MS12.8: Nonlinear Dynamics for Engineering Design

Most dynamic analyses of wind turbine towers are conducted in a simplified manner, only considering harmonic load and no nonlinear modal coupling. However, a more realistic model should take into account the coupled behavior, where the wind turbine rotor and tower are simultaneously influenced by each other. This study aims to explore the impact of modal coupling and the associated nonlinearities on the tower and turbine responses. A nonlinear model is developed based on the Lagrangian function of the coupled system, followed by the application of Hamilton's principle, resulting in a two-degree of freedom system of nonlinear equations of motion. The study also investigates the effect of imperfections in the form of blade mass distributions. The results highlight the significance of such coupling on the performance and reliability of wind turbine towers.

In this study, we develop an optimization procedure for the initial curvature of a mechanical beam that maximizes the inherent amplification of the forced transverse vibrations of the beam due to a nonlinear interaction with driven longitudinal vibrations. We focus on two possible cases, (i) direct amplification which is obtained when the driving frequency of the longitudinal vibrations is close to the eigenfrequency of the transverse mode, and, (ii) parametric amplification, which is obtained when the driving frequency of the longitudinal vibrations is close to twice the eigenfrequency of the transverse mode. By using a simple genetic algorithm scheme we find that the optimal curved beam enhances the amplification by a factor of 125 for direct amplification, and by a factor of 60 for parametric amplification.

Compared to traditional robotic systems, small-scale robots, ranging from several millimetres to micrometres in size, are capable of reaching narrower and vulnerable regions with minimal damage. However, conventional small-scale robots’ limited maneuverability and controlability hinder their ability to effectively navigate in the intricate environments, such as the gastrointestinal tract. Self-propelled capsule robots driven by vibrations and impacts emerge as a promising solution, holding the potentials to enhance diagnostic accuracy, enable targeted drug delivery, and alleviate patient discomfort during gastrointestinal endoscopic procedures. This paper builds upon our previous work on vibro-impact capsule robots, exploring the potential of nonlinear connecting springs to enhance its propulsion capabilities. Leveraging a recently developed mathematical model for vibro-impact capsule robots with a von Mises truss spring, we investigate the effects of negative stiffness and snap-back within the nonlinear structural spring on the robots’ propelling performance. By leveraging the negative stiffness of the von Mises truss, the capsule robot achieves a remarkably wider operational bandwidth for propelling speed compared to its linear counterpart. Within this band, the robot maintains a significantly higher average speed, enabling more efficient and robust locomotion. This work sheds light on the potential for integrating customised nonlinear structures with small-scale robots to tailor their dynamic performance, thereby unlocking new possibilities for enhanced functionality and maneuverability in diverse biomedical applications.

In continuation to [1], this paper gives a further step towards an improved reliability analysis of a dynamical system attractor, based on its dynamic integrity. Although the ideas are applicable to a broader class of problems within dynamical systems theory, they will be illustrated to discuss the load-carrying capacity of an imperfection-sensitive structure liable to buckle. The analysis uses the Monte Carlo method to assess the probability that the Global Integrity Measure is equal or larger than a prescribed value, considering the probability density functions of both the applied load and the imperfection parameter, provided the former is not larger than the buckling strength, Hence, a reliability measure can be made available to help engineers deciding whether a particular design is reliable, given it is safe, contributing to the improvement of current design practices