臺灣博碩士論文加值系統

本文目的在探討三明治蜂巢板之隔音性能。首先，將三明治板視為由多層介質所組合而成之複合板，而中間的芯材則為一彈性多孔材料，之後再利用Biot彈性理論分析聲音於多孔材中的傳播情形，並建立聲波在平板兩點間傳遞之轉換矩陣，最後藉由這些轉換矩陣來計算三明治蜂巢板之隔音性能。
為了驗證本文之理論，引用四組由Moore所量測之三明治複合板的數據，比較實驗數據與本文理論計算所得之數據，除Panel D因其結構與理論之基本假設不符外，其餘計算的結果皆大致符合，可證明本文理論之可行性，
以此理論作數值分析，藉由不同案例去探討芯材之相關參數，如厚度、密度與蜂巢孔徑，對隔音性能的影響。理論分析後發現，芯材厚度的變化會改變吻合效應所發生的頻率，進而影響整體之隔音性能。而芯材密度的改變亦會有類似的影響，吻合頻率會隨著芯材密度的減小而往低頻處移動，待密度超過某一定值後，此時吻合效應所發生的頻率則趨近一固定值。最後，由理論分析可知蜂巢孔徑對三明治板之穿透損失的影響甚微。

The purpose of this research is to discuss the sound insulation characteristics of honeycomb sandwich panel. At first, the sandwich panel is made of layered media and the center core was regarded as an elastic porous material. Thus, the Biot theory could be employed to analyze the waves propagated in fluid saturated porous material. The transfer matrix for waves propagated between two ends of the sandwich panel was established. The combination of these related matrices can be applied to evaluate the transmission loss.
To order to verify the present method, four sandwich panels which were measured by Moore are analyzed. The comparison of the transmission loss between experimental data and numerical predictions is reliable except the Panel D. In the case of Panel D, the fundamental settings are different from present method in this thesis.
Using the present method, several cases are set up to investigate related parameters of cores, such as thickness, density and cell size. The numerical results show that the coincident frequency will change with different thickness of the core and this variance in frequency will influence the sound insulation of the panel. In addition, the effect of core density is similar to the effect of core thickness. The coincident frequency will decrease with the increase of the core density until the core density increase to exceed certain limit. At the time, the coincidence will occur in the same frequency. Finally, cell size of the core doesn’t influence the transmission loss of sandwich panels.

第一章 序論 10
1.1 前言 10
1.2文獻回顧 11
1.3研究方法 13
第二章 Biot彈性多孔材理論 14
2.1彈性結構與剛性結構 14
2.2彈性多孔材之應力與應變關係 16
2.2.1 應力與應變之關係 16
2.2.2 流體為空氣之簡化 18
2.3 Biot Theory的慣性耦合效應 20
2.3.1 慣性力的求得 20
2.3.2 慣性耦合項與折曲度的關係 22
2.4 多孔材料的波動方程式 24
2.5 多孔材料中的壓縮波與剪力波 26
2.5.1 壓縮波部份 26
2.5.2 剪力波部份 28
2.5.3 空氣中Biot波在多孔材料內的討論 29
第三章 聲波於多層材料中傳遞之計算 31
3.1 轉換矩陣 31
3.1.1 多孔材的轉換矩陣 32
3.1.2 彈性固體的轉換矩陣 38
3.1.3 流體的轉換矩陣 40
3.2 邊界轉換矩陣 43
3.2.1 流體至流體間之邊界轉換矩陣 44
3.2.2 彈性固體至彈性固體間之邊界轉換矩陣 44
3.2.3 多孔材至多孔材間之邊界轉換矩陣 45
3.2.4 流體至彈性固體間之邊界轉換矩陣 46
3.2.5 流體至多孔材間之邊界轉換矩陣 47
3.2.6 彈性固體至多孔材間之邊界轉換矩陣 48
3.3 轉換矩陣中相關參數之整理 50
3.3.1 彈性係數 P 、Q、R 50
3.3.2 波數(wave number) 51
3.3.3 多孔材的密度 、、 53
3.4 由轉換矩陣求解穿透損失 54
第四章 文獻比對 57
4.1 三明治保利龍板 58
4.1.1 Panel A之穿透損失 60
4.1.2 相關參數之決定 65
4.1.3 Panel B板之穿透損失 69
4.2 三明治蜂巢板之隔音性能分析 72
4.2.1 Panel C之穿透損失 75
4.2.2 相關參數之決定 80
4.2.3 Panel D之穿透損失 83
第五章 三明治蜂巢板之理論分析 86
5.1芯材厚度對隔音性能之影響 88
5.2芯材密度對隔音性能之影響 92
5.2.1 蜂巢芯材密度對隔音性能之影響 93
5.2.2 發泡芯材密度對隔音性能之影響 101
5.3特徵長度對隔音性能之影響 103
第六章 結論與展望 108
6.1 結論 108
6.2 未來展望 110
參考文獻 111

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