Effects of Incident Nearfield Waves on the Reflection Coefficients for Flexural Vibrations with a Nonlinear Boundary

Abstract

PurposeThis paper studies how a nearfield incident wave affects reflection coefficients for an Euler–Bernoulli beam attached to a cubic nonlinear boundary stiffness.MethodsA number of time-harmonic nearfield and propagating waves are incident on the boundary at different frequencies, these being integer multiples of the fundamental (lowest) frequency. Reflected waves also at frequencies multiple of the fundamental frequency are produced as a result. Reflection coefficients are normalized with respect to the incident propagating wave’s amplitude at the fundamental frequency. The reflection coefficients, which rely on the amplitudes of the incident waves, are calculated using a series of equations. The harmonic balance method is used to truncate these equations, and they are then solved numerically.ResultsIn order to compare numerical findings to the case in which only propagating waves are incident, a mix of incident nearfield and propagating waves is considered. Furthermore, the effects of nonlinearity on the net propagating excited wave are shown.ConclusionIt is shown that nearfield waves can have a profound effect on the reflection coefficients.