scholarly journals Multiple-Scale Analysis of a Tunable Bi-Stable Piezoelectric Energy Harvester

2020 ◽  
Vol 1 (2) ◽  
Author(s):  
Feng Qian ◽  
Nicole Abaid ◽  
Lei Zuo
Keyword(s):  
Energy Harvester ◽  
Multiple Scale ◽  
High Order ◽  
Stable System ◽  
Scale Analysis ◽  
Analytical Strategy ◽  
Piezoelectric Energy ◽  
Coupling Terms ◽  
The Stability ◽  
Multiple Scale Analysis

Abstract This paper presents the theoretical modeling and multiple-scale analysis of a novel piezoelectric energy harvester composed of a metal cantilever beam, piezoelectric films, and an axial preload spring at the moveable end. The harvester experiences mono- and bi-stable regimes as the stiffness of preload spring increases. The governing equations are derived with two high-order coupling terms induced by the axial motion. The literature shows that these high-order coupling terms lead to tedious calculations in the stability analysis of solutions. This work introduces an analytical strategy and the implementation of the multiple-scale method for the harvester in either the mono- or bi-stable status. Numerical simulations are performed to verify the analytical solutions. The influence of the electrical resistance, excitation level, and the spring pre-deformation on the voltage outputs and dynamics are investigated. The spring pre-deformation has a slight influence on the energy harvesting performance of the mono-stable system, but a large effect on that of the bi-stable system.

Modification of Friction-Induced Instability in a Disk System Through Dither Excitation Forces

2007 ◽  
Author(s):  
Michael A. Michaux ◽  
Al Ferri ◽  
Kenneth A. Cunefare
Keyword(s):  
Floquet Theory ◽  
Frictional Contact ◽  
Annular Plate ◽  
Multiple Scale ◽  
Scale Analysis ◽  
Combined System ◽  
Disk System ◽  
The Stability ◽  
Rotor Model ◽  
Multiple Scale Analysis

This paper employs a continuous rotor model and a contacting SDOF system to examine dither’s role in stabilizing friction-induced oscillations. The disc rotor is modeled by a thin, clamped-free annular plate. Under the action of tangential dither, the frictional contact load is represented by a sinusoidally-varying follower force. The stability of the combined system, with and without dither signals, is assessed using multiple-scale analysis and Floquet theory. It is shown that dither is capable of quenching instabilities at some rotor speeds while at the same time producing new instabilities at other rotor speeds. The results suggest that one mechanism by which dither can suppress squeal is by changing the rotor speeds at which squeal vibrations occur.

Multiple scale analysis of factors influencing the distribution of an invasive aquatic grass

2008 ◽  
Vol 11 (8) ◽  
pp. 1903-1912 ◽  
Author(s):  
Sarina E. Loo ◽  
Ralph Mac Nally ◽  
Dennis J. O’Dowd ◽  
James R. Thomson ◽  
P. S. Lake
Keyword(s):  
Multiple Scale ◽  
Scale Analysis ◽  
Factors Influencing ◽  
Multiple Scale Analysis

scholarly journals Experiment and Theory on the Nonlinear Vibration of a Shallow Arch Under Harmonic Excitation at the End

2005 ◽  
Vol 74 (6) ◽  
pp. 1061-1070 ◽  
Author(s):  
Jen-San Chen ◽  
Cheng-Han Yang
Keyword(s):  
Steady State ◽  
Excitation Frequency ◽  
Multiple Scale ◽  
Steady State Response ◽  
Scale Analysis ◽  
Jump Phenomenon ◽  
Shallow Arch ◽  
State Response ◽  
Geometrical Imperfection ◽  
Multiple Scale Analysis

In this paper we study, both theoretically and experimentally, the nonlinear vibration of a shallow arch with one end attached to an electro-mechanical shaker. In the experiment we generate harmonic magnetic force on the central core of the shaker by controlling the electric current flowing into the shaker. The end motion of the arch is in general not harmonic, especially when the amplitude of lateral vibration is large. In the case when the excitation frequency is close to the nth natural frequency of the arch, we found that geometrical imperfection is the key for the nth mode to be excited. Analytical formula relating the amplitude of the steady state response and the geometrical imperfection can be derived via a multiple scale analysis. In the case when the excitation frequency is close to two times of the nth natural frequency two stable steady state responses can exist simultaneously. As a consequence jump phenomenon is observed when the excitation frequency sweeps upward. The effect of geometrical imperfection on the steady state response is minimal in this case. The multiple scale analysis not only predicts the amplitudes and phases of both the stable and unstable solutions, but also predicts analytically the frequency at which jump phenomenon occurs.

scholarly journals Multiple-scale analysis of quantum systems

1996 ◽  
Vol 54 (12) ◽  
pp. 7710-7723 ◽  
Author(s):  
Carl M. Bender ◽  
Luís M. A. Bettencourt
Keyword(s):  
Multiple Scale ◽  
Quantum Systems ◽  
Scale Analysis ◽  
Multiple Scale Analysis
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