Geodesic
Asymptotics of spectrum and eigenharmonics of the discrete string containing a bead of vanishing mass
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 29, Tome 264 (2000), pp. 164-181

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A discrete string with fixed endpoints containing a finite number of pointlike masses (beads) is under consideration. Behaviour of eigenfrequences and eigenharmonics of the string when one of the masses tending to zero is studied. 
@article{ZNSL_2000_264_a10,
     author = {V. S. Kolezhuk},
     title = {Asymptotics of spectrum and eigenharmonics of the discrete string containing a bead of vanishing mass},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {164--181},
     publisher = {mathdoc},
     volume = {264},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_264_a10/}
}
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V. S. Kolezhuk. Asymptotics of spectrum and eigenharmonics of the discrete string containing a bead of vanishing mass. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 29, Tome 264 (2000), pp. 164-181. http://geodesic.mathdoc.fr/item/ZNSL_2000_264_a10/