Abstract
We study vibrational properties of non-homogeneous materials. These are idealized materials composed by one dimensional chains of harmonic oscillators represented by an alternating sequence of particles and springs. Although the system is linear, thus possesses exact explicit solutions, the formulas for the solutions can be complicated. Homogeneous chains are used as basic building blocks for the characterization of the system global dynamics. In particular, we determine the solutions for a system composed of two distinct homogeneous chains in terms of the original solutions for these two homogeneous chains, when uncoupled. We explore different kinds of possible couplings, each with a distinct physical meaning.
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Acknowledgements
The authors would like to thank the referees for the several comments made in order to improve the presentation.
The work leading to this paper was partially supported by CIMA-UE through Grant UID/MAT/04674/2019 of FCT—Fundação para a Ciência e a Tecnologia, Ministério da Educação e Ciência and BROCQ- project LT20-03-0247-FEDER-017659, Portugal 2020.
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Bandeira, L., Ramos, C.C. Non-homogeneous Chain of Harmonic Oscillators. Math.Comput.Sci. 16, 3 (2022). https://doi.org/10.1007/s11786-022-00522-x
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DOI: https://doi.org/10.1007/s11786-022-00522-x