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Free vibrations of axisymmetric shells: Parabolic and elliptic cases
2017
Asymptotic Analysis
Approximate eigenpairs (quasimodes) of axisymmetric thin elastic domains with laterally clamped boundary conditions (Lam{\'e} system) are determined by an asymptotic analysis as the thickness ($2\varepsilon$) tends to zero. The departing point is the Koiter shell model that we reduce by asymptotic analysis to a scalar modelthat depends on two parameters: the angular frequency $k$ and the half-thickness $\varepsilon$. Optimizing $k$ for each chosen $\varepsilon$, we find power laws for $k$ in
doi:10.3233/asy-171426
fatcat:ewlxmh6cergqthvbautozgtaqa