Determination of the complex shear modulus of a filled elastomer from a vibrating sandwich beam

Abstract

Abstract : A technique for determining the complex shear modulus of a linear viscoelastic material from damped free vibrations of sandwich beams is presented. The sandwich beams consist of thin steel facings and cores of a filled elastomer. In such construction the facing experiences only extensional vibrations and the core only shear when the difference in stiffness between core and facing is large. The mathematical analysis of such a system involves, in general, two complex moduli of the core. However, the relative rigidity of the facings allows the elimination of the complex Young's modulus from the equations, thereby leading to a direct evaluation of the complex shear modulus. Experimental results for a wide range of temperatures and frequencies are presented for a potassium chloride filled polyurethane solid propellant. With the aid of an Arhenius type temperature-time shift function the shear modulus and damping constant are evaluated over eight decades of frequency. (Author)