MS07.8: Nonlinear Phenomena in Mechanical and Structural Systems

The system of two elastically coupled pendulums in a magnetic field is considered when the inertial characteristics of the pendulums differ significantly. In this case, both coupled and localized nonlinear normal modes (NNMs) can be observed. Such modes are constructed by the multiple scales method. The stability of NNMs is studied using a numerical-analytical procedure, which is related to the Lyapunov stability criterion. This stability is assessed by estimating orthogonal variations from the trajectories in the system configuration space. Regions of stability/instability of such modes in the system parameter space are obtained. Numerical simulation includes the construction of trajectories of NNMs in phase and configuration spaces and frequency spectrum, which allows us to detect regular or complex behavior of the system, both for small and significant initial deviations of the pendulums.

Chaotic dynamics occur in rotating shafts mounted on sliding bearings under specific design and operating conditions. Despite the fact that chaos does not definitely prevent the operation of rotating machines, it may result to higher frictional power loss and temperature rise in bearings, compared to the case when periodic or quasi-periodic motions evolve in the operation; it is also likely to compromise the integrity of the system when whirling orbits evolve in a large extent. A rotor-bearing system consisting of a rigid rotor mounted on two journal bearings is used in this work to produce chaotic dynamics. The chaotic operation regimes of the system are first detected estimating Lyapunov exponents, 0-1 test for chaos, and Poincare maps. Sliding bearings of active geometry are included in the physical model to enable the Ott-Grebogi-Yorke (OGY) control method as a reference solution to convert chaotic oscillations to periodic. The benefits from controlling chaos in the rotating system are investigated for a set of designs, considering frictional power loss, together with further aspects of integrity and operability of the system. It is found that the OGY method is able to control the chaotic response to periodic with low control effort, and creates potential for smooth periodic motions in high-speed systems like automotive turbochargers and turbopumps.

The paper investigates the nonlinear dynamical behavior of a linear oscillator (LO) attached to an unsymmetrical nonlinear energy sink (UNES) using the frequency energy plot (FEP). The UNES considered incorporates a purely cubic stiffness element on one side of the equilibrium position and a linear restoring coupling stiffness on the other side. The obtained FEP of the LO-UNES system reveals various kinds of backbone curves. Five continuous backbones of 1:1 resonance between the LO and the UNES at different frequency levels below the LO natural frequency were obtained. This kind of UNES also has a fundamental backbone of several subharmonic resonance branches, which further assist in resonance captures during targeted energy transfer (TET) and UNES energy dissipation. Accordingly, the considered UNES design provides a more enhanced capability of TET than Type I NES, which only employs a purely cubic stiffness force.

This paper examines the design and mathematical modeling of a MEMS sensor leveraging a mode localization based phenomenon. The design suggests a sensitive electrostatically excited clamped-clamped shallow arch micro-beam with an initial curvature designed to replicate one of the three first bending modes of a doubly-clamped beam. The analysis reveals that, through a suitable arrangement of the shallow arch beam’s initial profile, along with proper tuning of its mid-point initial rise and applied DC voltage, a bi-stable behavior can be achieved, resulting in a substantial stroke. Additionally, mode crossing and veering are observed, indicating a coupling between the symmetric and asymmetric modes of vibrations. This shows the potential for employing such a design as a mode-localized MEMS-based sensor.