Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Eigenfrequencies of the non-collinearly coupled Euler-Bernoulli beam system with dissipative joints


Author: William H. Paulsen
Journal: Quart. Appl. Math. 55 (1997), 437-457
MSC: Primary 73K12; Secondary 35P20, 73D30, 73K05
DOI: https://doi.org/10.1090/qam/1466142
MathSciNet review: MR1466142
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Abstract: In this paper, we will compute asymptotically the eigenfrequencies for the in-plane vibrations of the general non-collinear Euler-Bernoulli beam equation with dissipative joints. Many different kinds of dampers are allowed, even within the same structure. This generalizes a previous result for collinear structures. Matrix techniques are used to combine asymptotic analysis with the wave propagation method. We will find that if the lengths of the beams are rational, there will be a finite number of ``streams'' of eigenfrequencies, and, like the collinear case, each lies asymptotically to a vertical line.


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DOI: https://doi.org/10.1090/qam/1466142
Article copyright: © Copyright 1997 American Mathematical Society


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