An Exact Solution for Response Spectral Density of a Single-Degree-of-Freedom System Under Both Parametric and Additive White Noise Excitations

2002 ◽  
Vol 69 (3) ◽  
pp. 399-400 ◽  
Author(s):  
M. F. Dimentberg ◽  
Y. K. Lin
Keyword(s):  
Exact Solution ◽  
Spectral Density ◽  
White Noise ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Additive White Noise

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.

Transients in Simple Undamped Oscillators Under Inertial Disturbances

1959 ◽  
Vol 26 (2) ◽  
pp. 217-223
Author(s):  
Antongiulio Dornig
Keyword(s):  
Exact Solution ◽  
Maximum Amplitude ◽  
Degree Of Freedom ◽  
Inertial Forces ◽  
Constant Acceleration ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Approximate Formulas

Abstract Single-degree-of-freedom systems acted upon inertial forces are often found in technical applications. In this paper we shall study the transients in the vibrations of the system due to a change in speed in the machine in which the inertial forces are generated. We shall state the problem in the most general case, and then study the starting and the stopping with constant acceleration. After giving the exact solution of the problem we shall derive very simple approximate formulas for the determination of the maximum amplitude reached in these transients.

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