In recent years, the rapid advancement of unmanned technologies has led to the development of various sophisticated unmanned systems. Among these, drones, particularly multirotor drones, have become a critical component of intelligent equipment manufacturing. Multirotor drones offer distinct advantages in terms of power system coupling, structural simplicity, actuator response speed, power source stability, safety, and control precision compared to fixed-wing drones, helicopters, and flapping-wing aircraft. Consequently, multirotor drones are widely employed in fields such as disaster rescue, agricultural plant protection, and logistics transportation. However, the unique blade motion of multirotor drones induces harmonic vibrations under motor excitation, often leading to structural resonance, primarily manifested as bending modes. This vibration can adversely affect the stability of flight precision and payload performance, making vibration suppression a focal point of research.
Traditional approaches to vibration reduction in multirotor drones have focused on structural optimization and damping mechanisms, but investigations into the inherent vibration characteristics of composite materials used in these structures remain limited. The vibration response mechanisms resulting from changes in composite material layup are not well understood. Therefore, this study addresses the pronounced resonance observed during flight tests of a specific quadcopter multirotor drone by conducting a systematic vibration characterization through finite element analysis. We perform modal and harmonic response analyses to identify vibration sources, corresponding mode shapes, and natural frequencies. Based on simulation results, we optimize and improve the composite layup structure of the drone arms, elucidating the vibration response mechanisms of macroscopic composite laminated structures and revealing how changes in composite structure influence the overall vibration characteristics of multirotor drones.
We begin by establishing a finite element model of the entire multirotor drone using Altair Hypermesh software. The model is appropriately simplified by converting components such as equipment, batteries, motors, and propellers into mass points, applied at their respective centers of gravity using RBE3 elements. Connections via rivets or bolts are simplified using RBE2 elements. The spring connections between the arm tubes and the fuselage plates in the deployed state are modeled as 1D annular cross-section beam elements. The arm tubes, upper and lower fuselage plates, and rotating connectors are meshed with shell elements, while metal components like mounting bases and hooks are modeled with solid elements. The final finite element model is depicted in the figure above.
The materials used include composite laminates for the fuselage plates and arm tubes, with a surface layer of 3K carbon fiber fabric and an inner layer of T700 carbon fiber unidirectional tape arranged in a specific layup sequence. Metal components are made from 7075 aluminum alloy and 30CrMnSi high-strength alloy steel. The technical parameters of these materials are summarized in Tables 1 and 2.
| Material Category | Young’s Modulus E (GPa) | Shear Modulus G (GPa) | Poisson’s Ratio NU | Density RHO (g/cm³) |
|---|---|---|---|---|
| 7075 Aluminum Alloy | 72 | 27 | 0.3 | 2.75 |
| 30CrMnSi | 210 | 80 | 0.3 | 7.85 |
| Material Category | E1 (GPa) | E2 (GPa) | NU12 | G12 (GPa) | G1Z (GPa) | G2Z (GPa) | Density RHO (g/cm³) | Thickness t (mm) |
|---|---|---|---|---|---|---|---|---|
| 3K Carbon Fiber Fabric | 54.1 | 54.1 | 0.2 | 3.18 | 3.18 | 3.18 | 1.55 | 0.225 |
| T700 Carbon Fiber Unidirectional Tape | 126 | 6.65 | 0.33 | 2.65 | 2.65 | 2.65 | 1.55 | 0.125 |
For modal analysis, we use the OptiStruct finite element analysis software with the Normal modes analysis type and the EIGRL block Lanczos method. The frequency range is set to 500 Hz, solving for natural frequencies and mode shapes. The first ten natural frequencies, excluding rigid body modes, are listed in Table 3.
| Mode | Natural Frequency (Hz) | Mode | Natural Frequency (Hz) |
|---|---|---|---|
| 1 | 14.64 | 6 | 40.92 |
| 2 | 15.34 | 7 | 41.72 |
| 3 | 15.35 | 8 | 49.93 |
| 4 | 31.66 | 9 | 54.22 |
| 5 | 39.21 | 10 | 84.38 |
The mode shapes corresponding to these frequencies indicate that the first three modes involve horizontal swinging of the arms around the center point, while the fourth and sixth modes exhibit vertical swinging. The tenth mode shows torsional vibration around the vertical axis. Notably, the fourth natural frequency at 31.66 Hz coincides with the excitation frequency of the motors at 1,900 rpm (approximately 31.67 Hz), explaining the observed resonance in flight tests.
We proceed with harmonic response analysis using the modal superposition method. A sinusoidal force of 100 N at 31 Hz is applied to each rotor, directed along the normal to the rotor plane. The frequency sweep range is 0 to 200 Hz. The amplitude-frequency response curves and displacement contours reveal peak amplitudes and accelerations at 31 Hz and 44.5 Hz, with values of 555.36 mm and 27.37 mm for displacement, and 21.070 m/s² and 2.140 m/s² for acceleration, respectively. The vibration propagates from the rotor ends, causing significant resonance in the arms.
To mitigate this resonance, we optimize the composite layup structure of the arms. The optimization follows symmetric and balanced layup principles, varying the content of 0°, 45°, and 90° plies and examining the effects of neutral plane orientation and ply count. The general eigenvalue problem for modal analysis is given by:
$$(K – \omega^2 M)\phi = 0$$
where \(K\) is the stiffness matrix, \(M\) is the mass matrix, \(\omega\) is the natural frequency, and \(\phi\) is the mode shape. For harmonic response, the equation of motion is:
$$M\ddot{x} + C\dot{x} + Kx = F e^{i\omega t}$$
where \(C\) is the damping matrix, \(x\) is the displacement vector, and \(F\) is the amplitude of the harmonic force.
We first investigate the effects of ply orientation and position changes. Six layup schemes with dispersed ply distributions are analyzed, as detailed in Table 4. The harmonic response results show that the positive and negative directions of 45° plies have a negligible impact on amplitude, with variations less than 0.05%. Similarly, changes in the position of 0° plies relative to the neutral plane result in amplitude variations below 0.15%, which are insignificant.
| Scheme | Thickness (mm) | Number of Plies | Layup Sequence |
|---|---|---|---|
| F-1 | 2 | 13 | [(±45)/-45/45/0/45/0/90]s |
| F-2 | 2 | 13 | [(±45)/45/-45/0/-45/0/90]s |
| F-3 | 2 | 13 | [(±45)/45/0/-45/0/45/90]s |
| F-4 | 2 | 13 | [(±45)/-45/0/45/0/-45/90]s |
| F-5 | 2 | 13 | [(±45)/0/45/0/-45/45/90]s |
| F-6 | 2 | 13 | [(±45)/0/-45/0/45/-45/90]s |
Next, we explore the influence of neutral plane changes and 0° ply count. Schemes with 0° and 90° neutral planes and varying 0° ply counts are evaluated, as listed in Table 5. The results demonstrate that for a 0° neutral plane, increasing the number of 0° plies shifts the frequency to the right and reduces the amplitude. Compared to a single 0° ply, frequencies increase by 8.06%, 12.90%, and 17.74%, while amplitudes decrease by 29.28%, 31.66%, and 40.04%, respectively. Similar trends are observed for a 90° neutral plane, with frequency increases of 12.28%, 21.05%, and 26.32%, and amplitude reductions of 32.15%, 43.65%, and 48.53%.
| Scheme | Thickness (mm) | Number of Plies | Layup Sequence |
|---|---|---|---|
| A | 2 | 13 | [(±45)/-45/0/45/90/-45/0]s |
| B | 2 | 13 | [(±45)/0/-45/0/45/90/0]s |
| C | 2 | 13 | [(±45)/0/-45/0/45/0/0]s |
| D | 2 | 13 | [(±45)/0/0/45/0/0/0]s |
| E | 2 | 13 | [(±45)/-45/45/0/45/-45/90]s |
| F | 2 | 13 | [(±45)/-45/45/0/45/0/90]s |
| G | 2 | 13 | [(±45)/0/-45/0/-45/0/90]s |
| H | 2 | 13 | [(±45)/0/0/-45/0/0/90]s |
Comparing neutral planes, the 0° neutral plane consistently yields better vibration characteristics. For the same number of 0° plies, the 0° neutral plane shows frequency increases of 8.06%, 4.48%, 1.43%, and 1.37%, and amplitude reductions of 22.91%, 17.93%, 1.34%, and 2.51% over the 90° neutral plane. This improvement is attributed to the anisotropic nature of composite laminates, where the 0° plies effectively counteract bending moments in the vertical direction. However, as the number of 0° plies increases beyond a certain point, the anisotropy diminishes, reducing the vibration suppression effect.
The optimization of the layup structure for the multirotor drone arms effectively mitigates harmonic response by shifting frequencies and reducing amplitudes. By altering the neutral plane and increasing the number of 0° plies, the harmonic response frequency can be shifted by over 12%, and the vibration amplitude can be reduced by more than 31%. Thus, for this and similar multirotor drone configurations, we recommend prioritizing a 0° neutral plane layup and reasonably increasing the number of 0° plies, ideally 3 to 4 layers, to optimize vibration characteristics.
In conclusion, our study addresses the resonance phenomenon in a small multirotor drone through detailed vibration characterization and composite layup optimization. We find that changes in the positive and negative directions of 45° plies and the position of 0° plies have negligible effects on vibration characteristics. In contrast, the neutral plane orientation significantly influences frequency and amplitude, with the 0° neutral plane providing superior performance. Increasing the number of 0° plies consistently shifts frequencies higher and reduces amplitudes, though the effect diminishes with excessive 0° plies due to reduced anisotropy. Therefore, for optimal vibration performance in multirotor drones, we advocate for a 0° neutral plane layup with 3 to 4 layers of 0° plies. This research offers valuable insights for vibration reduction in multirotor drones during development and provides a technical reference for future structural optimizations.