Piezoelectric Power Generation from the Vortex-Induced Vibrations of a Semi-Cylinder Exposed to Water Flow

The aim of this work is to design a piezoelectric power generation system that extracts power from the vibration of a cantilever beam. A semi-cylinder placed in a water stream and attached to the beam is excited into vortex-induced vibrations (VIV), which triggers the piezoelectric deformation. The mechanical system is modelled using parametric equations based on Hamilton’s extended principle for the cantilever beam and the modified Van der Pol model for the bluff body (the semi-cylinder). These equations are simulated using the MATLAB software. The dimensions of the model, the flow velocity and the resistance are treated as design parameters and an optimization study is conducted using MATLAB to determine the combination of optimal values at which maximum power is extracted. The key findings of this research lie in the identification of the effect of changing the design parameters on output power. In addition to the numerical simulation, a finite element analysis is carried out on the bluff body and the hydrodynamic forces and velocity profiles are observed. It is determined that the vibration amplitudes increase with increasing diameter of the bluff body, length of the bluff body and water velocity.

Van der Pol Model in Two-Delay Differential Equation Representation

The Van der Pol equation is the mathematical model of a second-order ordinary differential equation with cubic nonlinearity. In this paper, the differential equation of the Van der Pol model and RLC (resistor - inductor-capacitor) circuit are deduced from a delay differential equation. The Van der Pol delay model contains two delays, which opens the way for the re-use of its applications. Also, the model for Parkinson's disease modification is described as the Van der Pol model.

Lyapunov-based Methods for Maximizing the Domain of Attraction

This paper investigates Lyapunov approaches to expand the domain of attraction (DA) of nonlinear autonomous models. These techniques had been examined for creating generic numerical procedures centred on the search of rational and quadratic Lyapunov functions. The outcomes are derived from all investigated methods: the method of estimation via Threshold Accepted Algorithm (TAA), the method of estimation via a Zubov technique and the method of estimation via a linear matrix inequality (LMI) optimization and genetic algorithms (GA). These methods are effective for a large group of nonlinear models, they have a significant ability of improvement of the attraction domain area and they are distinguished by an apparent propriety of direct application for compact and nonlinear models of high degree. The validity and the effectiveness of the examined techniques are established based on a simulation case analysis. The effectiveness of the presented methods is evaluated and discussed through the study of the renowned Van der Pol model.

Vortex-Induced Vibration Analysis of a Composite Riser System Based on the Transfer Matrix Method for Multibody Systems

Vortex-induced vibration (VIV) is one of the main reasons for failure of risers. Therefore, it is very important to predict the VIV behavior of risers by establishing an efficient model suitable for the field of ocean engineering. Based on the transfer matrix method for multibody systems (MSTMM), the main idea about simulating the vibration characteristics and fluid-structure interaction of a marine riser system is presented in this paper for the first time, using the MSTMM coupled with a Van der Pol model. The influence of different parameters, such as riser length, top tension, stream speed and steel joints, on the dynamic response of the riser is investigated.

A van der Pol Based Reduced-Order Model for Non-Synchronous Vibration (NSV) in Turbomachinery

This paper demonstrates the potential of using a multi-degree-of-freedom, traditional van der Pol oscillator to model non-synchronous vibration (NSV) in turbomachinery. It is shown that the two main characteristics of NSV are captured by the reduced-order, van der Pol model. First, a stable limit cycle oscillation (LCO) is maintained for various conditions. Second, the lock-in phenomenon typical of NSV is captured for various fluid-structure frequency ratios. This research identifies values and significance of the coupling parameters used in the van der Pol model. These coefficients are chosen to model confirmed instances of experimental NSV, and to develop a preliminary design tool that engineers can use to better design turbomachinery for NSV. Specifically, coefficient tuning from experimental instances of NSV are considered to identify the unknown coupling coefficients in the van der Pol model. The goal of future research will be to identify values and significance of the coupling parameters used in the van der Pol model, to match these coefficients with confirmed instances of experimental NSV, and to develop a preliminary design tool that engineers can use to better design turbomachinery for NSV. Proper orthogonal decomposition (POD) CFD techniques and coefficient tuning from experimental instances of NSV have been considered to identify the unknown coupling coefficients in the van der Pol model. The finalization of this preliminary-design research will be completed in future research.

Modeling and simulating the nerve axon as a thin-film microstrip

Since Hodgkin and Huxley described the nerve axon as a cable (H–H model), many efforts have been made to find more approximated transmission line models representing the nerve axon. This paper describes a simple model that represents the nerve axon in two parts: the internodal space as a lossy thin-film microstrip line and the node of Ranvier as an active complex load. The complex load terminating the transmission line is given by the variable impedance of a tunnel diode. First, the internodal space is circuitally analyzed and electromagnetically simulated as a lossy thin-film microstrip line terminated on a complex fixed load. The transmission line circuit theory, the two-port network analysis, and a two-dimensional finite difference time domain method are used for such a task by forcing a strip subatomic metallization. Then, the transfer function of the internodal space, cascaded with the node of Ranvier, is equated to the transfer function of a transmission line section that includes a tunnel diode. This procedure is carried out in order to obtain the diode's variable impedance. The diode was introduced by Nagumo, Arimoto, and Yoshizawa for simulating the nerve axon as an active transmission line. The active transmission line is represented by the FitzHugh simplified H–H model known as the Bonhoeffer–van der Pol model.