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.
Large and Infinite Mass–Spring–Damper Networks
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.
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Leyden, K., Sen, M., and Goodwine, B. (February 21, 2019). "Large and Infinite Mass–Spring–Damper Networks." ASME. J. Dyn. Sys., Meas., Control. June 2019; 141(6): 061005. https://doi.org/10.1115/1.4042466
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