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Self-excited Oscillations of a String on an Elastic Foundation Subject to a Nonlinear Feed-forward Force by O. Gottlieb; A. Cohen is a Engineering article available to read on EtoBox.

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We investigate the self-excited oscillations of a string on an elastic foundation that is subject to a nonlinear feed-forward force. The feed-forward follows that of a model first proposed by Steele and Baker [1] for an active cochlear, and is due to the gain factor profile which depends on the string displacement. In order to determine the bifurcation structure induced by the nonlinear feed-forward mechanism, we formulate a taut string initial-boundary-value problem with periodic boundary conditions which is reduced to a finite order modal dynamical system. We employ an asymptotic multiple-scales method to obtain slowly varying evolution equations that enable an analytical derivation of the periodic system response and analysis of its orbital stability. The resulting bifurcation structure includes multiple regions of both stable and unstable coexisting periodic solutions defined by primary and secondary Hopf stability thresholds. Numerical verification of the bifurcation structure determines the accuracy of the analytically predicted periodic self-excited response and reveals the existence of quasiperiodic combination-tone solutions and complex nonstationary solutions that emerge

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Author

O. Gottlieb; A. Cohen

Publisher

Elsevier Science; Elsevier ; Elsevier Ltd.; Elsevier BV (ISSN 0020-7403)

Published

2010

Language

EN

Field

Engineering (Physical Sciences)