between the numerical analysis and FEM analysis due to mass increase showed a maximum error rate of 3.3%, thus verifying the mathematical modeling’s adequacy through the analysis results.

The FEM analysis was conducted on a fixed-fixed beam by applying a total mass of 2.17 kg, which includes the actual optical equipment mass of 1.7 kg and vibration isolator plate mass of 0.47 kg intended for attachment to the fixed-fixed beam. The FEM analysis with the experimental mass applied is shown in Figure 10.

The first natural frequency of the fixed-fixed beam obtained through FEM analysis is 10.89 Hz, showing a 0.9% error rate compared to the numerical analysis result of 10.99 Hz. Through comparative analysis between numerical analysis and FEM analysis, a fixed-fixed beam simulating the drone’s first natural frequency was implemented.

3.3. FEM Analysis of a Fixed-Fixed Beam including Vibration Isolator

Rubber, a material that embodies both the damping and stiffness properties, was equivalently modeled using the Kelvin-Voigt theory, which incorporates a viscoelastic model to accurately represent the interaction between the rigid and non-rigid parts of rubber. The spring contact boundary conditions were applied to the top and bottom plates of the vibration isolator. Figure 11b illustrates the method used to input the variables for the spring contact condition. The FEM analysis was conducted with stiffness values (K) of 1.796, 2.902, and 4.652 N/mm for the spring contact condition. These values were derived from the stiffness measurement experiments at hardness levels of 30, 50, and 70, respectively. Damping was applied through the mathematical analysis of a mass-spring-damper model.

For the FEM analysis (depicted in Figure 12), both ends of the beam, assumed to represent a drone, were fixed, and the optical equipment weighing 1.7 and 2.0 kg was applied as a point mass.

Through FEM analysis, the natural frequencies within the drone’s operational frequency band of 40–85 Hz were identified.

Figure 13 presents the FEM analysis results depicting the natural frequencies and mode shapes for stiffness levels of 30, 50, and 70. During the evaluation process for the FEM analysis, the natural frequencies due to bending of the vibration isolator mounted on the fixed-fixed beam were confirmed. Figure 13a,d,g represent the first natural frequencies with stiffness levels of 30 presenting 9.44 Hz, 50 presenting 10.72 Hz, and 70 presenting 11.04 Hz. Figure 13b,e,h represent the second natural frequencies with stiffness levels of 30 presenting 50.29 Hz, 50 presenting 58.09 Hz, and 70 presenting 64.09 Hz. Figure 13c,f,i represent the third natural frequencies with stiffness levels of 30 presenting 71.31 Hz, 50 presenting 79.91 Hz, and 70 presenting 96.18 Hz. Also, considering the drone’s maximum takeoff weight, the mass of the optical equipment was set to 2.0 kg for additional FEM analysis.

Figure 14 presents the FEM analysis results depicting the natural frequencies and mode shapes for stiffness levels of 30, 50, and 70. During the evaluation process for the FEM analysis, the natural frequencies due to bending of the vibration isolator mounted on the fixed-fixed beam were confirmed. Figure 14a,d,g represent the first natural frequencies with stiffness levels of 30 presenting 9.10 Hz, 50 presenting 10.21 Hz, and 70 presenting 11.07 Hz. Figure 14b,e,h represent the second natural frequencies with stiffness levels of 30 presenting 49.47 Hz, 50 presenting 57.54 Hz, and 70 presenting 64.81 Hz. Figure 14c,f,i represent the third natural frequencies with stiffness levels of 30 presenting 71.99 Hz, 50 presenting 79.85 Hz, and 70 presenting 85.24 Hz.

The natural frequency of the vibration isolator mounted on a fixed-fixed beam, detected within the drone’s operational frequency band of 40–85 Hz using FEM results, can potentially cause instability in the drone’s operation. Therefore, it is necessary to avoid these frequencies to ensure stable drone performance.

4. Vibration Shaker Experiment: Analysis of Damping Characteristic

4.1. 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 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 13) confirmed these frequencies to be 9.44 Hz, 10.72 Hz, and 11.04 Hz, with the error rates in the first natural frequency determined to be 2.6%, 3.0%, and 1.4%, 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 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. The response at resonance points other than the first resonance point of the fixed-fixed beam is well demonstrated to be attenuated below 0 dB.

4.2. Comparative Analysis of FEM Analysis and Random Vibration Test

The similarity between the natural frequencies from the random vibration test and the FEM analysis was confirmed. The test results present a comparison between the discrepancy in the bending frequency between the FEM analysis and the random vibration test.

Table 6. Comparison between natural frequency in FEM analysis and resonance frequency in random vibration test.

Mass	Category	Hardness of 30			Hardness of 50			Hardness of 70
		First Natural Frequency	Section 1	Section 2	First Natural Frequency	Section 1	Section 2	First Natural Frequency	Section 1	Section 2
1.7 kg	FEM Analysis	9.4 Hz	50.2 Hz	71.3 Hz	10.7 Hz	58.1 Hz	79.9 Hz	11.0 Hz	64.1 Hz	96.2 Hz
	Random vibration test	9.2 Hz	49.6 Hz	70.8 Hz	10.4 Hz	57.6 Hz	80.4 Hz	11.2 Hz	65.6 Hz	91.6 Hz
	Error Rate	2.6%	1.2%	0.7%	3.0%	0.8%	0.6%	1.4%	2.3%	5.0%
2.0 kg	FEM Analysis	9.1 Hz	49.5 Hz	71.9 Hz	10.21 Hz	57.5 Hz	79.9 Hz	11.0 Hz	64.8 Hz	85.2 Hz
	Random vibration test	9.2 Hz	49.2 Hz	70.0 Hz	10.4 Hz	57.2 Hz	80.0 Hz	11.2 Hz	65.2 Hz	90.8 Hz
	Error Rate	1.0%	0.6%	2.6%	1.8%	0.5%	0.1%	1.1%	0.6%	6.5%

presents a comparison between the bending frequencies from the random vibration test results and the FEM analysis results. The maximum error rate between the FEM analysis and the test results was observed to be 5.0% for 1.7 kg and 6.5% for 2.0 kg. Additionally, two natural frequencies were identified for hardness levels of 30 and 50 within the operational frequency range, whereas only one natural frequency was confirmed for a hardness of 70 within the operational frequency band.

4.3. Analysis of Damping Characteristic of Vibration Isolators

The stiffness of the vibration isolator rubber was determined by comparing the extent of damping amount and damping performance from the vibration data at the bending frequency from the random vibration test.

Table 7. Random vibration test results according to hardness (amplitude unit = dB).

	Sensor Location	Magnitude
		Hardness of 30		Hardness of 50		Hardness of 70
		Section 1	Section 2	Section 1	Section 2	Section 1	Section 2
Random vibration	S1	7.02	14.36	8.84	12.90	7.07	10.47
	S2	−6.48	−8.62	−4.77	−11.20	−6.48	−16.10
Decibel reduction		13.50	22.98	13.61	24.1	13.55	26.57

presents the accelerance data at each resonance point from the random vibration test. The test results indicate that the vibration isolators exhibit a damping amount ranging from a minimum of 13.50 dB to a maximum of 13.61 dB in Section 1, and from a minimum of 22.98 dB to a maximum of 26.57 dB in Section 2, based on the stiffness.

Table 8. Damping performance of each vibration isolator (performance unit = ratio).

	Section	Hardness of 30	Hardness of 50	Hardness of 70
Random vibration test	Section 1	22.39	22.96	22.65
	Section 2	198.61	527.04	453.94

calculates the damping amount for each test using the damping values from Table 7 and Equation (2). $L_B$ is damping performance, A is amplitude of undamped data, and B is amplitude of damped data.

$$L_B=10{log}_{10}\frac{B}{A}$$

(2)

The results of the vibration tests indicated that the vibration isolator with a hardness of 70 exhibited a high damping performance of 453.94 in Section 2, demonstrating relatively higher damping capabilities when compared to the vibration isolators with hardness levels of 30 and 50.

The performance indicator of a vibration isolator is the damping ratio, which is a measure of how efficiently the isolator material dissipates the energy generated from vibrations and shocks. The damping ratio is calculated using the Q factor and is given as follows:

$$Q=\frac{1}{2\ast \zeta }$$

(3)

Table 9. Damping ratio of each vibration isolator.

	Section	Damping Ratio of 30	Damping Ratio of 50	Damping Ratio of 70
Random vibration test	Section 1	2.2%	1.8%	1.8%
	Section 2	1.9%	1.8%	1.9%

shows the damping ratios calculated using the FRF graphs from the random vibration test and Equation (3). The results of the random vibration tests reveal that the vibration isolator with a stiffness of 30 exhibits damping ratios of 2.2% and 1.9%, which are higher than those of the vibration isolators with stiffness of 50 and 70.

In this study, the comparative analysis of vibration characteristics showed that while a stiffness level of 30 had a high damping ratio in Section 1, two resonance points were identified within the operational frequency band. In the case of a stiffness level of 70, with only one resonance point and relatively high amounts of damping and performance, it was selected as the material for the vibration isolator.

5. Conclusions

In this paper, a vibration isolator suitable for 1.7 kg class optical equipment was developed, and a testing methodology was presented. The first natural frequency of the drone was simulated using a fixed-fixed beam (WDH: 30 × 3 × 540 [mm]) as an equivalent model. The vibration test using the fixed-fixed beam assessed damping within the operational frequency band of 40–85 Hz, based on criteria such as damping amount, damping ratio, and damping performance. The analysis of damping characteristics showed that while stiffness levels of 30, 50, and 70 exhibited similar damping amounts and performance in Section 1, stiffness 70 demonstrated the highest damping amount and performance in Section 2. Furthermore, within the operational frequency band, stiffness 70 had the fewest resonance frequencies, leading to the selection of the vibration isolator with a stiffness of 70. The test method using a fixed-fixed beam has the advantage of being able to simulate various drone vibration environments with simple modifications to boundary conditions, resulting in lower costs and time requirements compared to actual drone flight tests.

In future research, we will verify the damping performance of vibration isolators based on the vibration transmissibility considering the natural frequencies of optical equipment. Additionally, the damping characteristics of vibration isolators will be evaluated under various temperature conditions. Further experiments involving different types of drones and equipment will also be conducted to enhance the versatility of the system.