# Vibro-Acoustic Performance of a Sandwich Plate with Periodically Inserted Resonators
## 4 Conclusions  
The vibro-acoustic performance of a sandwich plate with periodic resonators was examined in this paper. The band-gap properties, forced response, and acoustic radiation were theoretically derived with closed-form solutions, and were all discussed with the purpose of examining the effects of periodic resonators on the overall acoustic radiation.  
For the infinite locally resonant (LR) sandwich plate examined in this paper, a new radiation zone was generated above the band-gap and the coincidence frequency was decreased, resulting in the total effective radiation zone being enlarged. Thus, ineffective radiation in a homogeneous sandwich plate may become effective radiation in an LR sandwich plate. For the finite LR sandwich plate examined in this paper, the periodic resonators had a minimal effect on radiation efficiency in the frequency regions below the fundamental frequency and above the coincidence frequency. Between these two frequencies, the radiation efficiency was decreased below and increased above the resonance frequency of the resonator. The effects of the periodic resonators on radiation efficiency could be physically explained by the effective mass of an LR unit, with decreased mass causing increased radiation efficiency and increased mass causing decreased radiation efficiency. The effective mass can be considered as an indicator of which part of a frequency region will be acoustically improved and which part will be acoustically deteriorated. This will be convenient and important for LR sandwich plate design.  
In the band-gap, acoustic radiation is significantly reduced because of the reduction in vibration, as there is no mode existing in the band-gap. In the frequency band close below the band-gap, acoustic radiation is also noticeably reduced, not only because of the suppression of vibration but also because of the lower radiation efficiency. In contrast, the introduction of periodic resonators to a sandwich structure also increases radiation power in the frequency band close above the band-gap, mainly because of the increased radiation efficiency. Fortunately, this increased radiation above the band-gap can be further reduced by introducing a small damping to the resonator by reducing the vibration response. Therefore, in order to improve the acoustic performance of a sandwich plate, the resonator should be tuned at or above the target frequency when damping is not applied in the resonator. When the resonator is damped, the design of band-gap may have more options.  
Conceptualization, Z.G.; data curation, J.P. and M.S.; formal analysis, Z.G.; investigation, J.P.; methodology, Z.G. and M.S.; resources, J.P. and M.S.; software, J.P. and M.S.; supervision, J.P.; validation, Z.G., J.P. and M.S.; visualization, J.P.; writing--original draft, Z.G.; writing--review and editing, J.P. and M.S.  
This research received no external funding.  
The first author acknowledges both the financial support from the Chinese Scholarship Council and the research-resource support from the University of Western Australia. The authors also gratefully acknowledge the proof reading and language help from [PERSON].  
The authors declare no conflicts of interest.