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Nonlinear interaction between elastic wave and contact interface, known to result in the so-called contact acoustic nonlinearity, is examined in a one-dimensional theoretical framework. The present analysis is based on a nonlinear interface stiffness model where the stiffness property of the contact interface is described as a function of the nominal contact pressure. The transmission/reflection coefficients for a normally incident harmonic wave, and the amplitudes of second harmonics as well as DC components arising at the contact interface are derived in terms of the interface stiffness properties and other relevant acoustic parameters. Implications of power-law relations between the linear interface stiffness and the contact pressure are examined in detail regarding the linear and nonlinear acoustic responses of the contact interface. Also, a plausible range of the relevant power-law exponent is provided from considerations based on the rough-surface contact mechanics. The analysis clarifies the qualitative contact-pressure dependence of various nonlinearity parameters based on different definitions. A particular power law is identified from existing experimental data for aluminum-aluminum contact, for which some explicit nonlinear characteristics are demonstrated. The theoretical contact-pressure dependence of the second harmonic generation at the contact interface is found to be in qualitative agreement with previous measurements.

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A self-excited vertical oscillation of dust particles in a Coulomb crystal has been observed. It occurs near the plasma-sheath boundary of a dc plasma operated at a low plasma density and gas pressure. The excitation of this spontaneous oscillation is attributed to the finite charging time of particles. As particles move, their charge varies with the local plasma conditions, but with a delay due to the charging time. As particles traverse the vertical electric potential gradient in the sheath, they gain energy. A model of this mechanism is developed to predict the instability threshold and the energy gain.