Geodesic
Low-frequency vibration modes of strongly
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 18 (2018) no. 4, pp. 447-457

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The dynamic behaviour of thin multi-layered structures, composed of contrasting “strong” and “weak” layers, is considered. An asymptotic procedure for analysing the lowest cutoffs is developed. A polynomial frequency equation is derived, along with the linear equations for the associated eigenforms corresponding to displacement variation across the thickness. For a five-layered laminate with clamped faces two term expansions for eigenfrequencies and eigenforms are compared with those obtained from the exact solution of the original problem for thickness resonances. 
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     author = {J. D. Kaplunov and L. A. Prikazchikova},
     title = {Low-frequency vibration modes of strongly},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {447--457},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ISU_2018_18_4_a7/}
}
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J. D. Kaplunov; L. A. Prikazchikova. Low-frequency vibration modes of strongly. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 18 (2018) no. 4, pp. 447-457. http://geodesic.mathdoc.fr/item/ISU_2018_18_4_a7/