MS07.3: Nonlinear Phenomena in Mechanical and Structural Systems

Gear transmission systems constitute a key component in a multitude of applications such as transportation, manufacturing, industry, etc. As such, dynamic analysis of such systems is a powerful tool during the design and operation of machinery incorporating geared connections. Gear transmission systems, while being the most powerful method of motion transmission in terms of torque, suffer from considerable vibrations due to the gear meshing phenomena that appear during operation. The need for analyzing such non-linear phenomena has led to the development of multiple gear meshing models, incorporating the effects of non-linear contact force models [1], hertzian contact effects [2], time-varying backlash [3] and stiffness [4] as well as the modeling of faults mechanisms [5]. While multiple cases of gear dynamic analysis are mentioned in literature, due to the complexity of gear meshing mechanism, there are almost no reports available for analysis of large geared systems that simultaneously incorporate modeling of the detailed gear meshing phenomena. To this end, this work aims to provide an analytical formulation for gear meshing forces, incorporating the effects of time-varying stiffness in the model while also being suitable for dynamic analysis of large geared systems and the modeling of fault mechanisms.

Shallow arches have been used as architectural structures dating back to antiquity. Historically, these structures have been studied under static conditions for their use as load-bearing elements. However, in recent years the dynamic phenomena of the shallow arches, such as snap-through instabilities, have been explored to create multistable mechanical metamaterials (MMM) assembled from arrays of connected shallow arches. Two varieties of shallow arches can be used to assemble such an array: elastically deformed arches (buckled beams) and plastically deformed arches. Using a combination of both types of arches grants additional control of the properties of the MMM such as transition wave speed on non-reciprocity behavior. While the non-linear dynamic behavior of elastically deformed buckled beam has been extensively studied, the plastically deformed arch has not yet been investigated in depth. In this work, we explore the non-linear dynamics of the plastically deformed shallow arch in comparison to its elastic counterpart. Notably, the properties of the plastically deformed arch differ based on which stable configuration the arch is in. As an effect of the asymmetries in the potential energy landscape of the plastically deformed arch, the two stable configurations have different linear equivalent stiffnesses. These differences affect the structure’s natural frequency and non-linear frequency response. This results in the plastically deformed arch capable of changing its properties simply by reconfiguring between stable equilibrium points.

The effects of noisy fluctuations in an orthogonal metal cutting model with regenerative and frictional effects of a turning operation are examined. Dynamical investigations on the tool have been carried out by considering various bifurcation parameters such as depth of cut, rake angle, flank angle, and static friction coefficients. The stochastic connotations of bifurcations, namely the P and D bifurcations undergone by the system in the presence of multi-stable attractors are explored in this study.

A non-linear model to describe the constitutive behaviour of composites reinforced with carbon nanotubes is presented. The model is formulated in order to adequately represent the damping effects introduced by carbon nanotubes, assuming the occurrence of stick-slip motion. The primary goal is to provide an improved alternative for dynamic numerical analysis of components reinforced with carbon nanotubes. This work presents the main considerations and basis for the mathematical formulation of the model.