Cite this article as:
Kaplunov J. D., Prikazchikova L. A. Low-Frequency Vibration Modes of Strongly Inhomogeneous Elastic Laminates. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2018, vol. 18, iss. 4, pp. 447-457. DOI: https://doi.org/10.18500/1816-9791-2018-18-4-447-457
Low-Frequency Vibration Modes of Strongly Inhomogeneous Elastic Laminates
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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