MS09.3: Nonlinear Dynamics in Engineering Systems

Previous research on parametric vibration of pipes has primarily focused on straight configurations. This paper investigates the nonlinear parametric resonance characteristics of slightly curved pipes. Approximate analytical solutions for instability boundary and amplitude-frequency response of pipe parametric resonance are derived. Analytical solutions exhibit excellent agreement with numerical solutions. The mechanism of transition from hardening characteristics to softening of pipes with initial curvature is analyzed for the first time. Then the condition for linear response characteristics is defined by achieving a balance between the square nonlinearity and the cubic. The results show that both natural frequencies and instability boundaries increase as the initial curved amplitude grows. Moreover, modes exchange results in the interchange of instability boundaries in the parametric vibration. The transformation between softening and hardening characteristics of the response under the second-order mode is a unique phenomenon of parametric vibration. Notably, the response intensifies significantly when the parametric vibration of the pipe reaches an intermediate linear state. Finally, the influence of pipe length, outer diameter, and wall thickness on the critical initial curved amplitude that maximizes the response are explored. The research results provide a reference for the rational design of the size of offshore pipes to avoid excessive vibration.

Multi-constrained pipes conveying high-speed fluid, such as aircraft hydraulic control lines, operate in harsh vibration environments. In addition, one or more natural frequencies of the pipe system may fall within the frequency band of environmental excitation. As a result, resonance fatigue can occur, leading to system failure or even catastrophic accidents. Therefore, much attention has been paid to the design of pipe systems with low vibration levels. In this work, a typical hydraulically controlled slender pipe is taken as the object. The dynamic model of the pipe system is set up to obtain the vibration characteristics. By comparing the natural frequency of the pipe with the frequency band of the environmental excitation, a data set of the absolute safety length and the absolute resonance length of the pipe is obtained. Based on the genetic programming (GP) algorithms extensively trained from the data set, the GP model is proposed to accurately predict the absolute safety length and absolute resonance length of pipes. Therefore, mathematical expressions are obtained for the variation of the absolute safety length and absolute resonance length with the location, stiffness, and number of retaining clips. The proposed GP model, as a critical component of the design strategy, effectively bridges the data set with the prediction results, thereby completing the design strategy for low vibration level pipes conveying fluid. In summary, this work combines machine learning methods to suppress pipe system vibration through inverse dynamics design, which provides insights for the design of low vibration pipe systems.

This contribution presents the computational model of the tilting pad journal bearing with a detailed model of elastic contact between the journal and the pads. The lightly loaded upper pads can exhibit self-excited vibration called pad fluttering for several operating conditions. This motion can further result in potential undesirable contact damaging the pad due to repeatable hits of two solid bodies. The magnitude of the elastic force has a significant impact on the service life of the pad and the whole rotor system, potentially. The evaluated elastic force in the contact between the journal and the pad is further used to describe the mechanism of the pad's damage, resulting in qualitative changes on the sliding surface.

The hemodynamics may be represented by a set of ordinary differential equations such as a Van der Pol Oscillator mathematical model. Changing the parameters of the equations, it is possible to reproduce both normal or atypical heart dynamics, such as ventricular and atrial flutter, ventricular and atrial fibrillation, supraventricular extrasystole, Torsade de Point and other abnormal conditions.The importance of mathematical modeling is to study such conditions, to allow predictions of these undesired dynamics, to assist medical doctors or paramedicals in decision-making and technological solutions development involving medical devices or therapies.