Non-reciprocal acoustics in a viscous environment

Investigating the impact of shear and bulk viscosity on the damping of confined acoustic modes in phononic crystal sensors

Phononic crystal (PnC) sensors are recognized for their capability to control acoustic wave propagation through periodic structures, presenting considerable potential across various applications. Despite advancements, the effects of fluid viscosity on PnC performance remain intricate and inadequately understood. This study theoretically investigates the influence of shear (dynamic) and bulk viscosity on acoustic wave damping in defective one-dimensional phononic crystal (1D PnC) sensors designed for detecting liquid analytes. Acetic acid with varying viscosities is considered to fill a cavity layer intermediated by a multilayer stack of lead and epoxy. The effects of dynamic and bulk viscosity on the resonance characteristics of the defective mode were analyzed. Numerical results reveal that increased dynamic viscosity leads to substantial broadening and decreased intensity of resonance peaks, accompanied by a shift to higher frequencies due to enhanced elastic wave attenuation and damping. At low dynamic viscosity (η = 0.2 ηd), numerous resonance peaks with varying intensities are observed. However, at higher viscosities (η = 2.0 ηd to η = 10.0 ηd), only one prominent peak appears in the spectrum. The intensity of this resonant peak starts at 98% for η = 2 ηd and decreases to 58.8% as the dynamic viscosity increases to η = 10 ηd. Additionally, the combined effect of dynamic and bulk viscosity introduces further damping, causing a strong shift of the resonance peak to higher frequencies, along with an increase in the full width at half maximum (FWHM) and a decrease in the quality factor (QF). These findings emphasize the necessity of incorporating both shear and bulk viscosity in the design of PnC sensors to enhance their sensitivity and accuracy in practical applications. This theoretical framework provides critical insights for optimizing sensor performance and bridging gaps between theoretical predictions and experimental observations, especially in 1D PnCs, offering potential solutions to challenges in real-world PnC sensor applications.

Effects of viscous dissipation in propagation of sound in periodic layered structures

Propagation and attenuation of sound through a layered phononic crystal with viscous constituents is theoretically studied. The Navier-Stokes equation with appropriate boundary conditions is solved and the dispersion relation for sound is obtained for a periodic layered heterogeneous structure where at least one of the constituents is a viscous fluid. Simplified dispersion equations are obtained when the other component of the unit is either elastic solid, viscous fluid, or ideal fluid. The limit of low frequencies when periodic structure homogenizes and the frequencies close to the band edge when propagating Bloch wave becomes a standing wave are considered and enhanced viscous dissipation is calculated. Angular dependence of the attenuation coefficient is analyzed. It is shown that transition from dissipation in the bulk to dissipation in a narrow boundary layer occurs in the region of angles close to normal incidence. Enormously high dissipation is predicted for solid-fluid structure in the region of angles where transmission practically vanishes due to appearance of so-called "transmission zeros," according to El Hassouani, El Boudouti, Djafari-Rouhani, and Aynaou [Phys. Rev. B 78, 174306 (2008)]. For the case when the unit cell contains a narrow layer of high viscosity fluid, the anomaly related to acoustic manifestation of Borrmann effect is explained.

Tuning the decay of sound in a viscous metamaterial

Using analytical results for viscous dissipation in phononic crystals, we calculate the decay coefficient of a sound wave propagating at low frequencies through a two-dimensional phononic crystal with a viscous fluid background. It is demonstrated that the effective acoustic viscosity of the phononic crystal may exceed by two to four orders of magnitude the natural hydrodynamic viscosity of the background fluid. Moreover, the decay coefficient exhibits dependence on the direction of propagation; that is, a homogenized phononic crystal behaves like an anisotropic viscous fluid. Strong dependence on the filling fraction of solid scatterers offers the possibility of tuning the dissipative decay length of sound, which is an important characteristic of any acoustic device. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.

Acoustic Metasurface-Aided Broadband Noise Reduction in Automobile Induced by Tire-Pavement Interaction

The primary noise sources of the vehicle are the engine, exhaust, aeroacoustic noise, and tire-pavement interaction. Noise generated by the first three factors can be reduced by replacing the combustion engine with an electric motor and optimizing aerodynamic design. Currently, a dominant noise within automobiles occurs from the tire-pavement interaction over a speed of 70-80 km/h. Most noise suppression efforts aim to use sound absorbers and cavity resonators to narrow the bandwidth of acoustic frequencies using foams. We demonstrate a technique utilizing acoustic metasurfaces (AMSes) with high reflective characteristics using relatively lightweight materials for noise reduction without any change in mechanical strength or weight of the tire. A simple technique is demonstrated that utilizes acoustic metalayers with high reflective characteristics using relatively lightweight materials for noise reduction without any change in mechanical strength or weight of the tire. The proposed design can significantly reduce the noise arising from tire-pavement interaction over a broadband of acoustic frequencies under 1000 Hz and over a wide range of vehicle speeds using a negative effective dynamic mass density approach. The experiment demonstrated that the sound transmission loss of AMSes is 2-5 dB larger than the acoustic foam near the cavity mode, at 200-300 Hz. The proposed approach can be extended to the generalized area of acoustic and vibration isolation.