Basic Response Functions of Simple Inertoelastic and Inertoviscous Models
Publication: Journal of Engineering Mechanics
Volume 143, Issue 11
Abstract
Motivated by the growing interest in suppressing vibrations with supplemental rotational inertia, this paper examines and constructs the basic frequency-response functions and subsequently derives the corresponding causal time-response functions of elementary mechanical networks that involve the inerter, a two-node element in which the force-output is proportional to the relative acceleration of its end-nodes. This is achieved by extending the relationship between the causality of a time-response function and the analyticity of its corresponding frequency-response function to the case of generalized functions. This paper shows that all frequency-response functions that exhibit singularities along the real frequency axis need to be enhanced with the addition of a Dirac delta function or with its derivative, depending on the strength of the singularity. It is shown that because of the inerter, some basic time-response functions exhibit causal oscillatory response, in contrast to the decaying exponentials that originate from dashpots. Most importantly, the inerter emerges as an attractive response-modification element because in some cases it absorbs the singular response of the solitary spring or dashpot.
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Acknowledgments
The assistance of Dr. H. Alexakis with the management of the electronic document is appreciated.
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Published In
Journal of Engineering Mechanics
Volume 143 • Issue 11 • November 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Nov 12, 2016
Accepted: May 8, 2017
Published online: Aug 16, 2017
Published in print: Nov 1, 2017
Discussion open until: Jan 16, 2018
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