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- W2087264112 abstract "If R is two-dimensional, the eigenvalues Xi(k) are proportional to the squares of the frequencies of a membrane covering R and elastically supported on the boundary B. If R is three-dimensional they are proportional to the squares of the frequencies of an acoustic resonator with elastic walls B. For k = so we have the boundary condition u = 0. In this case the eigenvalues are decreasing domain functionals so that lower bounds can be found immediately. This, however, is not true for finite k. In Section 2 we give the easily computed lower bound (2.11) for Xl(k) for any two-dimensional R and the analogue (2.15) for three-dimensional R. Equality is attained when R is a rectangle or parallelepiped. It is shown" @default.
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- W2087264112 date "1957-12-01" @default.
- W2087264112 modified "2023-10-18" @default.
- W2087264112 title "Lower Bounds for Vibration Frequencies of Elastically Supported Membranes and Plates" @default.
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- W2087264112 doi "https://doi.org/10.1137/0105012" @default.
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