MS09.2: Nonlinear Dynamics in Engineering Systems

Unmanned aerial vehicles (UAVs) are gaining popularity in various industrial applications, particularly in agriculture. Monitoring their condition during flight is crucial, with special attention to the propulsion system. A failure in this system can halt the aircraft mid-flight, potentially leading to disaster. In a recent study, researchers attempted to detect and identify damage in a DC motor within an octocopter. They achieved this by analyzing voltage signals recorded by piezoelectric sensors placed on each arm during tethered flight. The simulated damage involved altering the PWM pulse width from 20% to 80% in 20% increments. By isolating non-linear features sensitive to changes in periodicity, the researchers not only detected damage but also determined its severity. The findings from this study will contribute to the development of an effective aircraft control algorithm. Such an algorithm is essential for real-time monitoring of the propulsion system, ensuring safe operation even in the event of failure.

In this work, we delve into the realm of time-frequency analysis techniques, with a particular emphasis on their application to nonlinear signals commonly encountered in various scientific and engineering domains. These signals, often exhibiting non-stationary and nonlinear characteristics, are crucial in the study of chaotic dynamics. Our focus is on the MultiSynchrosqueezing Transform (MSST), a emergent method for capturing the intricate structures and evolving features of these complex signals. Time-frequency analysis techniques, including MSST, are instrumental in examining the evolving characteristics of nonlinear signals. We begin by exploring a wide array of dynamical systems, setting the stage for a deeper understanding of their nonlinear behaviors. Classical methods like the Short-Time Fourier Transform, Wavelet Transform, Hilbert Transform, and the Wigner-Ville distribution have been extensively employed in analyzing non-stationary phenomena. Alongside MSST, our study highlights the enhanced capability of MSST in characterizing the unique aspects of chaotic and nonlinear dynamics.

Pipes are widely used in aircraft, ships and other engineering fields. The vibration of the pipe will affect the reliability of the system and even cause accidents. Therefore, the vibration control of the pipe is of great significance. Most of the existing literatures consider the linear constitutive relationship to establish the pipe model, namely Hooke's law. However, with the continuous development of hyperelastic materials, it has become a novel idea to apply them to vibration control of pipes. In this paper, the nonlinear constitutive relationship of the hyperelastic material is considered, and it is combined with the flexible pipe to form a laminated pipe. Furthermore, the dynamic characteristics of the laminated pipe were further investigated. By combining Maxwell model and Yeoh hyperelastic model, the mathematical model of nonlinear forced vibration with a simply supported visco-hyperelastic laminated pipe is established. The influence of hyperelastic coefficient on the natural frequency of the pipe is analyzed by Galerkin truncation method. Based on the harmonic balance method (HBM), the forced vibration response of the pipe is analyzed. And the results are verified by the differential quadrature element method (DQEM). The results show that compared with the single-layer pipe, the visco-hyperelastic layer has little effect on the natural characteristics of the laminated pipe, but it can effectively improve the vibration control. This also provides a theoretical basis for the application of laminated pipes.