Experimental study of the level-dependent softening of carbon particle stacks

Abstract

Recently, it has been observed that a particle stack’s elastic modulus and damping change with incident levels. Hence, the measured normal incidence absorption coefficient also varies: i.e., the quarter-wave resonance peak shifts to a lower frequency and grows broader under progressively higher incident sound levels. Therefore, models with strain-dependent modulus and damping have been developed for sand particles based on a series of cyclic triaxial tests, while more recently, a velocity-dependent modulus was proposed to model the acoustically induced elastic softening for the hollow glass beads. To investigate the nature of this nonlinear behavior, the absorption coefficients of a 30 mm carbon particle stack were measured under four types of band-passed input signals (i.e., 500–1000 Hz, 500–2000 Hz, 500–4000 Hz, and 500–8000 Hz), each with 15 levels in steps of 1 dB. The input signals were designed to span the resonance frequency and to extend beyond to various degrees. The integrated sound pressure level, velocity, and displacement at the particle stack surface were calculated and were used to normalize the changing modulus and damping. It was found that only the total rms surface displacement can align the changing properties for all measurements.