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research-article

Large and Infinite Mass-Spring-Damper Networks

[+] Author and Article Information
Kevin Leyden

PhD Graduate, Aerospace & Mechanical Engineering, University of Notre Dame, Notre Dame, Indiana 46556
kleyden@alumni.nd.edu

Mihir Sen

Professor Emeritus, Aerospace & Mechanical Engineering, University of Notre Dame, Notre Dame, Indiana 46556
msen@nd.edu

Bill Goodwine

Professor, Aerospace & Mechanical Engineering, University of Notre Dame, Notre Dame, Indiana 46556
billgoodwine@nd.edu

1Corresponding author.

ASME doi:10.1115/1.4042466 History: Received November 17, 2017; Revised December 28, 2018

Abstract

This paper introduces mechanical networks as a tool for modeling complex unidirectional vibrations. Networks of this type have branches containing massless linear springs and dampers, with masses at the nodes. Tree and ladder configurations are examples demonstrating that the overall dynamics of infinite systems can be represented using implicitly defined integro-differential operators. Results from the proposed models compare well to numerical results from finite systems, so this approach may have advantages over high-order differential equations.

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