Realisation of a locally resonant metamaterial on the automobile panel structure to reduce noise radiation

https://doi.org/10.1016/j.ymssp.2018.11.050Get rights and content

Highlights

  • A locally resonant metamaterial (LRM) concept is applied to a dash insulation panel.

  • An attachable local resonator is proposed for the realisation of the LRM concept.

  • The stop band of LRM is predicted using a finite element-based unit cell analysis.

  • Reductions in vibration and noise radiation are validated experimentally.

Abstract

This study aims to demonstrate the reduction in noise and vibration of an automobile dash panel structure by applying a locally resonant metamaterial (LRM). LRMs are implemented by adding a subwavelength array of local resonators to a host structure. Here, the minimum repeated structure is called a unit cell. Owing to dynamic absorption in a unit cell, LRM has a stop band (or also called a band gap), which is a frequency band in which waves cannot propagate. Taking advantage of the stop band, various studies have been conducted on mechanical noise and vibration problems. However, no case has yet been published regarding the application of LRMs to industrial structures such as automobile dash panels because of their complex shape. To overcome the difficulties of LRM realisation in dash panels, an attachable local resonator (ALR) is proposed in this study. The proposed ALR consists of a local resonator and a permanent magnet to be attached on the dash panel surface. To predict the stop band formation, a finite element-based unit cell analysis method is developed, and several ALRs are designed based on the stop band. The designed ALRs are applied to an actual automobile dash panel structure and the acoustic and vibration responses are measured. The measurement results demonstrate that the vibration and noise radiation from the dash panel structure are greatly reduced in the designed stop bands.

Introduction

Metamaterials are artificially engineered materials that exhibit exceptional properties [1], [2]. The engineered properties of metamaterials are generated not from the chemical composition but from the designed mechanical structures that are often made of repeated unit cells. Because the unit cell is considerably smaller than the wavelength of interest, repeated unit cells can be considered as a homogenised novel material, i.e. a metamaterial. The key concept of metamaterials was first suggested in the field of optics [3], [4] and has been expanded to various fields of physics such as elastic wave [5], solid mechanics [6], heat transfer [7], fluid mechanics [8], and acoustics including vibro-acoustics [9], [10], [11], [12]. This study deals with the vibro-acoustic application of a metamaterial to reduce noise and vibration of mechanical structures.

Focusing on noise and vibration applications, previously studied metamaterials can be classified into locally resonant metamaterial (LRM) [9], acoustic black hole [10], membrane-type acoustic metamaterial [11], and metaporous [12]. Of these metamaterials, this study concentrates on LRM that is constructed by adding an array of local resonators to a host structure. The most attractive feature of LRM in noise and vibration applications is the stop band, i.e. the frequency band with no free wave propagation [9]. The stop bands induced in LRMs originate from the interaction between propagating waves and local resonators arranged on a subwavelength scale. Specifically, the formation of stop bands can be described based on the Fano-type interference between incoming waves and the waves re-radiated from the local resonators [13]. In contrast to phononic crystals, periodicity is not a strict requirement for the generation of stop bands in LRMs [14]. Furthermore, the spatial scale of LRM can be much smaller than the wavelength of interest (i.e. subwavelength scale) [14], [15], [16], [17], [18]. These two attractive features make LRM highly advantageous for noise and vibration reduction in mechanical structures.

Studies on noise radiation and insulation using stop bands were initiated with the fabrication of a sonic crystal composed of a silicon rubber and a lead ball by Liu in 2000 [9]. Following Liu’s study, Xiao proposed a thin plate consisting of periodically arranged lumped resonators to attenuate the vibration response [15], [16] and airborne noise [17]. Li and Oudich proposed an analytical model of LRM based on the equivalent material property theory and the plane wave expansion method, respectively [18], [19]. Claeys showed that tuning a resonator produces a stop band at low frequencies [20], and the radiation efficiency of the plate structure constructed with LRM was significantly reduced in the stop band [21]. Based on these studies, Claeys implemented an enclosure-type LRM and experimentally proved that the enclosure was lighter and exhibited a higher insertion loss than conventional enclosures at the confined frequency band, i.e. the stop band [14]. Recently, various LRM structures, such as viscoelastic membrane [22], wave guide type [23], cylinder type [24], porous material type [25], and laminate type [26] have been researched.

Although numerous studies have been conducted on LRMs, its application to complex industrial structures, such as automobile dash panels, has not been studied yet. With this background, this study aims to demonstrate the reduction in noise and vibration of dash panels by applying LRM. The dash panel located between the engine bay and passenger compartment is an important noise transmission path for both structure-borne noise (i.e. radiation from vibrations) and airborne noise (i.e. transmission from acoustic sources). Conventionally, in order to improve the noise, vibration, and harshness performance of dash panels, methods of increasing the panel thickness or adding stiffeners have been used. However, these methods may also significantly increase the weight of the structure, resulting in the side effect of lowering the fuel efficiency. Given the importance of fuel efficiency, a lightweight design is one of the most important considerations in the automotive industry. Relative to this, LRM has advantages of being lightweight and recent studies have demonstrated that it can be a possible alternative to conventional noise insulation techniques [14], [25], [26]. However, applying LRM to dash panels is a challenging task because the panel has a highly complex shape with many bead patterns and holes on the surface. Moreover, changing the dash panel for LRM realisation is very difficult as it is manufactured through a systematic process. As it is very difficult to directly handle the manufacturing process, this study presents a method for implementing LRM on a dash panel that has already been produced.

The goal of this study is to apply the academic LRM theory to a real application, i.e. on the dash panel. To achieve this goal, a practical method of realising LRM on the dash panel is presented. The presented method uses attachable local resonators (ALRs) that can be fixed to the surface of the dash panel with a permanent magnet. The reason for using a permanent magnet is to easily demonstrate various cases without changing the host structure. Although a permanent magnet is used here, other fastening elements (e.g. bolt-nut, rivets, and welds) can also be employed. Because the ALR is attachable, it is not subject to difficulties of realisation such as complex-shaped surfaces and changes in structure.

This research begins with a brief review of the unit cell modelling scheme to predict the stop band in Section 2. In this study, a dispersion equation for the stop band analysis is constructed by combining the equation of motion of a unit cell with the Floquet–Bloch theory [27], [28], [29]. The ALR design is presented with the target problem in Section 3. In Section 4, numerical results are presented in order to tune the ALR to three different target frequencies based on stop bands. Finally, in Section 5, the reduction in acoustic and vibration responses are demonstrated by measurements.

We claim the following as the main contribution of this study.

  • The LRM theory is applied to a host structure of industrial complexity (i.e. automobile dash panel) for the first time. This study is a step ahead of recent studies [14], [25], [26] towards industrial applications of LRMs for the reduction in noise radiation. An ALR design is proposed for the practical realisation of LRM to the automobile dash panel. The reduction in radiated noise based on the stop band theory is experimentally verified.

Section snippets

Methodology

To provide an overview of the LRM discussed in this study, we begin with a brief summary of the methodology used for the stop band identification. As discussed in many previous studies on LRM, the stop band can be identified in the dispersion curve that defines the relation between the frequency ω and wave vector k of propagating waves [9], [14], [15], [16], [17], [19], [20], [21], [22], [23], [24], [25], [26]. In this section, the fundamental theories to obtain the dispersion curve using the

Metamaterial concept

This section specifies the target problem covered in this study and presents the LRM design to be applied for the problem.

Numerical results

This section presents the numerical results of the LRM unit cells with ALRs tuned to three different target frequencies (150 Hz, 750 Hz, and 1200 Hz). Tuning of the parameters of ALRs is based on the method discussed in Section 3. The stop bands of LRM are predicted based on the dispersion curve, which is described in Section 2. For the FE modelling of the ALR and unit cell, a MATLAB in-house code based on the classic plate theory is used. However, other commercial FE codes (e.g. COMSOL, Ansys,

Experimental results

This section presents experimental results to verify the improvements in vibration and noise radiation performance of the dash panel by applying LRM.

Discussion on practical issues for industrial application

In this last section, we shortly discuss the hurdles that should be overcome for the successful application of LRM to the automobile industry. Following are discussions on three main hurdles.

Conclusions

In this study, the concept of LRM was applied to an automobile dash panel structure for noise and vibration reduction. For a practical application of LRM, an ALR using a permanent magnet was proposed. Using the FE-based unit cell analysis method, ALRs were designed for three different target frequencies (150, 750, and 1200 Hz). The designed ALRs were applied to an actual dash panel structure and the vibration response and acoustic pressure were measured. In the measurement results, the

Acknowledgements

This work was supported by Hyundai Motor Company and a National Research Foundation of South Korea (NRF) grant funded by the Korean government (NRF-2017R1A2A1A05001326).

References (43)

  • A. Berry et al.

    Structural acoustics and vibration behavior of complex panels

    App. Acoust.

    (1994)
  • P.A. Deymier
    (2013)
  • G. Ma et al.

    Acoustic metamaterials: From local resonances to broad horizons

    Sci. Adv.

    (2016)
  • V.E. Pafomov

    Transition radiation and Cerenkov radiation

    Soviet. Phys.

    (1959)
  • J.B. Pendry et al.

    Magnetism from conductors and enhanced nonlinear phenomena

    IEEE T. Microw. Theory

    (1999)
  • J. Li et al.

    Experimental demonstration of an acoustic magnifying hyperlens

    Nat. Mater.

    (2009)
  • T.A. Schaedler et al.

    Ultralight metallic microlattices

    Science

    (2011)
  • R. Schittny et al.

    Experiments on transformation thermodynamics: molding the flow of heat

    Phys. Rev. Lett.

    (2013)
  • M. Farhat et al.

    Broadband cylindrical acoustic cloak for linear surface waves in a fluid

    Phys. Rev. Lett.

    (2008)
  • Zhengyou Liu et al.

    Locally resonant sonic materials

    Science

    (2000)
  • Philip A. Feurtado et al.

    Transmission loss of plates with embedded acoustic black holes

    J. Acoust. Soc. Am.

    (2017)
  • Cited by (0)

    View full text