Viscoelastic components employed for vibration isolation or shock absorption in automobiles, machines and buildings are often subject to a high level of static compression. From the dynamic design point of view, it is essential to predict complex stiffness of the viscoelastic components accurately and efficiently, which requires first of all information about the complex modulus of the viscoelastic materials under operational environmental conditions, especially under the static compression. Although several approximate formulas were developed to predict the dynamic properties of viscoelastic materials subject to heavy static deformation, most of the studies were concerned with static extension rather than compression under which most vibration or shock isolators actually operate.
In this study, a procedure to estimate complex modulus of incompressible viscoelastic materials from stiffness measurements as functions of frequency under heavy compressive pre-strain is presented. Measurements of the complex modulus from two kinds of circular cylindrical specimens subject to static compression are conducted. As bonding of the specimen at its both ends is inevitable in compression test, it is necessary to compensate for the bonding effects in treating the experimental data. The bonging effect is computed in this study that concerns heavy static compression by applying a finite element code to the specimen.
In order to represent the modulus as functions of pre-strain and frequency, two existing method are introduced and then, two new methods are investigated. Lianis proposes a formula that takes into account the coupling between the frequency and the static pre-strain effects is presented. This formula can predict the complex modulus successfully in the uni-axial deformation, but it is still a little complicated equation and has to be modified to be able to predict other deformational conditions. Morman proposes a formula that assumes that the complex modulus can be obtained by multiplication of the frequency effects at a reference pre-strain and the static modulus, but the formula is shown not so successful.
The new procedure presented in this study is obtained by modification of the Morman’s formula. The Morman’s formula assumes that the trend of the dynamic modulus at a frequency versus static compression is same that of the static modulus. In reality, trend of the static modulus is different from that of the dynamic modulus. So, it is necessary to exploit the trend of dynamic modulus rather than the static modulus.
In order to consider the trend of dynamic modulus, the relaxation modulus, which is a function of frequency, in the Morman’s equation is substituted by a function of frequency and pre-strain. After that, two methods are proposed in this study. One combines the frequency effects at a static compression and the static compression effects at a chosen frequency. Another takes into account the gradient of storage and loss modulus. Finally, experimental results were treated by these new methods and performance and practical limitation of the methods are comparatively discussed.
