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Research Papers

Large and Infinite Mass–Spring–Damper Networks

[+] Author and Article Information
Kevin Leyden

Aerospace & Mechanical Engineering,
University of Notre Dame,
Notre Dame, IN 46556
e-mail: kleyden@alumni.nd.edu

Mihir Sen

Professor Emeritus
Aerospace & Mechanical Engineering,
University of Notre Dame,
Notre Dame, IN 46556
e-mail: msen@nd.edu

Bill Goodwine

Professor
Aerospace & Mechanical Engineering,
University of Notre Dame,
Notre Dame, IN 46556
e-mail: billgoodwine@nd.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received November 17, 2017; final manuscript received December 28, 2018; published online February 21, 2019. Assoc. Editor: Dumitru I. Caruntu.

J. Dyn. Sys., Meas., Control 141(6), 061005 (Feb 21, 2019) (8 pages) Paper No: DS-17-1570; doi: 10.1115/1.4042466 History: Received November 17, 2017; Revised December 28, 2018

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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Figures

Grahic Jump Location
Fig. 1

Tree configuration. is input, is fixed. Components are indicated by .

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Fig. 2

Ladder configuration. is input, is fixed. Components are indicated by .

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Fig. 3

Single component of admittance Y. is input, is fixed.Admittance operator of a component is indicated by .

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Fig. 4

Single node of mass m. F1, F2, and F3 are forces on the node.

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Fig. 5

Tree configuration for n =1

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Fig. 6

Tree configuration for n =2

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Fig. 7

Tree configuration with no mass (n =3 shown); is input, is fixed

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Fig. 8

Large tree approximation and elongation of frequency band suggesting half-order behavior for finite trees

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Fig. 9

Time-domain excitation at frequency π/2 rad/s showing agreement between tree and approximation

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Fig. 10

Time-domain excitation at frequency 20π rad/s showing agreement between tree and adjusted approximation

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Fig. 11

Frequency response showing large approximation and fractional-order behavior for ladders

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