Pulsation Oscillations of Cavities in Rubber

Abstract

The oscillation behavior of a spherical cavity in an infinite elastic medium is calculated for the case of an incident spherical dilatational wave entirely reflected at the cavity walls. It is shown that there exists for every Poisson's constant 0⩽σ⩽0.5 a frequency for which the amplitude of the oscillating cavity walls becomes a maximum. It is also shown that the amplitude resonance curves are symmetrical and that, assuming loss-free material, they have a finite half-width, which is caused by radiation losses and depends only on the ratio of shear wave and dilatational wave velocity. Pulsation oscillations of spherical, rotational-elliptical, cylindrical, and cubic cavities in rubber blocks were examined experimentally. The pulsation oscillations were excited by means of a sound source coupled to the surface of the rubber block. The sound pressure inside the cavities was measured with a probe microphone. The experimental results for spherical cavities are compared with the theory. Good agreement is found with respect to the resonance frequencies.

Underwater sound transmission through arrays of disk cavities in a soft elastic medium

“…7 There has been renewed interest in monopole resonant scattering in soft media for experimental studies of phononic crystals and phenomena associated with random distributions of scatterers. [8][9][10] The influence of cavity shape on natural frequency was studied in Meyer et al 6 where a variety of shapes molded into rubber were examined experimentally. Deviations from spherical predictions were noticed for large aspect ratio (AR) shapes as also found in Ivansson. 11 Recent numerical work 12 has shown that the monopole resonance frequency of an evacuated sphere in a soft medium can be reduced by a factor of up to 6 by distorting the shape into a high AR oblate spheroid keeping the volume constant.…”

“…[1][2][3][4][5] Early work 6 identified that monopole resonance is obtained when the circumference of the cavity equals twice the shear wavelength. For soft elastic media, such as silicone rubber, the shear wave speed is typically two orders of magnitude smaller than the compression wave speed and therefore long-wavelength acoustic resonance is obtained much like the Minnaert resonance of a gas bubble in a liquid.…”

Superabsorption of acoustic waves with bubble metascreens

“…1: the bubble meta-screen consists of a layer of gas cylinders in a soft solid, here organized on a square lattice. It has been shown that, at low frequencies, providing that the aspect ratio of the cylinders is close to unity and the shear modulus µ of the soft solid is not too high (µ < 10 MPa), the cavities can be modeled as spherical bubbles of the same volume [17][18][19]. In particular, the cavities exhibit a low-frequency resonance, similar to the Minnaert resonance: !…”

Acoustic Waves in Bubbly Soft Media

“…There exists a special class of solid media called soft media (or weakly compressible media), for which the inequality >> is satisfied ( and are the Lamé coefficients) [1][2][3][4][5][6]. Such media with very small shear stiffness are dynamically similar to liquids to a great extent and exhibit strongly a "water-like" characteristic and, therefore, are also associated with the name of "water-like" media.…”

“…Consequently, it is of academic as well as practical significance to make a comprehensive study on the acoustic waves in a bubbly soft medium. Attempts to theoretically investigate the bubble dynamics in a soft medium go back many decades [1][2][3][4]. Meyer et al have performed the early measurements of the resonance frequency of a bubble in rubbers [1].…”