In order to use viscoelastic materials efficiently for sound and vibration control, or to qualify newly developed materials, knowledge of the Young's modulus and loss factor is essential. These material properties, the so-called complex Young's modulus, are frequently treated as dynamic characteristics because of their dependence upon the frequency.
Many techniques have been developed, and verified for measuring the complex Young's modulus of viscoelastic materials. They are usually selected on the basis of the environmental conditions of interest, and convenience of experimentation. Among them, it is advantageous to use the transfer function method for detailed frequency analysis. In this method, a cylindrical or prismatic specimen is excited into longitudinal vibration at one end, the other end being loaded by a mass. The complex Young's modulus can be calculated after having measured the transfer function: i.e., the vibration amplitudes of the specimen ends and the phase angle between them. At the procedure to derive the Young's modulus from the measured transfer function, it becomes an important problem how to model the specimen-added mass system for the purpose of yielding the correct values. The strict modeling of the system is very difficult, because the characteristics of the system is dependent on the Poisson's ratio as well as the complex Young's modulus, and its boundary conditions are hard to deal with. Even if it were possible, using that model would require input of the Poisson's ratio of the material. Many practical models have been proposed to express the characteristics of the system in terms of the complex Young's modulus and the other readily measurable constants except for the Poisson's ratio, and the shapes of the specimen to be less affected by the Poisson's ratio were recommended, due to the difficulties of measuring the Poisson's ratio. But these techniques can be shown to be apt to lead into incorrect estimation of the Young's modulus. Thus the measure of the Young's modulus necessitates a relatively simple method which estimates the Poisson's ratio and derives the Young's modulus from the relation between the measured transfer function, Young's modulus, and the Poisson's ratio.
There are some cases in which the Poisson's ratio should be known in addition to the (complex) Young's modulus. The finite element method(FEM) can be mentioned as a case. FEM has been used as a powerful tool for the analysis of a variety of structures in many branches of engineering. In recent years there has been a widespread interest in applying the FEM to the analysis of various structures treated with viscoelastic materials for vibration and noise control. For this purpose, the Poisson's ratio is necessary as input data, in addition to complex Young's modulus. Especially in case of the structures with the shape to the bulk-compressed, input of the correct value of the Poisson's ratio is required.
In this study, for application of FEM in a practical way, a method is proposed to determine both the complex Young's modulus and the Poisson's ratio of a viscoelastic material simultaneously by using two solid specimens, one of which is somewhat long, and the other short, with the helps of finite element analyses of the specimens on the assumption that the Poisson's ratio is real and constant with respect to the frequency. An example of the method is illustrated for a neoprene rubber, and the obtained Young's modulus and Poisson's ratio is applied to the finite element analysis of the neoprene mount. Finally the practicality of the method is discussed from the comparison of the results of analysis to the experimental results.