Adaptive-passive vibration isolation between nonrigid machines and nonrigid foundations using a dual-beam periodic structure with shape memory alloy transverse connection

This paper examines the problem of broadband vibration control of nonrigid systems employing periodic structures with tunable parameters. It investigates this by using a semi-two-dimensional model that applies a dual-beam periodic structure with transverse branches as a parameter-tunable isolator. Conventional study of vibration control problems, including the problem of vibration control by periodic structures, usually reduces systems to equivalent single-or multi-mount models with only a unidirectional translation at a mounting point. This assumption of decoupling leads to the erroneous prediction of vibratory power transmission when designing an isolator for a nonrigid system. Such a periodic structure involves the coupling of vibrations between different mounting points and different directions of motion and is therefore a reasonable simulation of the real-life problem. However, its application as a periodic isolator has not been proposed previously. The configuration of shape memory alloy (SMA) branches and non-SMA dual beams is proposed in order that this structure can effectively exploit the advantages of SMA materials, namely their significantly varying Young's moduli which can be tuned to adjust and widen the stop bands, and can prevent the associated limitation of hysteresis. Equations are derived governing the vibration transmitted through any number of periodic mounts between nonrigid machines and foundations. Based on the derived results, two methodologies are developed to determine the proper Young's moduli of the SMA branches and minimize the transmitted power. The numerical results demonstrate that the adaptive SMA branches at the proper temperatures are able to attenuate broadband vibration by adjusting the locations and broadening the widths of stop bands. With the application of a semi-two-dimensional periodic structure to broadband vibration isolation, this paper provides an approach and supporting methodologies for broadband vibration control using periodic structures.