scholarly journals Secondary Resonance Energy Harvesting with Quadratic Nonlinearity

Materials ◽  
2020 ◽  
Vol 13 (15) ◽  
pp. 3389
Author(s):  
Guoce Zhang ◽  
Bo Zhang
Keyword(s):  
Steady State ◽  
Mechanical Strain ◽  
Period Doubling ◽  
Time History ◽  
Resonance Energy ◽  
Quadratic Nonlinearity ◽  
Stable Steady State ◽  
Structural Dynamic ◽  
Secondary Resonances ◽  
Piezoelectric Energy

Piezoelectric energy harvesters can transform the mechanical strain into electrical energy. The microelectromechanical transformation device is often composed of piezoelectric cantilevers and has been largely experimented. Most resonances have been developed to harvest nonlinear vibratory energy except for combination resonances. This paper is to analyze several secondary resonances of a cantilever-type piezoelectric energy harvester with a tip magnet. The conventional Galerkin method is improved to truncate the continuous model, an integro-partial differential equation with time-dependent boundary conditions. Then, more resonances on higher-order vibration modes can be obtained. The stable steady-state response is formulated approximately but analytically for the first two subharmonic and combination resonances. The instability boundaries are discussed for these secondary resonances from quadratic nonlinearity. A small damping and a large excitation readily result in an unstable response, including the period-doubling and quasiperiodic motions that can be employed to enhance the voltage output around a wider band of working frequency. Runge–Kutta method is employed to numerically compute the time history for stable and unstable motions. The stable steady-state responses from two different methods agree well with each other. The outcome enriches structural dynamic theory on nonlinear vibration.

scholarly journals Results of the Marine Ice Sheet Model Intercomparison Project, MISMIP

2012 ◽  
Vol 6 (3) ◽  
pp. 573-588 ◽  
Author(s):  
F. Pattyn ◽  
C. Schoof ◽  
L. Perichon ◽  
R. C. A. Hindmarsh ◽  
E. Bueler ◽  
...  
Keyword(s):  
Steady State ◽  
Adaptive Mesh Refinement ◽  
Ice Sheet ◽  
Adaptive Mesh ◽  
Stable Steady State ◽  
Fixed Grid ◽  
Approximate Analytical Solutions ◽  
Grounding Line ◽  
Intercomparison Project ◽  
Line Positions

Abstract. Predictions of marine ice-sheet behaviour require models that are able to robustly simulate grounding line migration. We present results of an intercomparison exercise for marine ice-sheet models. Verification is effected by comparison with approximate analytical solutions for flux across the grounding line using simplified geometrical configurations (no lateral variations, no effects of lateral buttressing). Unique steady state grounding line positions exist for ice sheets on a downward sloping bed, while hysteresis occurs across an overdeepened bed, and stable steady state grounding line positions only occur on the downward-sloping sections. Models based on the shallow ice approximation, which does not resolve extensional stresses, do not reproduce the approximate analytical results unless appropriate parameterizations for ice flux are imposed at the grounding line. For extensional-stress resolving "shelfy stream" models, differences between model results were mainly due to the choice of spatial discretization. Moving grid methods were found to be the most accurate at capturing grounding line evolution, since they track the grounding line explicitly. Adaptive mesh refinement can further improve accuracy, including fixed grid models that generally perform poorly at coarse resolution. Fixed grid models, with nested grid representations of the grounding line, are able to generate accurate steady state positions, but can be inaccurate over transients. Only one full-Stokes model was included in the intercomparison, and consequently the accuracy of shelfy stream models as approximations of full-Stokes models remains to be determined in detail, especially during transients.

scholarly journals Nonlinear Dynamics and Stability Analysis of a Three-Cell Flying Capacitor DC-DC Converter

2021 ◽  
Vol 11 (4) ◽  
pp. 1395
Author(s):  
Abdelali El Aroudi ◽  
Natalia Cañas-Estrada ◽  
Mohamed Debbat ◽  
Mohamed Al-Numay
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Monodromy Matrix ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Simple Expression ◽  
Buck Converter ◽  
State Variables ◽  
Bifurcation Phenomena ◽  
The Stability

This paper presents a study of the nonlinear dynamic behavior a flying capacitor four-level three-cell DC-DC buck converter. Its stability analysis is performed and its stability boundaries is determined in the multi-dimensional paramertic space. First, the switched model of the converter is presented. Then, a discrete-time controller for the converter is proposed. The controller is is responsible for both balancing the flying capacitor voltages from one hand and for output current regulation. Simulation results from the switched model of the converter under the proposed controller are presented. The results show that the system may undergo bifurcation phenomena and period doubling route to chaos when some system parameters are varied. One-dimensional bifurcation diagrams are computed and used to explore the possible dynamical behavior of the system. By using Floquet theory and Filippov method to derive the monodromy matrix, the bifurcation behavior observed in the converter is accurately predicted. Based on justified and realistic approximations of the system state variables waveforms, simple and accurate expressions for these steady-state values and the monodromy matrix are derived and validated. The simple expression of the steady-state operation and the monodromy matrix allow to analytically predict the onset of instability in the system and the stability region in the parametric space is determined. Numerical simulations from the exact switched model validate the theoretical predictions.

scholarly journals Suppression of marine ice sheet instability

2018 ◽  
Vol 857 ◽  
pp. 648-680 ◽  
Author(s):  
Samuel S. Pegler
Keyword(s):  
Steady State ◽  
Rapid Assessment ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Stable Steady State ◽  
Ice Shelf ◽  
West Antarctic Ice Sheet ◽  
West Antarctic ◽  
Grounding Line ◽  
The Stability

A long-standing open question in glaciology concerns the propensity for ice sheets that lie predominantly submerged in the ocean (marine ice sheets) to destabilise under buoyancy. This paper addresses the processes by which a buoyancy-driven mechanism for the retreat and ultimate collapse of such ice sheets – the marine ice sheet instability – is suppressed by lateral stresses acting on its floating component (the ice shelf). The key results are to demonstrate the transition between a mode of stable (easily reversible) retreat along a stable steady-state branch created by ice-shelf buttressing to tipped (almost irreversible) retreat across a critical parametric threshold. The conditions for triggering tipped retreat can be controlled by the calving position and other properties of the ice-shelf profile and can be largely independent of basal stress, in contrast to principles established from studies of unbuttressed grounding-line dynamics. The stability and recovery conditions introduced by lateral stresses are analysed by developing a method of constructing grounding-line stability (bifurcation) diagrams, which provide a rapid assessment of the steady-state positions, their natures and the conditions for secondary grounding, giving clear visualisations of global stabilisation conditions. A further result is to reveal the possibility of a third structural component of a marine ice sheet that lies intermediate to the fully grounded and floating components. The region forms an extended grounding area in which the ice sheet lies very close to flotation, and there is no clearly distinguished grounding line. The formation of this region generates an upsurge in buttressing that provides the most feasible mechanism for reversal of a tipped grounding line. The results of this paper provide conceptual insight into the phenomena controlling the stability of the West Antarctic Ice Sheet, the collapse of which has the potential to dominate future contributions to global sea-level rise.

scholarly journals Affinity series of genetically encoded high sensitivity Förster Resonance Energy Transfer sensors for sucrose

2020 ◽  
Author(s):  
Mayuri Sadoine ◽  
Mira Reger ◽  
Ka Man Wong ◽  
Wolf B. Frommer
Keyword(s):  
Energy Transfer ◽  
Steady State ◽  
Resonance Energy Transfer ◽  
Resonance Energy ◽  
Forster Resonance Energy Transfer ◽  
Förster Resonance Energy Transfer ◽  
Detection Range ◽  
Steady State Levels ◽  
Förster Resonance

ABSTRACTGenetically encoded fluorescent sugar sensors are valuable tools for the discovery of transporters and for quantitative monitoring of sugar steady-state levels in intact tissues. Genetically encoded Förster Resonance Energy Transfer sensors for glucose have been designed and optimized extensively, and a full series of affinity mutants is available for in vivo studies. However, to date, only a single improved sensor FLIPsuc-90µΔ1 with a Km for sucrose of ∼90 µM is available for sucrose monitoring. This sucrose sensor was engineered on the basis of an Agrobacterium tumefaciens sugar binding protein. Here, we took a two-step approach to first systematically improve the dynamic range of the FLIPsuc nanosensor and then expand the detection range from micromolar to millimolar sucrose concentrations by mutating a key residue in the binding site. The resulting series of sucrose sensors may allow systematic investigation of sucrose transporter candidates and comprehensive in vivo analyses of sucrose concentration in plants. Since FLIPsuc-90µ also detects trehalose in animal cells, the new series of sensors can be used to investigate trehalose transporter candidates and monitor trehalose steady-state levels in vivo as well.

scholarly journals System Approach from Biomass Combustion in Packed Bed Reactor

2007 ◽  
Vol 7 (1 & 2) ◽  
pp. 16 ◽  
Author(s):  
Anhkien Le ◽  
Le Xuan Hai ◽  
V. N. Sharifi ◽  
J. Swithenbank
Keyword(s):  
Steady State ◽  
Transition Period ◽  
Computing Time ◽  
Substrate Inhibition ◽  
Simple Algorithm ◽  
Packed Bed ◽  
Packed Bed Reactor ◽  
Biomass Combustion ◽  
Stable Steady State ◽  
State Tests

A simple algorithm originally proposed by Choong, Paterson and Scott (2002) was tested on a model of an isothermal controlled-cycled stirred tank reactor with substrate inhibition kinetics, (r = 1 ~c). In previous work, this reacting system had been shown to exhibit steady-state multiplicity. The transition period of this system to the stable steady state is sometimes characterized by very slow change followed by a very rapid convergence to the stable steady state. Tests of the Choong-Paterson-Scott algorithm showed that the feature, which prevents premature termination of the calculations prior to reaching the true steady state, is very useful for this system. However, tests of the stopping criterion showed that the other feature of reducing the computing time was not realized in this system.

scholarly journals Nonlinear Dynamics of the Rigid Drum for Vibratory Roller on Elastic Subgrades

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Lun Liu ◽  
Fenghui Wang ◽  
Shupeng Sun ◽  
Weiming Feng ◽  
Chao Guo
Keyword(s):  
Nonlinear Dynamics ◽  
Phase Diagram ◽  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Period Doubling ◽  
Time History ◽  
Nonlinear Dynamic Model ◽  
Compaction Process ◽  
Adjustment Strategy ◽  
Vibratory Compaction

In this paper, a coupling nonlinear dynamic model of the drum and subgrade is established for the vibratory roller. The dynamic characteristics of the rigid drum of the vibratory roller in the process of vibratory compaction are comprehensively investigated by time history, phase diagram, frequency spectrum, Poincare map, and bifurcation diagram. During the compaction process, the stiffness of the subgrade increases and the motion of the rigid drum of the vibratory roller changes from a single period to multiple periods and finally enters chaos by the way of period doubling. Moreover, the roller parameters also significantly affect the dynamic characteristics of the rigid drum and the compaction effect of the subgrade. Based on detailed numerical results, a parameter adjustment strategy about the roller frequency and nominal amplitude is proposed, which can avoid the “bouncing” of the drum during compaction and improve the compaction efficiency.

Heuristic control of bipedal running: steady-state and accelerated

Robotica ◽  
2011 ◽  
Vol 29 (6) ◽  
pp. 939-947
Author(s):  
A. D. Perkins ◽  
K. J. Waldron ◽  
P. J. Csonka
Keyword(s):  
Steady State ◽  
Experimental System ◽  
Legged Robots ◽  
Stable Steady State ◽  
Control Laws ◽  
Mechanical Coupling ◽  
Ankle Joints

SUMMARYThe design, control, and actuation of legged robots that walk is well established, but there remain unsolved problems for legged robots that run. In this work, dynamic principles are used to develop a set of heuristics for controlling bipedal running and acceleration. These heuristics are then converted into control laws for two very different bipedal systems: one with a high-inertia torso and prismatic knees and one with a low-inertia torso, articulated knees, and mechanical coupling between the knee and ankle joints. These control laws are implemented in simulation to achieve stable steady-state running, accelerating, and decelerating. Stable steady-state running is also achieved in a planar experimental system with a semiconstrained torso.

Analysis of chemical kinetic systems over the entire parameter space - I. The Sal’nikov thermokinetic oscillator

1988 ◽  
Vol 416 (1851) ◽  
pp. 391-402 ◽  
Keyword(s):  
Steady State ◽  
Parameter Space ◽  
Limit Cycles ◽  
Stable Limit Cycle ◽  
Chemical Kinetic ◽  
Phase Portraits ◽  
Stable Steady State ◽  
Stable Limit ◽  
Unstable Steady State ◽  
Undamped Oscillations

In this series of papers we re-examine, using recently developed techniques, some chemical kinetic models that have appeared in the literature with a view to obtaining a complete description of all the qualitatively distinct behaviour that the system can exhibit. Each of the schemes is describable by two coupled ordinary differential equations and contain at most three independent parameters. We find that even with these relatively simple chemical schemes there are regions of parameter space in which the systems display behaviour not previously found. Quite often these regions are small and it seems unlikely that they would be found via classical methods. In part I of the series we consider one of the thermally coupled kinetic oscillator models studied by Sal’nikov. He showed that there is a region in parameter space in which the system would be in a state of undamped oscillations because the relevant phase portrait consists of an unstable steady state surrounded by a stable limit cycle. Our analysis has revealed two further regions in which the phase portraits contain, respectively, two limit cycles of opposite stability enclosing a stable steady state and three limit cycles of alternating stability surrounding an unstable steady state. This latter region is extremely small, so much so that it could be reasonably neglected in any predictions made from the model.

Fluid dynamics of flapping aquatic flight in the bird wrasse:three-dimensional unsteady computations with fin deformation

2002 ◽  
Vol 205 (19) ◽  
pp. 2997-3008 ◽  
Author(s):  
Ravi Ramamurti ◽  
William C. Sandberg ◽  
Rainald Löhner ◽  
Jeffrey A. Walker ◽  
Mark W. Westneat
Keyword(s):  
Fluid Dynamics ◽  
Steady State ◽  
Three Dimensional ◽  
Force Production ◽  
Time History ◽  
The Body ◽  
Vertical Acceleration ◽  
Field Variation ◽  
Pectoral Fin ◽  
Pectoral Fins

SUMMARY Many fishes that swim with the paired pectoral fins use fin-stroke parameters that produce thrust force from lift in a mechanism of underwater flight. These locomotor mechanisms are of interest to behavioral biologists,biomechanics researchers and engineers. In the present study, we performed the first three-dimensional unsteady computations of fish swimming with oscillating and deforming fins. The objective of these computations was to investigate the fluid dynamics of force production associated with the flapping aquatic flight of the bird wrasse Gomphosus varius. For this computational work, we used the geometry of the wrasse and its pectoral fin,and previously measured fin kinematics, as the starting points for computational investigation of three-dimensional (3-D) unsteady fluid dynamics. We performed a 3-D steady computation and a complete set of 3-D quasisteady computations for a range of pectoral fin positions and surface velocities. An unstructured, grid-based, unsteady Navier—Stokes solver with automatic adaptive remeshing was then used to compute the unsteady flow about the wrasse through several complete cycles of pectoral fin oscillation. The shape deformation of the pectoral fin throughout the oscillation was taken from the experimental kinematics. The pressure distribution on the body of the bird wrasse and its pectoral fins was computed and integrated to give body and fin forces which were decomposed into lift and thrust. The velocity field variation on the surface of the wrasse body, on the pectoral fins and in the near-wake was computed throughout the swimming cycle. We compared our computational results for the steady, quasi-steady and unsteady cases with the experimental data on axial and vertical acceleration obtained from the pectoral fin kinematics experiments. These comparisons show that steady state computations are incapable of describing the fluid dynamics of flapping fins. Quasi-steady state computations, with correct incorporation of the experimental kinematics, are useful when determining trends in force production, but do not provide accurate estimates of the magnitudes of the forces produced. By contrast, unsteady computations about the deforming pectoral fins using experimentally measured fin kinematics were found to give excellent agreement, both in the time history of force production throughout the flapping strokes and in the magnitudes of the generated forces.

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