The way in which a nonlinear spring affects the reflection coefficients at the end of a rod and a beam is investigated in this paper. The specific type of nonlinearity considered is of the hardening and softening Duffing-type, which has both linear and cubic stiffness. The magnitudes and the phases of the reflection coefficients for longitudinal and flexural waves are determined. This is achieved by using the harmonic balance approach and the results are verified by comparing the incoming and the outgoing power from the boundary. It is shown that the main effect of the nonlinearity is to change the phase, except in the case of an incident evanescent wave when there is also a jump in the magnitude of the reflection coefficient. In addition, when the nonlinearity is of the softening type, a jump phenomenon occurs in the reflection coefficients.

Wave reflection at the end of a waveguide supported by a nonlinear spring / M.J. Brennan; E. Manconi; B. Tang; V. Lopes Jr. - (2014), pp. 2019-2025. ((Intervento presentato al convegno 9th International Conference on Structural Dynamics (EURODYN) tenutosi a Porto, Portugal nel 30 June - 2 July 2014.

Wave reflection at the end of a waveguide supported by a nonlinear spring

MANCONI, Elisabetta;
2014

Abstract

The way in which a nonlinear spring affects the reflection coefficients at the end of a rod and a beam is investigated in this paper. The specific type of nonlinearity considered is of the hardening and softening Duffing-type, which has both linear and cubic stiffness. The magnitudes and the phases of the reflection coefficients for longitudinal and flexural waves are determined. This is achieved by using the harmonic balance approach and the results are verified by comparing the incoming and the outgoing power from the boundary. It is shown that the main effect of the nonlinearity is to change the phase, except in the case of an incident evanescent wave when there is also a jump in the magnitude of the reflection coefficient. In addition, when the nonlinearity is of the softening type, a jump phenomenon occurs in the reflection coefficients.
978-972-752-165-4
Wave reflection at the end of a waveguide supported by a nonlinear spring / M.J. Brennan; E. Manconi; B. Tang; V. Lopes Jr. - (2014), pp. 2019-2025. ((Intervento presentato al convegno 9th International Conference on Structural Dynamics (EURODYN) tenutosi a Porto, Portugal nel 30 June - 2 July 2014.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2765974
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