A Nonlinear Analysis of the Wahl–Fischer Torsional Instability

2020 ◽  
Vol 88 (2) ◽  
Author(s):  
E. F. Infante ◽  
S. Doughty
Keyword(s):  
Large Amplitude ◽  
Linear Analysis ◽  
Mathematical Explanation ◽  
Nonlinear Methods ◽  
Strongly Nonlinear ◽  
Instability Problem ◽  
Torsional Instability ◽  
Mechanical Devices ◽  
Trans Asme ◽  
Nonlinear Nature

Abstract This is an extension to a previous study of the Wahl–Fischer torsional instability problem (Infante and Doughty, “An Old Problem Reconsidered: The Wahl–Fischer Torsional Instability Problem”, J. Appl. Mech. Trans. ASME, 2020, 87(10), p. 101004). There, we provided a mathematical explanation of the reasons for the existence of torsional oscillations observed in numerical simulations and in actual mechanical devices such as the exhaust fan system studied by Wahl and Fischer. That explanation was mostly based on linear analysis. This paper presents an additional mathematical explanation of the nature and form of the large self-excited oscillations, due to the strongly nonlinear nature of the system and the large amplitude of these oscillations. Because the oscillations are large, their study requires the use of nonlinear methods.

High-frequency vibration energy harvesting from repeated impulsive forcing utilizing intentional dynamic instability caused by strong nonlinearity

2016 ◽  
Vol 28 (4) ◽  
pp. 468-487 ◽  
Author(s):  
Kevin Remick ◽  
D Dane Quinn ◽  
D Michael McFarland ◽  
Lawrence Bergman ◽  
Alexander Vakakis
Keyword(s):  
Energy Harvesting ◽  
Mechanical System ◽  
High Frequency ◽  
Large Amplitude ◽  
Electromechanical Coupling ◽  
Dynamic Instability ◽  
Vibration Energy ◽  
Primary System ◽  
Vibration Energy Harvesting ◽  
Strongly Nonlinear

The work in this study explores the excitation of high-frequency dynamic instabilities to enhance the performance of a strongly nonlinear vibration-based energy harvesting system subject to repeated impulsive excitations. These high-fraequency instabilities arise from transient resonance captures (TRCs) in the damped dynamics of the system, leading to large-amplitude oscillations in the mechanical system. Under proper forcing conditions, these high-frequency instabilities can be sustained. The primary system is composed of a grounded, weakly damped linear oscillator, which is directly subjected to impulsive forcing. A light-weight, damped nonlinear oscillator (nonlinear energy sink, NES) is coupled to the primary system using electromechanical coupling elements and strongly nonlinear stiffness elements. The essential (nonlinearizable) stiffness nonlinearity arises from geometric and kinematic effects resulting from the traverse deflection of a piano wire coupling the two oscillators. The electromechanical coupling is composed of a neodymium magnet and inductance coil, which harvests the energy in the mechanical system and transfers it to the electrical system which, in this present case, is composed of a simple resistive element. The energy dissipated in the circuit is inferred as a measure of energy harvesting capability. The large-amplitude TRCs result in strong, nearly irreversible energy transfer from the primary system to the NES, where the harvesting elements work to convert the mechanical energy to electrical energy. The primary goal of this work is to numerically and experimentally demonstrate the efficacy of inducing sustained high-frequency dynamic instability in a system of mechanical oscillators to achieve enhanced vibration energy harvesting performance. This work is a continuation of a companion paper (Remick K, Quinn D, McFarland D, et al. (2015) Journal of Sound and Vibration Final Publication) where vibration energy harvesting of the same system subject to single impulsive excitation is studied.

Robust Stabilization of Large Amplitude Ship Rolling in Beam Seas

1997 ◽  
Vol 122 (1) ◽  
pp. 108-113 ◽  
Author(s):  
Shyh-Leh Chen ◽  
Steven W. Shaw ◽  
Hassan K. Khalil ◽  
Armin W. Troesch
Keyword(s):  
Large Amplitude ◽  
Controller Design ◽  
Sliding Mode ◽  
Robust Stabilization ◽  
Vertical Plane ◽  
Singularly Perturbed Systems ◽  
Strongly Nonlinear ◽  
Beam Seas ◽  
Dynamics And Control ◽  
And Control

The dynamics and control of a strongly nonlinear 3-DOF model for ship motion are investigated. The model describes the roll, sway, and heave motions occurring in a vertical plane when the vessel is subjected to beam seas. The ship is installed with active antiroll tanks as a means of preventing large amplitude roll motions. A robust state feedback controller for the pumps is designed that can handle model uncertainties, which arise primarily from unknown hydrodynamic loads. The approach for the controller design is a combination of sliding mode control and composite control for singularly perturbed systems, with the help of the backstepping technique. It is shown that this design can effectively control roll motions of large amplitude, including capsize prevention. Numerical simulation results for an existing fishing vessel, the twice-capsized Patti-B, are used to verify the analysis. [S0022-0434(00)02701-5]

Non Linear Analysis of Ship Motions and Loads in Large Amplitude Waves

2010 ◽  
Author(s):  
G Mortola ◽  
◽  
A Incecik ◽  
O Turan ◽  
S E Hirdaris ◽  
...  
Keyword(s):  
Large Amplitude ◽  
Linear Analysis ◽  
Ship Motions ◽  
Non Linear

Nonlinear electron-acoustic waves in a multi-species plasma

1980 ◽  
Vol 24 (1) ◽  
pp. 169-180 ◽  
Author(s):  
B. Buti
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Large Amplitude ◽  
Space Plasmas ◽  
Strongly Nonlinear ◽  
Electron Acoustic Waves ◽  
Electron Acoustic ◽  
Ion Species

Propagation of electron-acoustic waves in a strongly nonlinear magnetoplasma with two ion species is investigated. The presence of the second ion component affects the dynamics of these solitary waves in a variety of ways. Besides solitons, supersonic holes (density depressions) are produced by sufficiently large- amplitude perturbations. Heavier and hotter ions are more favourable to the holes. Applications of the present investigations to space plasmas are pointed out.

An Old Problem Reconsidered: The Wahl–Fischer Torsional Instability Problem

2020 ◽  
Vol 87 (10) ◽  
Author(s):  
E. F. Infante ◽  
S. Doughty
Keyword(s):  
Differential Equations ◽  
Qualitative Analysis ◽  
Induction Motors ◽  
Mechanical Systems ◽  
Exhaust System ◽  
Electromechanical Systems ◽  
Physical Systems ◽  
Instability Problem ◽  
Torsional Instability ◽  
Central Purpose

Abstract The phenomenon of torsional instabilities found in rotating mechanical systems powered by induction motors was encountered in the late 1930s by Wahl and Fisher in a turnpike exhaust system. Subsequently, this phenomenon has been repeatedly found to affect a number of similar physical systems and has led to a number of studies and analysis that have clarified the reasons for these instabilities, associated with the torque characteristics of induction motors. Surprisingly, none of these studies have presented a mathematical qualitative analysis of the eigenvalues of the differential equations that describe such electromechanical systems. This is the central purpose of this paper. It depends on the identification and exploitation of a particular “central” solution to the differential equations that describe the system, and of its relationship to a simpler formulation of the same system. This turns out to be a rather modest mathematical endeavor which, however, yields result that illuminate the nature of the instabilities encountered and provides a designer of such systems with the tools to abate or avoid these instabilities.

scholarly journals Interactions of large amplitude solitary waves in viscous fluid conduits

2014 ◽  
Vol 750 ◽  
pp. 372-384 ◽  
Author(s):  
Nicholas K. Lowman ◽  
M. A. Hoefer ◽  
G. A. El
Keyword(s):  
Solitary Wave ◽  
Viscous Fluid ◽  
Solitary Waves ◽  
Water Waves ◽  
Large Amplitude ◽  
Wave Interactions ◽  
Weakly Nonlinear ◽  
Strongly Nonlinear ◽  
Nonlinear Solitary Waves

AbstractThe free interface separating an exterior, viscous fluid from an intrusive conduit of buoyant, less viscous fluid is known to support strongly nonlinear solitary waves due to a balance between viscosity-induced dispersion and buoyancy-induced nonlinearity. The overtaking, pairwise interaction of weakly nonlinear solitary waves has been classified theoretically for the Korteweg–de Vries equation and experimentally in the context of shallow water waves, but a theoretical and experimental classification of strongly nonlinear solitary wave interactions is lacking. The interactions of large amplitude solitary waves in viscous fluid conduits, a model physical system for the study of one-dimensional, truly dissipationless, dispersive nonlinear waves, are classified. Using a combined numerical and experimental approach, three classes of nonlinear interaction behaviour are identified: purely bimodal, purely unimodal, and a mixed type. The magnitude of the dispersive radiation due to solitary wave interactions is quantified numerically and observed to be beyond the sensitivity of our experiments, suggesting that conduit solitary waves behave as ‘physical solitons’. Experimental data are shown to be in excellent agreement with numerical simulations of the reduced model. Experimental movies are available with the online version of the paper.

Symmetry Design in Flexure Systems Using Kinematic Principles

2013 ◽  
Author(s):  
Jingjun Yu ◽  
Shouzhong Li ◽  
Shusheng Bi ◽  
Guanghua Zong
Keyword(s):  
High Performance ◽  
Screw Theory ◽  
Mathematical Explanation ◽  
Symmetrical Design ◽  
Dynamic Performances ◽  
Living Organisms ◽  
Improving Accuracy ◽  
Mechanical Devices ◽  
Effective Use

Inspiration for the creation of mechanical devices often comes from observing the natural structures and movements of living organisms. Understanding the wide use of modularity and compliance in nature may lead to the design of high-performance flexure systems or compliant devices. One of the most important nature-inspired paradigms for constructing flexure systems is based on the effective use of symmetry. With a rigid mathematical foundation called screw theory and Lie group. The research of this paper mainly focuses on: (i) Mathematical explanation or treatment of symmetry design wildly used in flexure systems, concerning with a series of topics such as the relationship between degree of freedom (DOF), constraint, overconstraint, decouple motion and symmetrical geometry, and How to guarantee the mobility unchanged when using symmetry design? (ii) A compliance-based analytical verification for demonstrating that the symmetry design can effectively improve accuracy and dynamic performances. (iii) The feasibility of improving accuracy performance by connecting symmetry design with the principle of elastic averaging. The whole content is organized around a case study, i.e. symmetrical design of 1-DOF translational flexure mechanisms. The results are intent to provide a rigid theoretical foundation and significant instruction for the symmetry design philosophy in flexure systems using kinematic principles.

scholarly journals Vibration attenuation in a nonlinear flexible structure via nonlinear switching circuits and energy harvesting implications

2019 ◽  
Vol 30 (7) ◽  
pp. 965-976 ◽  
Author(s):  
Tarcisio Silva ◽  
David Tan ◽  
Carlos De Marqui ◽  
Alper Erturk
Keyword(s):  
Energy Harvesting ◽  
Frequency Response ◽  
Large Amplitude ◽  
Short Circuit ◽  
Flexible Structures ◽  
Primary Resonance ◽  
Resonance Excitation ◽  
Flexible Structure ◽  
Strongly Nonlinear ◽  
Nonlinear Switching

We study the suppression of strongly nonlinear vibrations of a flexible structure by using nonlinear switching circuit techniques, namely the synchronized switch damping on short circuit and the synchronized switch damping on inductor circuit, as well as energy harvesting implications through the synchronized switch harvesting on inductor circuit combined with the same nonlinear structure. Nonlinear switching shunts have been mostly explored for suppressing linear resonance in flexible structures. However, such flexible structures can easily undergo undesired resonant bifurcations and exhibit co-existing large- and small-amplitude branches in their frequency response. In this work, we investigate a strongly nonlinear and weakly coupled flexible structure for suppressing its large-amplitude periodic response branch under primary resonance excitation. The synchronized switch damping on short circuit and synchronized switch damping on inductor circuit damping techniques are employed and compared with the baseline (near short circuit) frequency response. It is shown that the synchronized switch damping on inductor circuit can substantially reduce the large-amplitude branch, offering the possibility of entirely suppressing undesired bifurcations. Energy harvesting implications are also explored by using the same structure as a wideband energy harvester. While the harvested power can be boosted with a synchronized switch harvesting on inductor circuit, the large-amplitude branch of the harvester is significantly shortened due to the strong shunt damping effect as a trade-off.

Sign in / Sign up

Export Citation Format

Share Document