Piecewise-linear restoring force surfaces for semi-nonparametric identification of nonlinear systems

2007 ◽  
Vol 54 (1-2) ◽  
pp. 123-135 ◽  
Author(s):  
Matthew S. Allen ◽  
Hartono Sumali ◽  
David S. Epp
Keyword(s):  
Nonlinear Systems ◽  
Piecewise Linear ◽  
Nonparametric Identification ◽  
Restoring Force

Miniaturized Broadband Vibration Energy Harvester With Piecewise-Linear Asymmetric Restoring Force

2019 ◽  
Author(s):  
Arata Masuda ◽  
Feng Zhao
Keyword(s):  
Energy Harvester ◽  
Piecewise Linear ◽  
Experimental Studies ◽  
Resonance Peak ◽  
Vibration Energy ◽  
Restoring Force ◽  
Vibration Energy Harvester ◽  
Resonance Band ◽  
Compact Size ◽  
The Asymmetry

Abstract This paper presents a design study of a miniaturized broadband nonlinear vibration energy harvester (VEH) with piecewise-linear restoring force based on a mechanically-sprung resonator with stoppers. It is commonly recognized that a VEH based on a nonlinearly-sprung resonator can show broadband frequency characteristics while keeping its maximum power performance due to its bent resonance peak. The resonator to be investigated in this study consists of a magnet composite as a mass moving through an induction coil, two planar springs, and mechanical stoppers. The magnet composite is comprised of two repelling cylindrical magnets and a steel disk between them, all encapsulated in a thin stainless-steel cylinder. The planar springs with spiral-like shape are respectively connected to the both ends of the magnet composite so that they provide soft linear stiffness in a compact size. The mechanical stoppers installed to constrain the deformation of the spring give the resonator piecewise-linear hardening characteristics which effectively broaden the resonance band. In this study, the prototype VEH developed in the previous study is presented, and the gaps between the springs and stoppers are adjusted so that the resultant piecewise-linear restoring force shows symmetric or asymmetric property with respect to the equilibrium point. Experimental studies and analyses are carried out to examine the performance of the presented VEH in terms of the frequency response. The comparison of three different configurations of the stopper illustrates how the asymmetry in the bilinear restoring force affects the shape of the resonance peak. It is also suggested that the asymmetry may help the VEH operate in broader band by exploiting its ability of tailoring the resonance characteristics, which still needs further investigation.

Dynamics of a Piecewise-Linear Oscillator With Limited Power Supply

2009 ◽  
Author(s):  
Silvio L. T. de Souza ◽  
Ibereˆ L. Caldas ◽  
Jose´ M. Balthazar ◽  
Reyolando M. L. R. F. Brasil
Keyword(s):  
Power Supply ◽  
Piecewise Linear ◽  
Basins Of Attraction ◽  
Point Of View ◽  
Restoring Force ◽  
Rich Variety ◽  
Coexistence Of Attractors ◽  
Limited Power ◽  
Limited Power Supply ◽  
Basins Of Attractions

We discuss dynamics of a vibro-impact system consisting of a cart with an piecewise-linear restoring force, which vibrates under driving by a source with limited power supply. From the point of view of dynamical systems, vibro-impact systems exhibit a rich variety of phenomena, particularly chaotic motion. In our analyzes, we use bifurcation diagrams, basins of attractions, identifying several non-linear phenomena, such as chaotic regimes, crises, intermittent mechanisms, and coexistence of attractors with complex basins of attraction.

scholarly journals Restoring Force Surface Analysis of Nonlinear Vibration Data From Micro-Cantilever Beams

2006 ◽  
Author(s):  
Matthew S. Allen ◽  
Hartono (Anton) Sumali ◽  
David S. Epp
Keyword(s):  
Functional Form ◽  
Piecewise Linear ◽  
Cantilever Beams ◽  
Restoring Force ◽  
Vibration Data ◽  
Surface Method ◽  
Highly Nonlinear ◽  
Nonlinear Dynamic Characteristics ◽  
Restoring Forces ◽  
Micro Cantilever

The responses of micro-cantilever beams, with lengths ranging from 100-1500 microns, have been found to exhibit nonlinear dynamic characteristics at very low vibration amplitudes and in near vacuum. This work seeks to find a functional form for the nonlinear forces acting on the beams in order to aide in identifying their cause. In this paper, the restoring force surface method is used to non-parametrically identify the nonlinear forces acting on a 200 micron long beam. The beam response to sinusoidal excitation contains as many as 19 significant harmonics within the measurement bandwidth. The nonlinear forces on the beam are found to be oscillatory and to depend on the beam velocity. A piecewise linear curve is fit to the response in order to more easily compare the restoring forces obtained at various amplitudes. The analysis illustrates the utility of the restoring force surface method on a system with complex and highly nonlinear forces.

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