Point spectra and normal modes of the Rayleigh loaded string with damping
We describe the point spectra of some dissipative version of the celebrated “Rayleigh loaded string”, an elastic string of finite length carrying a number n ≥ 1 of equally spaced, equal point masses, which is a basic model that exhibits a band structure and appears in many applied areas. We...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade
2025-01-01
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| Series: | Theoretical and Applied Mechanics |
| Subjects: | |
| Online Access: | https://doiserbia.nb.rs/img/doi/1450-5584/2025/1450-55842500010F.pdf |
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| Summary: | We describe the point spectra of some dissipative version of the celebrated
“Rayleigh loaded string”, an elastic string of finite length carrying a
number n ≥ 1 of equally spaced, equal point masses, which is a basic model
that exhibits a band structure and appears in many applied areas. We
consider the case in which the dissipation is due to a viscous damping due
to the interaction string-environment, a standard model for internal
visco-elastic dissipation (the Kelvin-Voigt model), and their combined
presence. We show that the point spectrum of each of these damped versions
of the Rayleigh loaded string is a continuous deformation of the point
spectrum of the unloaded elastic strings with that damping and that presents
a band structure similar to that of the undamped case. We also provide
explicit analytical expressions for the eigenfunctions, for any value of n. |
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| ISSN: | 1450-5584 2406-0925 |