Sound radiation characteristics analysis for the honeycomb reinforced laminated structures with viscoelastic material fillers through the asymptotic homogenous method

Abstract

In this study, the sound radiation characteristics of the laminated structures reinforced by honeycomb and composed by viscoelastic material was investigated. Temperature- and frequency-dependent behaviors of the viscoelastic material were considered in this analysis, those parameters affected the dynamics effective properties of the composite structure. After the dynamic equivalent effective stiffness and the dynamic deformation of the structure are determined according to the homogenous asymptotic method, the sound radiation behaviors of the structures in fields of frequency and temperature are achieved. Consequently, the sound radiation characteristic, such as the sound pressure in far-field and the sound radiation efficiency that influenced by the geometry dimensions of the honeycomb structure was examined. Finally, the study is validated by the degeneration method with a degeneration mathematical model that performed in the published literature.

Introduction

Stiffened laminate structures are extensively applied in practical engineering, such as the laminate shells/plates structures and equipment in aviation, navigation and aerospace fields, duo to that the laminated structure has high stiffness [1], [2] and strength [3], [4], low weight behaviors [5]. Same as a traditional stiffened type for the engineering structure, such as single direction [6], [7], [8] and double direction stiffened structure [9], [10], [11], the honeycomb stiffened laminated plates and shells are employed as the sound barriers and sound reduction structures in engineering [12], [13], [14]. Considering the strength behavior of the honeycomb reinforced structure, it is applied often to resist the damage and failure for impacting [15], [16], [17], [18], [19] and buckling/post-buckling [20], [21], [22], [23]. Therefore, the dynamic behaviors of the honeycomb reinforced laminated structure had attracted plenty of researchers in the field engineering. In order to achieve effective in-plane stiffnesses of the honeycomb reinforced laminate structure, considering the corresponding thickness effect, the closed-form appropriate approach and finite element method were applied by Becker [1], their analysis showed that equivalent stiffness of the structure can be largely increased by the honeycomb reinforcements. Furthermore, Paik et al. [24] presented a theoretical and experimental study, investigated the strength characteristics of aluminum sandwich panels reinforced with aluminum honeycomb reinforcement, such as the buckling, ultimate and crushing strength behaviors of the honeycomb reinforced structures. In engineering applications for the honeycomb reinforcement plates/shells structure, the elastic material is considered as the traditional choice, however, in recent years, the composites material-based honeycomb reinforcements were introduced into the application. Such as the Nomex material made honeycomb structure was applied to improve the stiffness of the laminate structure for resisting impacting energy [17], [25], [26]. Meanwhile, to achieve a special stiffness behavior in terms of shear deformation, traditional honeycomb reinforcements were modified and improved to form and establish, such as the gradient and hierarchical honeycomb [27], [28]. In generally, those developed and improved configurations of honeycomb structures are based on the mechanical behaviors of the traditional honeycomb structures.

In the process of investigation and application, according to the loading applied direction and the deformation of the honeycomb structures, the honeycomb reinforcements configurations can be categorized as in-plane and out-plane models. The in-plane honeycomb configuration is usually applied to enhance the toughness of the structures by increasing the energy absorption or dissipation from the outside. The out-plane honeycomb configuration is often utilized for improving the structure’s stiffness. It seems the two configurations are hardly comprised together duo to that the structure/material’s stiffness and toughness show mutual conflict with each other. The approach to solve this problem and provide a method to increase the structure’s stiffness and enhance the mechanical energy dissipate/absorb is required to take into consideration. Considering the sound and mechanical energy dissipation behaviors for the viscoelastic material [29] and the stiffness increment for the honeycomb structures, the viscoelastic material is introduced into the honeycomb reinforcements laminate structures in this work. The viscoelastic material is extensively and successfully utilized in engineering for dissipating and absorbing the sound and/or vibration in the field for the dynamic structures, especially in transportation, aviation, and aerospace, in those areas the frequency characteristic of the structure should be considered [11], [30], [31].

As all of us known that the sound and noise are usually generated by the vibrating of the structure, the sound radiation behaviors are mainly determined on the vibration surface according to the energy propagation and transmission between the mechanical energy and sound energy. Therefore, to achieve a relative smaller sound energy, the structure for a vibrating surface can be designed to control and reduce the sound energy. Usually, we have two methodologies, the first way is decreasing the strength of the structure for reducing the sound radiation efficiency, and the second method is dissipating and absorbing the vibration energy for the vibrating structure. However, for a honeycomb reinforced structures application in engineering, it’s strength and stiffness ability should be initially provided to keep the structure’s safety and functionality. Consequently, the first method for reducing sound radiation efficiency is not available sometimes. However, the second method is applicable, the key question is how can we design a structure that can dissipate and absorb a large amount of vibration energy on the vibrating structure with reasonable stiffness and strength? This is the original intention of this paper.

The current investigation is based on the former research, in which the honeycomb reinforced laminated structure was established, in order to provide a large amount energy dissipation and absorption for the elastic wave propagation, the fillers that made by the viscoelastic material are embedded in the vacancy of the honeycomb reinforced structures. Finally, both the equivalent stiffness and elastic wave dissipation behaviors are enhanced. Considering this phenomenon and the relationship between the sound and vibration, this structure can be applied in engineering to reduce the sound radiation efficiency for a determined external excitation and weaken the sound power in the infinite far-field.

Once the viscoelastic material is applied in the honeycomb reinforced laminate structures, the frequency- and temperature-dependent behaviors of the equivalent dynamic characteristic of the composite laminated structure are required to consider. Furthermore, the sound radiation properties of the viscoelastic material embedded laminated structure with honeycomb reinforcement are investigated in the frequency- and temperature-fields.