MS09.1: Nonlinear Dynamics in Engineering Systems

Micro- and nanoelectromechanical systems (MEMS and NEMS) can exhibit rich nonlinear dynamics. Therefore, they have been studied extensively over the last decades in various areas of academic research ranging from engineering over physics to fundamental mathematics. In addition to its intriguing fundamental phenomena, nonlinear dynamics also found interest in rather applied industrial domains such as MEMS sensors and actuators where it shows the ability to disturb many devices based on linear system concepts. In either case, being able to tailor the nonlinear dynamical effects by design is certainly of great use. A main source of nonlinear system behavior in MEMS originates from geometric nonlinearities. In this work, we apply node-based shape optimization to tune the geometrically nonlinear 3-wave coupling coefficients using a custom FE and optimization code. On the example of an industrial level MEMS gyroscope, we demonstrate that individual coupling coefficients can be both decreased and increased over several orders of magnitude by shape optimization, while satisfying typical constraints on manufacturability and operability of the device. The optimized designs contain unintuitive geometrical features which can only be found using a computer implemented algorithm. Our work demonstrates the power of shape optimization for tailoring the complex nonlinear dynamic properties of MEMS and NEMS resonators of arbitrary geometries. Therefore, we believe that our work finds applications in various areas of mechanical engineering.

The Hyperloop, a developing transportation system, reduces air resistance by housing the vehicle within a depressurized tube and eliminates contact friction through an electro-magnetic suspension/levitation system. Maintaining system stability poses a challenge due to the exceptionally high target velocities. The interplay between electro-magnetic and wave-induced instability has been previously studied by the authors, showing that stability domains drastically change above a certain vehicle velocity. The current study demonstrates that the anomalous Doppler waves (i.e., wave-induced instability) are causing this drastic change. This investigation offers physical insight into the mechanisms that can cause instability in the Hyperloop system.

Conventional means of vibration control are often costly or heavy devices which are only effective over a very narrow band of excitation frequencies. It is to this end that nonlinear vibration absorbers are of interest as they are known to be capable of effectively reducing vibrations at any frequency of excitation. This research addresses a novel use of Shape Memory Alloy (SMA) within a Nonlinear Vibration Absorber. The nonlinearity of the absorber comes from two sources: the nonlinear geometric stiffness due to the perpendicular orientation of Shape Memory Alloy wires and from the Pseudoelasticity effect. The effect of Pseudoelasticity of Shape Memory Alloy is first successfully modelled which includes the development of the equations of motion of the absorber coupled with a harmonically excited primary spring-mass system. Analysis is conducted numerically and experimentally for and highlights the potential of a Nonlinear Shape Memory Alloy Vibration Absorber capable of attenuating vibrations over a broad range of excitation frequencies.

This paper studies the underwater sound and seabed vibrations generated from pile installation via axial and/or torsional vibrations, namely the "Gentle Driving of Piles" (GDP) method. A non-linear pile-soil-water model is utilized in this numerical study, where the pile vibrations and the resulting fluid-soil wave motion are analyzed. A semi-analytical finite element approach is used for pile-soil-water modelling and the pile-soil interaction is based on Coulomb friction enhanced with a memory mechanism. The comparison between classical axial vibratory driving and GDP is considered, investigating the effect of torsion in noise abatement as well as the presence of super-harmonic resonance-like phenomena.