Research Projects

Conventional sound-insulating materials follow the “mass law,” which inversely relates the sound transmission coefficient (the ratio of transmitted to incident sound power) through a structure to its material properties—namely, mass density, frequency, and angle of incidence. Effective sound insulation at low frequencies requires very thick panels, which is often prohibitive in weight- and space-sensitive applications. Acoustic metamaterials are carefully designed structured composites that achieve a negative effective density and/or bulk modulus. If either of these properties is negative, the effective wavenumber becomes imaginary, causing the transmitted wave to decay exponentially. A negative effective density can be achieved using membrane-type materials. The objective of the proposed work is to design, mathematically model, analyze, and test ring mass–membrane and slotted ring mass–membrane acoustic metamaterials unit cells for low-frequency sound attenuation. Each unit cell consists of two identical circular, pretensioned membranes with added masses. The mathematical model of the mass–membrane unit cell involves modeling the vibrations of mass-loaded membranes and coupling them with the surrounding acoustic pressure fields to derive a fully coupled vibroacoustic model of the ring mass–membrane and slotted ring mass–membrane acoustic metamaterial unit cells. A mathematical model of the mass-loaded membrane, based on the linear wave equation and the collocation method, will be used to calculate its natural frequencies and mode shapes. The membrane model will accommodate an added mass of arbitrary shape and compute the membrane displacement in response to an incident harmonic pressure field. The surrounding acoustic domain will be modeled using the linear wave equation. Expressions for the acoustic pressure field in three regions—incident, intermediate, and transmitted—will be derived and used to couple with the membrane vibrations. The coupling between the structural and acoustic domains will be achieved using the linearized Euler equation. The acoustic pressure data will then be used to compute the sound transmission coefficient, sound absorption coefficient, sound transmission loss, and effective mass density of the two-layered unit cells. The predictions of the mathematical model will be verified using results from a commercial finite element solver and experimental data from prototype models of the ring and slotted ring mass–membrane unit cells. The project aims to use low-density polyethylene (LDPE) to fabricate a pre-tensioned membrane. First, a large membrane will be held under tension using a biaxial tensiometer. While under tension, a circular rim will be attached and glued near the center of the membrane using epoxy adhesive. After sufficient curing, the rim-supported membrane will be cut from the larger membrane and used to test the pretension using an indentation facility with a spherical probe. Once the pretension has been measured, additional ring or slotted ring masses will be glued to the membrane and attached to either side of a cylinder made of ABS plastic to form the acoustic metamaterial unit cell. This unit cell will then be tested for its acoustic properties using a four-microphone impedance tube. A laser Doppler vibrometer placed adjacent to the impedance tube will be used to measure membrane displacement and acceleration when excited by an acoustic plane wave. The proposed design and development of a membrane-based unit cell can further lead to the creation of secondary screens for attenuating low-frequency noise in aircraft and train windows, semi-transparent enclosures for sensitive equipment, passive acoustic filters for roadside installations, and more. Broadly, this work is expected to contribute significantly to the development of indigenous acoustic cloaking and screening solutions for a wide range of applications in the defense, industrial, and civilian sectors.