Vibration and sound properties of metamaterial sandwich panels with periodically attached resonators: Simulation and experiment study

Abstract

The vibration and sound properties of a type of metamaterial sandwich panels are investigated in this paper. The metamaterial sandwich panels consisting of a host sandwich panel and periodically attached resonant units are designed. Both the panels with and without damping are considered. Via the comparison of metamaterial and bare panels, the effects of the periodic design on wave propagation, vibration, sound radiation and sound transmission properties are analysed and compared numerically. The reduction on the vibration and sound is studied. The numerical results indicate that the vibration, sound radiation and sound transmission are significantly reduced over a wide frequency range. The reduction is obviously larger than that obtained only by increasing the mass. In addition, the experiment specimens of bare and metamaterial sandwich panels are designed. The vibration and sound properties of them are tested and compared. According to the experimental results, the reduction is also observed in a wide frequency range. The simulation results and corresponding analysis are verified. Further, the effects of structural parameters of sandwich panels on the reduction of vibration and sound properties from periodic design are investigated. Several typical cases are analysed concretely. The reasons for the reduction and other effects on the vibration and sound properties from periodic design are analysed. For the panels with various parameter settings, a nice reduction of vibration and sound is generated also form periodic design; on the other hand, the reduction characteristics are changed.

Introduction

Vibration and noise have become one of the major concerns for modern transportation vehicles [1], [2]. Panels and shells are widely used in cabin structures, and are important vibration and noise transmission paths. Correspondingly, the vibration and sound properties of those panels directly affect the acoustical environment inside the cabin. Especially, in order to reduce the weight, lightweight sandwich structures/materials are broadly used. However, the smaller weight and the supersonic wave propagation in relatively low frequency range of these lightweight structures usually result in poor acoustical performance [3]. Fig. 1 shows the schematic for several typical sandwich panels.

To control the cabin noise and increase the interior comfort, a meaningful work is to reduce the vibration, sound radiation and sound transmission of the cabin siding panels [4], [5]. Several approaches have been developed to achieve this goal, including structural design, utilizing dynamic absorber, damping treatment, sound absorption design, vibration isolation mass, active control and parameter optimization and so on [5], [6], [7], [8], [9], [10], [11]. Ruzzene et al. [12], Sun et al. [13] and Steven et al. [14] performed the structural-acoustic optimization of sandwich panels. Almgren et al. [15] studied the effect of damping treatments on vibration and sound radiation properties of sandwich panels. Song et al [4] introduced the typical approaches for vibration and sound reduction of the panels.

In the past two decades, the study of artificial periodic structures receives much attention, for instance, phononic crystals, acoustic metamaterials (AM) and so on. This type of structures have multi unique physical properties, including stop band, low frequency insulation, low frequency absorption, negative acoustical parameters, directional propagation, acoustic clocking and so on [16], [17], [18], [19], [20], [21], [22]. The periodic design has been introduced into the control of vibration and noise of panel structures [4], [23], [24], [25], [26], [27]. Wang et al [23] studied the wave propagation and vibration reduction properties of a metamaterial panel with lateral local resonators. Ruzzene et al. [28] investigated the propagation of elastic waves and the reduction of vibration in a periodic sandwich panel. Casadei et al. [29] studied the control of noise radiation of a flexible panel by the using of periodic shunted arrays. Zhou et al [30] studied the sound radiation properties of periodic perforated damping sandwich plate. Song et al. [31] investigated the reduction of the sound transmission of a periodic sandwich panel using the stop band concept. Chronopoulos et al [26] designed a composite metamaterials with embedded negative stiffness inclusions to enhance the sound insulation near the acoustic coincidence range. Liu et al [27] studied the enhancement of the sound insulation properties of a sandwich plate at the range near the coincidence frequency using locally resonant metamaterial design. Errico et al [32] investigated the effects of periodic embedded resonators on the sound transmission loss of curved sandwich structures loaded by turbulent boundary layer. Recently, multi researchers reviewed the studies on phononic crystals and acoustic metamaterials [16], [33], [34], [35].

Both the numerical methods and experimental methods are used in the studies of wave propagation, vibration and sound properties of periodic panels, and many achievements have been obtained [5], [12], [13], [14], [20], [24], [28], [29]. Petrone et al [36] investigated the acoustic power radiated by aluminium foam sandwich panels numerically and experimentally. Sheng et al [37] studied the vibration properties of a sandwich plate with viscoelastic periodic cores via numerical methods, and the experimental verification is also carried out. On one hand, both the numerical and experimental methods are competent for describing the variation of the dynamic properties of periodic sandwich panels compared to bare sandwich panels. On the other hand, due to the complexity of the things, the exact matching of the numerical results and the experimental results still is a problem for many of the studies. Benefitting by the contribution of the scholars working at the numerical methods and the equivalent parameter methods and so on, the calculation accuracy and efficiency of the numerical methods are improved effectively. For instance, Errico et al [38] proposed a numerical scheme used to simulate the sound transmission loss of complex curved sandwich panels and stiffened panels. Yang and Mace et al [39] studied the prediction of sound transmission and sound radiation of panels based on wave and finite element method. Mejdi and Atalla et al [40] developed the wave spectral finite element model for the prediction of sound transmission loss and damping of sandwich panels. Parrinello et al [41] combined the finite element method and transfer matrix representation for sound property calculation of periodic planar media. In addition, some computation methods for the vibroacoustic treatments based on periodic design were built recently also. Maglicano et al [42] developed the computation tools to study and design the periodic Biot-modeled foams. These works provide much convenience for obtaining the acoustic properties of periodic structures as well as designing the periodic treatments.

The previous work about periodic panels (including acoustic metamaterial panels, phononic panels and so on) has promised their potential applications for the reduction of vibration and sound. However, for the research of vibration and sound properties of periodic or metamaterial sandwich panels and the corresponding reduction effects, there is still some work needs to be advanced further. First, much of the work mainly concerns the wave propagation and vibration properties of periodic sandwich panels, while the work concerning their sound radiation and sound transmission properties is still less. Second, the vibration and sound properties around the stop band frequency ranges or the resonant frequencies of the attached resonators are analysed more. The vibration and sound properties in the whole frequency range receive less attention and need to be studied further. Third, the comprehensive comparison of the effects on vibration, sound radiation and sound transmission from periodic design is few. Especially, because of the complexity of the dynamic properties of sandwich panels, it is necessary to study the vibration and sound properties of periodic sandwich panels with different parameter settings systemically. Forth, more experimental study and validation work for the sound property variation from periodic design are needed. Note that there are some differences between the categories of metamaterial plates mentioned in this paper and of classical periodic plates (e.g., honeycomb sandwich plates, stiffened plates and so on), as analysed in [43]. The achievements on the computation/test, description and analysis of the vibration and sound of periodic structures do not deny the statements mentioned above. For instance, the sound properties of periodic plates are concerned in [39], [40], [41], [42], but the main aims of them are developing a high performance computation tool rather than obtaining the acoustic property variation and reduction effect from metamaterial design and the corresponding mechanisms.

In this paper, the vibration, sound radiation and sound transmission properties of the locally resonant metamaterial sandwich panel composed of a host sandwich panel and periodically attached stepped resonators are studied. This work is expanded from the authors’ former paper [44] submitted to a conference. In details, the analysis of the reasons of the vibration and sound property variation caused by periodic design is developed; the experimental studies for the vibration and sound reduction from periodic design are added and are compared with numerical studies; and the effects of the structural parameters on the vibration and sound properties of metamaterial sandwich panels are studied.

In Section 2, the structures of the sandwich panels and corresponding structural parameters are presented. The calculation models for the vibration and sound are introduced. The experimental specimens of the sandwich panels and the experimental systems are introduced. In Section 3, the variations of the wave propagation from periodic design are analysed. Via the comparison of the metamaterial and bare panels, the effects on the vibration and sound characteristics of the panels from periodic design are studied. Especially, the reduction of vibration and sound from periodic design is illustrated. The mechanism for these changes is analysed. Further, the experimental results are presented and analysed. The results form numerical calculation and experimental test are compared. In Section 4, the effects of structural parameters of the sandwich panels on their dynamic properties are investigated. In Section 5, the work is concluded.