Nonlinear tube waves

Christoph Klieber * David Johnson
* Corresponding author
Abstract : A tube wave is an acoustic normal mode in which the energy is confined to the vicinity of a fluid-filled cylinder within an elastic solid. In the current study, we report on nonlinear tube wave propagation in a water-filled steel pipe, in particular the evolution of various frequency components of a narrow-band (multiple-cycle) pulse train. The dispersive behavior of the tube wave requires a careful selection of the frequency combinations under study (phase matching). In a first series of experiments, a transducer launches a pulse train of a single initial frequency, $\omega$, and we examine the evolution of the pressure amplitude at its harmonic frequency, $2\omega$ (second harmonic generation). In a second series, we study a pulse train consisting of two different initial frequencies, $\omega_1$ and $\omega_2$. In addition to the second harmonics of each initial frequency, nonlinear effects lead to the generation of signals centered around the difference and sum frequencies, $\omega_2-\omega_1$ and $\omega_2+\omega_1$, respectively (three-wave mixing). We find that the evolution of all examined pressure amplitudes shows excellent agreement with our theoretical model, which, in addition, allows the determination of an effective nonlinearity parameter, $\beta$, of the system.
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Christoph Klieber, David Johnson. Nonlinear tube waves. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00811206⟩

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