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AIP Advances

Published Online: 13 November 2014 Accepted: October 2014

https://doi.org/10.1063/1.4901881 

■  Researchers

Junghwan Kook, Jakob S.Jensen

Department of Mechanical Engineering, Technical University of Denmark

■  Abstract

The aim of this paper is to investigate the enhancement of the damping ratio of a structure with embedded microbeam resonators in air-filled internal cavities. In this context, we discuss theoretical aspects in the framework of the effective modal damping ratio (MDR) and derive an approximate relation expressing how an increased damping due to the acoustic medium surrounding the microbeam affect the MDR of the macrobeam. We further analyze the effect of including dissipation of the acoustic medium by using finite element (FE) analysis with acoustic-structure interaction (ASI) using a simple phenomenological acoustic loss model. An eigenvalue analysis is carried out to demonstrate the improvement of the damping characteristic of the macrobeam with the resonating microbeam in the lossy air and the results are compared to a forced vibration analysis for a macrobeam with one or multiple embedded microbeams. Finally we demonstrate the effect of randomness in terms of position and size of microbeams and discuss the difference between the phenomenological acoustic loss model and a full thermoacoustic model.

■  Conclusion

In this paper we have studied the possible enhancement of macroscopic damping ratios by embedded microbeams vibrating in a lossy acoustic medium. The study encompassed the derivation of a simple theoretical model and a computational FE study using an acoustic-structure interaction model. The dissipation in the internal acoustic cavities was accounted for using a phenomenological model with a complex speed of sound and was also compared to a more advanced thermoacoustic-structure interaction analysis.

The theoretical model established the connection, under a number of simplifications, between an increased damping ratio of the microbeams and the resulting enhanced damping ratio of the macrobeam. The results indicated that an increased damping due to acoustic-structure interaction in internal air cavities could cause an increased overall damping ratio, as was observed experimentally for beams of porous materials. The computational FE study supported this conclusion both for the case of a single and multiple microbeams. In both cases, significant enhancement of the damping ratio was observed when we applied losses in the acoustic model for the internal air cavities. In the case where we applied randomness in the location and the thickness of the microbeams, we found that the location of the microbeams did not affect the damping properties, whereas reduced damping was observed when all microbeams were not alike and tuned with the macrobeam frequency. Finally, we demonstrated qualitative similarities between the time-harmonic response behavior when employing the simple, and computationally cheap phenomenological loss model, and the full thermoacoustic-structure interaction model.

As a next step, current work is in progress on optimizing the geometry of the microbeams in order to maximize the internal damping ratio. As we predict from this study, this will then reflect in an increased modal damping ratio of finite devices made of porous material and thus extending the possibilities for industrial applications.

* 관련 자료 

[신진연구자 인터뷰] 위상 최적화 기법의 개발 및 마이크로 구조체 설계 연구