正交異向性複合材料積層板聲學特徵之研究

Abstract

本篇論文主要探討非等向性複合材料平板之聲學性質，希望能藉由本研究更進一步了解複合材料板的聲波傳輸性質以及隔音效果。 本文使用傳輸矩陣法計算複合材料平板的聲音穿透損失，由於複合材料(FRP Fiber Reinforced Plastic)為異向性材料，而傳統的聲波傳輸矩陣法皆只適用於等向性材料，因此本文使用的為由傳統聲波傳輸矩陣推導延伸出可適用於非等向性複合材料的特殊傳輸矩陣。首先探討具橫斷面等向性的FRP，此部分使用的聲波傳輸矩陣為二維之數學模型。至於不具橫斷面等向性的FRP，則將二維數學模型擴展成三維。 由於在複合材料的應用上，常需依照使用需求的不同而採用不同的纖維積層製作複合材料，而傳統的聲波傳輸矩陣法皆適用於等向性材料且單一材質上，因此在本文中也進一步探討傳統傳輸矩陣應用在不同材料疊層上時，積層與積層之間邊界連續條件為應力連續或是應變連續的合理性，並以實驗驗證之。 另外，本文亦針對不同纖維編織方式之複合材料作機械及聲學特性的分析，進而計算出不同種類的纖維複合材料隔音效能，內容包括聲波入射複合材料表面之臨界角分析，以及複合材料積層板內的層間應力分佈，最後探討纖維補強型複合材料的積層順序對聲音穿透損失的影響。希望藉由本研究能對複合材料的聲學特性有更進一步的了解，進而廣泛應用。

The principal purpose in this study is to investigate the sound characteristics of FRP (Fiber reinforced plastics) materials. In this work, TMM (Transmission matrix method) was applied to estimate the sound transmission loss of a FRP plate. However, FRP materials almost process orthotropic or anisotropic material properties but the traditional TMM is only suitable for isotropic material. Therefore, the sound wave equation of orthotropic plates is formulated in the study and than the special TMM that suits FRP laminate is used in this investigation. There are many kinds and types of FRP materials in the industrial applications. The FRP material properties are various among the different kinds of FRP. Thus, the TMM should be adjusted to suit each various FRP laminate. In the study, as the FRP plate possesses transverse isotropic in in-plane, the two-dimension mathematical model is appropriate to analyze the acoustic characteristics of the plate. If the FRP plate is fully orthotropic, the three-dimension mathematical model which extended from two-dimension model will be suitable to the calculation. Further, at the boundaries between the layers of a FRP laminate, the discussion on boundary conditions is also analyzed with some experiments in the present work. There are two kinds of boundary conditions considered in the study, i.e. stress continuity and strain continuity. In the experimental results, the stress continuity is more appropriate to be used in the works than the strain continuity of boundary condition. Moreover, the other acoustic characteristics of FRP plates including the wave critical angle, the stress variations of each layer, and the sound transmission of the FRP plate were also estimated in the study.