A novel membrane-type acoustic metamaterial with a high sound transmission loss (STL) at low frequencies (⩽500Hz) was designed and the mechanisms were investigated by using negative mass density theory. This metamaterial’s structure is like a sandwich with a thin (thickness=0.25mm) lightweight flexible rubber material within two layers of honeycomb cell plates. Negative mass density was demonstrated at frequencies below the first natural frequency, which results in the excellent low-frequency sound insulation. The effects of different structural parameters of the membrane on the sound-proofed performance at low frequencies were investigated by using finite element method (FEM). The numerical results show that, the STL can be modulated to higher value by changing the structural parameters, such as the membrane surface density, the unite cell film shape, and the membrane tension. The acoustic metamaterial proposed in this study could provide a potential application in the low-frequency noise insulation.

Triboelectric nanogenerators (TENGs) are promising materials for harvesting mechanical energy from the environment. Although different structures and modes of TENGs have been designed in recent years, a theoretical model that can comprehensively describe all kinds of TENGs has not been developed yet. Therefore, in this work, a universal edge approximation based equivalent capacitance (EDAEC) method is used to demonstrate charge distributions and the electric field in TENGs, providing quantitative analysis for all modes of TENGs. Analytical models and the quantitative Q–V–x relationship are built for various TENGs, including the contact-separation (CS) mode, contact freestanding-triboelectric-layer (CFT) mode, single-electrode contact (SEC) mode, lateral sliding (LS) mode, sliding freestanding-triboelectric-layer (SFT) mode and single-electrode sliding (SES) mode. Furthermore, simulated results based on the finite element method are obtained to validate the results derived from the analytical models, which are in good agreement. This universal method for all modes of TENGs is a milestone for understanding the working principles of TENGs in-depth, optimizing TENGs' outputs, and revealing the relationships between different modes. This work presents a theoretical basis to guide the further development of TENGs in terms of structural design toward efficient energy harvesting.