Modeling the Dynamics of a Gyroscopic Rigid Rotor with Linear and Nonlinear Damping and Nonlinear Stiffness of the Elastic Support

This study analytically and numerically modeled the dynamics of a gyroscopic rigid rotor with linear and nonlinear cubic damping and nonlinear cubic stiffness of an elastic support. It has been shown that (i) joint linear and nonlinear cubic damping significantly suppresses the vibration amplitude (including the maximum) in the resonant velocity region and beyond it, and (ii) joint linear and nonlinear cubic damping more effectively affects the boundaries of the bistability region by its narrowing than linear damping. A methodology is proposed for determining and identifying the coefficients of nonlinear stiffness, linear damping, and nonlinear cubic damping of the support material, where jump-like effects are eliminated. Damping also affects the stability of motion; if linear damping shifts the left boundary of the instability region towards large amplitudes and speeds of rotation of the shaft, then nonlinear cubic damping can completely eliminate it. The varying amplitude (VAM) method is used to determine the nature of the system response, supplemented with the concept of “slow” time, which allows us to investigate and analyze the effect of nonlinear cubic damping and nonlinear rigidity of cubic order on the frequency response at a nonstationary resonant transition.

Constraint Analysis and Optimization of NES System Based on Variable Pitch Spring

This study proposes the realization of a device with a pure cubic stiffness mechanism to suppress a wide range of vibrations, which is known as the Nonlinear Energy Sink. Deciding how to construct a light, reliable NES device is always a challenge. According to our design, the device can counterbalance the undesirable linear stiffness that emerges from the intrinsic property of a variable pitch spring. Our goal is to reduce the mass of the spring while keeping the same cubic stiffness. Through the multifaceted analysis of the nonlinear constraint, we try to explore the full potential of NES device to reduce its mass. Meanwhile, a global search method, Multi Start, is applied by repeatedly running a local solver. Finally, a new design with different variable pitch distribution is proposed.

Hydrokinetic Power Conversion Using Vortex-Induced Oscillation with Cubic Restoring Force

A cubic-spring restoring function with high-deformation stiffening is introduced to passively improve the harnessed marine hydrokinetic power by using flow-induced oscillations/vibrations (FIO/V) of a cylinder. In these FIO/V experiments, a smooth, rigid, single-cylinder on elastic end-supports is tested at Reynolds numbers ranging from 24,000 < Re < 120,000. The parameters of the tested current energy converter (CEC) are cubic stiffness and linear damping. Using the second generation of digital virtual spring-damping (Vck) controller developed by the Marine Renewable Energy Laboratory (MRELab), the cubic modeling of the oscillator stiffness is tested. Experimental results show the influence of the parameter variation on the amplitude, frequency, energy conversion, energy efficiency, and power of the converter. All experiments are conducted in the low turbulence-free surface water (LTFSW) channel of the MRELab of the University of Michigan. The main conclusions are: (1) The nonlinearity in the cubic oscillator is an effective way to extend the vortex-induced vibration (VIV) upper branch, which results in higher harnessing power and efficiency compared to the linear stiffness cylinder converter. (2) Compared to the linear converter, the overall power increase is substantial. The nonlinear power optimum, occurring at the end of the VIV upper branch, is 63% higher than its linear counterpart. (3) The cubic stiffness converter with low harnessing damping achieves consistently good performance in all the VIV regions because of the hardening restoring force, especially at higher flow velocity.

Characterization of Real-world Vibration Sources and Application to Nonlinear Vibration Energy Harvesters

A tremendous amount of research has been performed on the design and analysis of vibration energy harvester architectures with the goal of optimizing power output. Often, little attention is given to the actual characteristics of common vibrations from which energy is harvested. In order to shed light on the characteristics of common ambient vibration, data representing 333 vibration signals were downloaded from the NiPS Laboratory “Real Vibration” database, processed, and categorized according to the source of the signal (e. g. vehicle, machine, etc.), the number of dominant frequencies, the nature of the dominant frequencies (e. g. stationary, band-limited noise, etc.), and other metrics. By categorizing signals in this way, the set of idealized vibration inputs (i. e. single stationary frequency, Gaussian white noise, etc.) commonly assumed for harvester input can be corroborated and refined. Furthermore, some heretofore overlooked vibration input types are given motivation for investigation. The classification determined that, of the set of signals used in the study, 64 % of the animal source signals are best described with nonstationary dominant frequencies, 58 % of machine source signals are best described with stationary frequencies, and vehicle source signals are poorly described by any one signal type used in the classification. Nonlinear harvesters with a cubic stiffness term have received extensive attention in the scholarly literature; a numerical simulation and optimization procedure were performed using several representative signals as vibration inputs to determine the prevalence with which such a nonlinear harvester architecture might provide improvement to power output. The analysis indicated that a nonlinear harvester architecture may prove beneficial in increasing power output over a linear counterpart if the signal contains a single, dominant frequency that is not stationary in time, as evidenced by a 14 % increase in harvester power output when employing an architecture with a nonlinear cubic stiffness function. Other studies have indicated that nonlinear architectures may be beneficial for signals with nonstationary frequencies or filtered noise. 53 % of the all characterized signals fall into categories that could potentially benefit from a nonlinear oscillator architecture.

Qualitative Identification of the Static Pull-In and Fundamental Frequency of One-Electrode MEMS Resonators

This paper attempts to qualitatively identify the static pull-in position, pull-in voltage, and fundamental frequency of one-electrode microresonators from a physical perspective. During theoretical derivation, a generalized one-degree-of-freedom (1-DOF) model in nondimensional form derived using the differential quadrature method (DQM) is first introduced and then transformed for frequency normalization. Based on the deduced formulas, the upper and lower bounds of the static pull-in position and pull-in voltage are both deduced through mathematical proof. To distinguish the monotonic and nonmonotonic behavior of the fundamental frequency versus direct current (DC) voltage, a critical condition decided only by cubic stiffness is then determined. For the first time, two extreme static positions, as well as the corresponding fundamental frequencies and DC voltages to identify different frequency behaviors are derived, and their variations versus cubic stiffness are then discussed and verified. During the simulation process, a high-order DQM and COMSOL 2D model are both applied for numerical analyses. Guided by nondimensional results, typical behaviors with specific physical parameters are examined in detail. Results demonstrate that the curve tendencies between all the qualitative results and quantitative numerical simulations in dimensional form agree well with each other, implying the possibility of using 1-DOF model to qualitatively discuss physical parameters effects on the system statics and dynamics.

Improved Modelling of a Nonlinear Parametrically Excited System with Electromagnetic Excitation

In this work, the nonlinear behaviour of a parametrically excited system with electromagnetic excitation is accurately modelled, predicted and experimentally investigated. The equations of motion include both the electromechanical coupling factor and the electromechanical damping. Unlike previous studies where only linear time-varying stiffness due to electromagnetic forces was presented, in this paper the effect of the induced current is studied. As a consequence, nonlinear parameters such as electromechanical damping, cubic stiffness and cubic parametric stiffness have been included in the model. These parameters are also observed experimentally by controlling the direct current (DC) and alternating current (AC) passed through the electromagnets. In fact, the proposed apparatus allows to control both linear and nonlinear stiffnesses and the independent effect of each parameter on the response is presented. In particular the effect of the cubic parametric stiffness on the parametric resonance amplitudes and the influence of cubic stiffness on the frequency bandwidth of the parametric resonance are shown. This model improves the prediction of parametric resonance, frequency bandwidth, and the response amplitude of parametrically excited systems and it may lead to refined design of electromagnetic actuators, filters, amplifiers, vibration energy harvesters, and magnetic bearings.

Robustness of Nonlinear Electromagnetic Vibration Energy Harvester Subjected to Random Excitation

Vibration Energy Harvesters (VEHs) are devices used to collect mechanical energy from the surrounding environment to supply low power electronic systems such as Wireless Sensor Nodes. In this paper, we introduce an electromagnetic VEH model and a semi-analytical method called Moment Equation Copula Closure (MECC) that is compared to Monte Carlo simulations. Those methods are then used to derive the maximum power that can be extracted from random vibration before analyzing the effect of cubic stiffness nonlinearity on the VEH robustness against the variation of the excitation spectrum. Unlike bistable nonlinearity, it is shown that Duffing nonlinearity can be used to enhance the VEH power density and robustness with a limited effect on the harvested power.