Maxwell-Voigt and Voigt Models for Vibration Isolation: Influence of Fractional Damping and Time Delay

Abstract

This paper presents results from a follow-up study of fractional damping and time delay. Fractional damping has been used in the literature to demonstrate certain advantages over integer-order damping in many applications involving viscoelastic characteristics. It is observed that fractional damping can be used to influence stability boundaries, natural frequencies and vibration amplitudes, thus providing modeling flexibility in predicting the response of an isolated system during preliminary design. Additionally, time delay or lag is known to be inherent in a damped system, therefore a direct representation of time delay in modeling the damping force is expected to enhance model fidelity. This paper investigates the use of Voigt and Maxwell-Voigt models that incorporate fractional damping and time delay. In this paper, fractional damping has been particularly introduced to investigate possible improvements in the frequency response. Results indicate that fractional damping can be used to significantly enhance the capability of the Voigt model. The influence of the fractional order is found to be analogous to the damping ratio in an integer-order model. Fractional order is seen to exhibit a somewhat limited influence on the Maxwell-Voigt model. However, attributes such as the peak frequency and maximum amplitude are seen to be directly influenced by the fractional order. Although time delay is seen to exhibit an influence on the frequency response, it needs to be limited within useful bounds. Overall, it is observed that fractional order and time delay can be used to improve the accuracy of the Voigt and Maxwell-Voigt models. These enhanced models can be used for the design and development of elastomeric isolators and vibration isolation systems.