MS07.4: Nonlinear Phenomena in Mechanical and Structural Systems

Stick-slip oscillations in drilling systems are a well-known example of self-excited oscillations established due to nonlinear discontinuous forces resulting from bit-rock and drillstring-wellbore interaction. Since the drillstring typically consists of multiple components with different inertia and/or stiffness, stick-slip oscillations have been observed at different frequencies in experimental data. However, analytical modelling of this phenomena is predominantly limited to the fundamental mode of oscillation, by using a lumped spring-masss model for the drilling system. In this study, we consider a multi degree-of-freedom model subjected to a discontinuous nonlinear force and investigate the establishment of limit cycles as a function of system and forcing parameters. Using numerical root finding algorithms and the method of averaging, we obtain a semi-analytical expression for the limit cycle amplitude(s), as well as the stability of the limit cycles. We observe that limit cycles can be established in any single natural mode of oscillation of the structure, or in a combination of modes depending upon the particular system parameters, which qualitatively match the results observed in numerical simulations of realistic drilling systems. Further, we also observe that in some cases, there can be multiple stable limit cycles that have distinct basins of attraction. These results will help in obtaining a map to predict a priori the nature of stick-slip oscillations that maybe realized for different drillstring configurations and help mitigate vibration-related failures while drilling.

Cracks and resonance stand out as primary factors contributing to the failure of engineering components subjected to dynamic loading. Numerous studies have affirmed that the existence of cracks can alter modal frequencies, thereby increasing the likelihood of resonance occurring at frequencies other than those originally designed for. Therefore, it is necessary to model for understanding influence of crack on modal coupling. In this work, we employ a model of a cantilever beam with a crack by introducing a singularity in the material stiffness within the dynamic equation of motion to study its effect on modal coupling. We derived equation of beam considering presence of shortening effect as well as geometric nonlinearities. We observe that mode shapes alters modal frequencies relative to a regular beam, which can lead to internal resonance.

The aim of the provided research is to study the nonlinear dynamics of a slender hinged-hinged beam subjected to base excitation. The beam is tested under tension or compression load, the later resulting in a post-buckling configuration. The forced change in axial load is executed by shifting one of the support hinges. To ensure a high flexibility of the tested specimen the beam is made of an carbon epoxy composite. A specific 18-layer stacking sequence of the laminate is implemented ensuring mechanical and dynamic macroscopic material properties, equivalent to isotropic ones. During the performed experiment the amplitude-frequency responses of the system are recorded. The frequencies are swept forward and backward in order to capture expected nonlinear phenomena e.g. saddle-node type bifurcation points. Initially, the resonance states around the new equilibria states are investigated. Moreover, the dynamics of the system subjected to high base excitation magnitudes is tested when snap-through effects occur.

The presented paper deals with experimental studies of a bistable shell to identify its basic nonlinear properties and define guidelines for a derivation of a reduced model of the shell. Based on measured time series of free vibrations and resonance characteristics basic parameters of the studied system are determined. Analysis of experimental data allowed for identification of natural frequencies, damping level, offset trend of the vibration center, softening and snap-through effects, etc. These information allowed to propose a description of a stiffness curve and a reduced model with piecewise linear stiffness and hysteresis loop, so that the mapping of free vibrations and resonance characteristics are as good as possible. As a result, a new reduced model of bistable shell will be proposed.