Turning-Point Peculiarities in the Near-Resonant Response of Slightly Tapered Membrane Strips

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Abstract
Unusual and surprising features of the response of a slightly tapered, nearly rectangular membrane, or analogous medium, excited at either the wider end or the narrower end and fixed on the other three sides are examined analytically. Radical differences between the two appear for the same “near-resonant” frequency. For excitation at the wider end, there can be a large-amplitude response in the wider half, while the narrower half remains almost undisturbed. For excitation at the narrower end, there is only small-amplitude response throughout. These peculiarities are associated with the presence of a “turning point,” in the sense of the WKB method used in the analysis.

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