Vibro-acoustic analysis of parallel barriers integrated with flexible panels

Abstract

In urban communities, parallel barriers are commonly erected for controlling environmental noise such as traffic and construction noise. However, owing to the multiple reflections between the parallel barriers, their performance may be worse than that of a single barrier. To improve the performance of parallel barriers, a small piece of flush-mounted panel backed by a slender cavity in an otherwise rigid wall of barriers is proposed. With the excitation of the incident wave from a sound source inside the parallel barriers, the flexible panel vibrates, and sound is radiated out to undergo acoustic interference with the sound field bounded by the parallel barriers. Consequently, the sound energy in this space and diffraction at the barrier top edge are reduced over a broad band in the low-frequency regime. A theoretical model for tackling the vibro-acoustic coupling between the sound field of the open cavity and the vibrating panel is established to investigate the noise reduction mechanism in the shadow zone. With optimal structural properties of the panel, an additional averaged insertion loss of approximately 5 dB can be achieved at 80–1000 Hz. The theorical results, which are experimentally validated, pave the way for the potential applications of the flexible panel devices (FPDs) for improving the noise reduction of parallel barriers.

Introduction

The mitigation of environmental noise with acoustic barriers is common in highly populated cities. These barriers are installed close to sound sources to reflect and block sound waves, thereby the direct propagation of the sound wave to the receiving zone can be intercepted. To reduce the noise on both roadsides, generally one more barrier is erected along the roadsides to form parallel barriers. However, their performance deteriorates when they are close to each other owing to multiple reflection, which forms a reverberant sound field in the space bounded by the parallel barriers and the intervening ground [1], [2], [3]. To deal with this deterioration, absorption layers have been added on the inner surfaces of parallel barriers [4,5]. However, the conventional porous absorptive materials cannot perform well at low frequencies and cause environmental problems such as the accumulation of dust and bacteria. Alternatively, barriers with acoustic soft top or different top profiles such as circular, T-shaped, and branched profiles have been proposed, and their performances have been evaluated [4], [5], [6], [7]. However, the top edges of the barriers are too bulky for low frequencies. To reduce multiple reflections, Monazzam and Fard designed a median barrier with inclined angle to redirect the incident sound upwards, thereby reducing the diffraction at the barrier top edge [8]. In addition, a wave trapping barrier was proposed by Pan et al. [9] and investigated theoretically by Yang et al. [2], in which the barrier inner wall is mounted with multiple trapezoid or triangular wedges. They pointed out that the wedges redirected the sound waves downward to the ground, and as a result, the sound was trapped within the space confined by the parallel barriers and the ground. Wang et al. [10] introduced the use of the inhomogeneous impedance accomplished by an array of slender tubes of varied depths on barrier wall surfaces. The acoustic trapped modes between the barriers are altered, which improves the noise reduction at the receiver.

Recently, the Helmholtz resonator (HR) was used to reduce the noise radiation from the parallel barriers [11]. The HR was mounted on the inner surface, and significant noise reduction was achieved around the resonator's natural frequency in the shadow zones. However, the noise reduction frequency range of the HR remains narrow although the array of resonators improves the reduction of multiple peak frequencies. To widen the working frequency range, this paper proposes to mount the inner surfaces of the parallel barriers with a flexible panel device (FPD) which is composed of a flexible panel and a compact backing cavity. The configuration of the FPD is similar to the panel silencer which was proposed by Huang [12] to attenuate the duct noise. To simplify the practical implementation, Wang et al. [13] replaced the simply supported boundary condition of the panel by the clamped-clamped one. The transmission loss was attractive from low to medium frequency range [14]. To further broaden the noise reduction band, the micro-perforations was introduced for the flexible panel by Wang et al. [15] and Xi et al.[16]. The micro-perforations was to compensate for the deficiency in the pass-band caused by the insufficient sound reflection due to the panel by absorbing sound through micro-perforations. Besides above studies, the use of flexible panel to influence the sound field inside or outside cavity has been found in many literatures [17], [18], [19], [20], [21]. For instance, Dowell and Voss [17] investigated a cavity-backed panel, and Pretlove [18] derived an expression for the vibration of cavity-backed panels using in-vacuum modes. Guy [19], Pan and Bies [20], and Tanaka et. al [21] investigated the influence of the flexible panel on the sound field of a confined cavity. Moreover, some researchers studied the structural–acoustic coupling between the sound field in the open space and a baffled cavity covered partially by a flexible structure [22], [23], [24]. These studies provide useful insight into the vibro–acoustic interaction and acoustic coupling of baffled open cavities. However, little attention has been paid to the noise control of open cavities formed by parallel barriers with flexible panel. Moreover, the mechanism of sound suppression in the open cavity system is different from that of a panel silencer in the duct. In this study, the flexible panel vibrates due to the incident sound and sound wave is subsequently radiated out to undergo acoustic interference with the original sound waves confined by the parallel barriers. This leads to the distortion of the sound field between the parallel barriers. With a proper design of the FPD, the sound intensity at the barrier top edge decreases, which improves the noise reduction in the shadow zone. Besides, the FPD is mounted on the inner surfaces of the barrier walls and can cooperate with the top treatments, such as the soft tops, thereby further increasing the noise reduction performance of the parallel barriers.

To analyze the performance of parallel barriers, diffraction theories [25,26] are conventionally used to predict the wave propagation into the shadow zone. However, these analytical methods are not capable of dealing with barriers with complex profiles, neither with the vibro-acoustic coupling and sound interference between the sound waves in the open cavity and the sound waves radiated from the vibrating panel of the FPD. For these cases, the finite element method (FEM) [2,10] or the boundary element method (BEM) [27,28] are a good option. In addition, a hybrid BEM–FEM coupling approach has been developed to study the acoustic performance when the acoustic barriers are considered acoustically elastic walls [29]. However, these numerical methods are insufficient in revealing the sound abatement mechanisms. The Finite Difference Time Domain (FDTD) approach, which is based on numerical integration of the linearized Euler equations in the time domain, has also been developed and applied in the simulation of sound propagation over barriers [30,31]. However, the huge computer times and memory consumption limit the wide application of FDTD in large scale problem [31]. Recently, the non-Hermitian Hamilton principle [32], [33], [34], which also called technically coupled mode theory, was applied by Tong et al.[35] and Wang et al.[11] to predict the acoustic performance of parallel barriers. In this method, the acoustic space of the parallel barriers is decoupled into two subspaces: a confined cavity space and a semi-infinite space. The sound field of the parallel barriers is represented by the coupled modal variables corresponding to these two sub-domains. In this study, the non-Hermitian Hamilton principle is adopted and further extended to deal with the vibro-acoustic coupling in acoustical open space.

The objectives of this study are: (1) establishing a theoretical model to deal with the vibro-acoustic behavior between the open cavity and vibrating panel; (2) conducting a systematic analysis of the structural-acoustic interaction of the parallel barriers with the flexible panel and backing cavity. (3) revealing the noise control mechanism of the FPD.