Vol. 10, No. 3, 2017

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The vibration spectrum of two Euler–Bernoulli beams coupled via a dissipative joint

Chris Abriola, Matthew P. Coleman, Aglika Darakchieva and Tyler Wales

Vol. 10 (2017), No. 3, 443–463

The asymptotic estimation of the vibration spectrum for a system of two identical Euler–Bernoulli beams coupled via each of the four standard types of linear dissipative joint has been solved for the case when one beam is clamped and the other beam is free at the outer ends. Here, we generalize those results and solve the problem for all 40 combinations of energy-conserving end conditions. We provide both asymptotic and numerical results, and we compare the various systems with an eye toward determining which configurations lead to asymptotically equivalent vibration spectra.

vibration, eigenfrequency, Euler–Bernoulli beam, dissipative
Mathematical Subject Classification 2010
Primary: 74H10, 74H15
Received: 7 November 2015
Revised: 21 January 2016
Accepted: 1 April 2016
Published: 14 December 2016

Communicated by Kenneth S. Berenhaut
Chris Abriola
Department of Mathematics and Statistics
University of New Hampshire
Durham, NH 03824
United States
Matthew P. Coleman
Department of Mathematics and Computer Science
Fairfield University
Fairfield, CT 06824
United States
Aglika Darakchieva
Department of Mathematics
University of Connecticut
Storrs, CT 06269
United States
Tyler Wales
Department of Mathematics
Louisiana State University
Baton Rouge, LA 70803
United States