Resonance frequencies and Young's modulus determination of magnetorheological elastomers using the photoacoustic technique

A simple and reliable methodology for determining the Young's modulus of magnetorheological elastomers is proposed based on the resonance frequencies of the amplitude of the photoacoustic signal. An explicit expression for the pressure changes within a photoacoustic cell, due to the thermal expansion of the air and the elastic bending of a clamped circular elastic membrane, is derived and analyzed. It is found that the resonance behavior of the amplitude of the photoacoustic signal is due to the contribution of the axial bending of its thickness. It is also shown that the Young's modulus of the membrane is proportional to its density, the square of its resonance frequencies and the fourth power of its radius, and inversely proportional to the square of its thickness. The application of the proposed approach to membranes made up of spherical microparticles of carbonyl iron powder embedded in a matrix of silicone rubber with weight concentrations of 0%, 5.2%, and 13.7% yields accurate and reproducible results, which are in good agreement with reported data in the literature. The highest accuracy on the measurement of the resonance frequencies and therefore on the Young's modulus is found for the first resonance peak. When a magnetic field is applied to the samples to modify their stiffness, it is observed that the Young's modulus increases with the magnetic field. This novel application of the photoacoustic technique opens the possibility of performing mechanical characterization of a broad diversity of magnetorheological membranes.