Technical note Enhanced transmission loss through lattice-supported micro-membranes Shunjian Qiu a,b , Shengming Li c , Xu Wang a,b,⇑ , Dongxing Mao a,b,⇑ a Institute of Acoustics, Tongji University, No. 1239 Siping Road, Shanghai 200092, China b College of Architecture and Urban Planning, Tongji University, No. 1239 Siping Road, Shanghai 200092, China c Shanghai Jianke Technical Assessment of Construction Co., Ltd, No. 568 Shenfu Road, Shanghai 200092, China article info Article history: Received 11 February 2019 Received in revised form 1 April 2019 Accepted 2 April 2019 Keywords: Acoustic micro-membranes Low frequency transmission loss Distributed-parameter model abstract Acoustic micro-membranes (AMMs) have theoretical advantages in terms of light weight yet high sound transmission loss (STL) at low frequency, but an actual medium- or large-scale specimen usually shows a significant performance degradation. Those lumped-parameter models developed so far lose their accu- racy on theoretically describing the actual sound transmission loss of such an assembly. In this paper, the influence of the frame vibration is explored, and an acoustic theory based on a distributed parameter sys- tem is established. By coupling the vibration of the frame and the membranes, this theory shows how the acoustic impedance of the assembly depends on the number of membrane cells and the dimensions of the membranes and frame. As the assembly becomes larger, its global response is no longer dominated by the membrane but by the frame, while the latter determines the upper limit of the STL of the whole assembly. Compared to the well-developed lumped-parameter model that works only for small-scale AMMs, this work provides a theoretical foundation for designing larger size yet high loss AMMs, and may pave the way for their use in noise control engineering. Ó 2019 Elsevier Ltd. All rights reserved. 1. Introduction With improvements in living standards and engineering speci- fications, sound insulation materials are now required to have higher sound transmission losses (STLs) at low frequencies. How- ever, due to the law of mass, increasing the STL of traditional mate- rials at low frequencies inevitably leads to high volume and mass, which has a large impact on what is practical. In order to obtain sound insulation materials with smaller volume, lighter weight, but higher STL, a number of structures, including double walls filled with porous materials [1] and perforated materials [2], have been studied. But even with these structures, it is still difficult to achieve high STL at low frequencies. The study on membrane-type acoustical materials has a long history dating back to 1950s [3–7]. In 2008, by shrinking the size of membranes into a deep-subwavelength scale, the micro- membrane materials spurred an intense interest for their remark- able sound insulation effect at low frequencies [8]. Since then, AMMs have been studied by many scholars [9–14]. In 2010, Yang realized that by changing the mass of blocks attached to the center of a membrane unit, attenuation of sound waves could be achieved over different frequency bands [15]. Such a membrane-type struc- ture has a thickness less than 15 mm and surface density of less than 3 kg/m 2 while still exhibiting an STL of 19.5 dB at around 200 Hz. Membrane units with different masses can be stacked into plates with a thickness of less than 60 mm and surface density of less than 15 kg/m 2 , demonstrating an average STL of >40 dB over a range of 50–1000 Hz. In 2015, a sandwich panel design, incorpo- rating honeycomb AMMs as the core material, was theoretically proven and experimentally verified by Sui [16]. This structure yielded a STL consistently greater than 50 dB at low frequencies. To theoretically explore the underlying working mechanism of the AMMs, a lumped-parameter model was established by Li and colleagues [17]. Their theoretical analysis of AMMs gives an intu- itive insight into how the performance varies with geometrical parameters, and reveals the advantage of AMMs over traditional materials by explaining why the membrane can have high STL at low frequencies. However, with an increase in the size of the AMMs, the formula of sound insulation derived from a single set of basic parameters no longer adequately describes the actual STL of the material. https://doi.org/10.1016/j.apacoust.2019.04.004 0003-682X/Ó 2019 Elsevier Ltd. All rights reserved. ⇑ Corresponding authors at: Institute of Acoustics, Tongji University, No. 1239 Siping Road, Shanghai 200092, China. E-mail addresses: xuwang@tongji.edu.cn (X. Wang), dxmao@tongji.edu.cn (D. Mao). Applied Acoustics 153 (2019) 127–131 Contents lists available at ScienceDirect Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust