Title

Basic Response Functions Of Simple Inertoelastic And Inertoviscous Models

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.

Publication Date

1-1-2017

Publication Title

Journal of Engineering Mechanics

Volume

143

Issue

11

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1061/(ASCE)EM.1943-7889.0001348

Socpus ID

85028009224 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85028009224

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