Random oscillations of a mechanical system with one degree of freedom under the action of a periodic force and ?white noise?

1983 ◽  
Vol 34 (5) ◽  
pp. 516-519
Author(s):  
Nguyen Dong An'
Keyword(s):  
White Noise ◽  
Mechanical System ◽  
Degree Of Freedom ◽  
Periodic Force

Model Reduction of Piezoelectric Energy Harvesters Subject to Band-Limited, Stochastic Base Excitation

2012 ◽  
Author(s):  
Adam M. Wickenheiser
Keyword(s):  
White Noise ◽  
Design Optimization ◽  
Broadband Noise ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Energy Harvesters ◽  
White Noise Excitation ◽  
Single Degree ◽  
Piezoelectric Energy ◽  
Band Limited

In many scenarios where vibration energy harvesting can be utilized — particularly those involving bio-motions or environmental disturbances — energy sources are broadband and non-stationary. On the other hand, design procedures have been predominantly developed for harmonic or white noise excitation, specifically for single degree of freedom approximations of the transducer. In this paper, a general approach for design optimization of cantilevered, piezoelectric energy harvesters in the presence of band-limited, white-noise excitation is outlined. For this study, human and vehicular motions are considered; these complex waveforms are distilled into a small set of dominant features with regard to their impact on the power output of the device. Criteria based on modal participation factors, including pre-filtering of the disturbance, are used in guiding the reduction of the input and plant degrees of freedom in order to make the design optimization problem tractable. This process determines the error in assuming a low-order model for the transducer in the presence of broadband noise that may excite multiple modes of vibration. Furthermore, this study considers the quantitative impact of charge cancellation in higher modes and the benefits of inserting multiple electrodes along the length. To illustrate these methods, energy harvesters are designed for acceleration data collected from walking and car idling. It is shown that a simple method that is a generalization of naïve approaches that assume harmonic or white noise excitation and a single degree of freedom can determine which simplifications are appropriate and the inaccuracies that can be expected from them.

Uniformly Bounded Input Gives Ultimately Bounded Output: On the Dynamics of a Piecewise Linear Beam System

1999 ◽  
Author(s):  
Marcel F. Heertjes ◽  
Marinus J. G. van de Molengraft ◽  
Jan J. Kok
Keyword(s):  
Periodic Solution ◽  
Piecewise Linear ◽  
Wave Force ◽  
Degree Of Freedom ◽  
Harmonic Force ◽  
Periodic Force ◽  
Beam System ◽  
Bounded Input ◽  
Uniformly Bounded

Abstract A periodically excited piecewise linear beam system is studied. The beam system consists of a supported multi-degree-of-freedom beam with one-sided spring. This system is proved to have a 1-periodic solution to any uniformly bounded periodic force applied along the beam. The existence of a 1-periodic solution will be shown numerically and experimentally for both a harmonic force and a block-wave force.

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