Abstract
This paper is concerned with the development of upper bounds on the energy harvesting performance of a general multi-degree-of-freedom nonlinear electromechanical system that is subjected to random base motion and secondary applied periodic forces. The secondary forces are applied with the aim of enhancing the energy harvested from the base motion, and they may constitute direct excitation, or they may produce parametric terms in the equations of motion. It is shown that when the base motion has white noise acceleration then the power input by the base is always πS0M/2 where S0 is the single sided spectral density of the acceleration, and M is the mass of the system. This implies that although the secondary forces may enhance the energy harvested by causing a larger fraction of the power input from the base to be harvested rather than dissipated, there is an upper limit on the power that can be harvested. Attention is then turned to narrow band excitation, and it is found that in the absence of secondary forces a bound can be derived for a single degree of freedom system with linear damping and arbitrary nonlinear stiffness. The upper bound on the power input by the base is πMmax[S(ω)]/2, where S(ω) is the single sided base acceleration spectrum. The validity of this result for more general systems is found to be related to the properties of the first Wiener kernel, and this issue is explored analytically and by numerical simulation.
Highlights
The subject of harvesting energy from ambient vibration has been a topic of much research interest over recent years, as evidenced by the reviews presented in [1,2]
The main conclusions that can be drawn from the present work are as follows: (1) The power input by white noise base acceleration to a nonlinear multi-degree-of-freedom system of the very general type represented by Eq (12), is given by Eq (51) and depends only on the total mass of the system and the spectral density of the white noise
This result was demonstrated previously in Ref. [11] for the case in which the equations of motion do not depend explicitly on time t; the present work has extended this result to systems with parametric and direct secondary excitations
Summary
The subject of harvesting energy from ambient vibration has been a topic of much research interest over recent years, as evidenced by the reviews presented in [1,2]. Langley / Journal of Sound and Vibration 339 (2015) 247–261 application, it would be helpful if general guidelines were available to highlight good design features and to draw attention to any fundamental physics that might bound the performance of the device regardless of the detailed design This topic was addressed in [11], where a bound was derived for the power that can be harvested from any multi-degree-offreedom nonlinear electromechanical system under white noise base acceleration. When there are no secondary forces, it has been found that the condition always holds for a single-degree-of-freedom system with linear damping and any form of nonlinear stiffness; this type of system has been studied extensively in the energy harvesting literature (for example [7,8]) and so the result has application to existing design concepts. Throughout the analysis it is assumed that the random base motion is not affected by the presence of the system, and the analysis is directed solely at energy harvesting devices under prescribed base motions, rather than more general systems such as vibration absorbers which are designed to significantly modify the base motion
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
