三明治板之聲傳行為研究及設計

Abstract

平滑的聲壓曲線和較大的聲壓值為好揚聲器的必要條件，好的板抗彎強度使聲壓平滑，輕的板使聲壓值提高。本文將蜂窩結構應用於三明治平面揚聲板，使用不同磅數的紙張製作板的心層，製程上追求板的質量必須接近巴沙木板，使製成的板材可應用於揚聲器。製成板材後，以樑三點彎矩實驗反求面層材料楊氏模數E值，和芯層材料剪力模數G值，以板平壓實驗反求芯層材料楊氏模數E值，代入實體3D模型計算聲壓曲線，和實驗比較確定模型無誤後，以此實體模型為基準，討論兩個簡化模型的適用範圍，在適用的範圍下大幅縮短數值計算的時間，加速揚聲器的設計。本文並討論如何調整三明治結構參數使聲壓曲線平滑，並使聲壓值提高。發現蜂窩揚聲板的各個幾何設計參數常是只對一個板等效常數有很大的影響，芯層材料厚度主要影響到板等效剪力常數Gyz，面板厚度主要影響到板等效密度，蜂窩芯層厚度則主要影響到板單位密度抗彎強度，板等效密度。芯層材料加厚導致的密度增加，或面板變薄所導致的抗彎強度減小都可藉由蜂窩芯層厚度做加強。而板的等效參數往往直接影響到揚聲器的聲壓表現，本文利用此發現探討如何調整蜂窩三明治板幾何參數，最後以實體3D模型的聲壓曲線證實參數調整確實達到目的。最後以一層等效模型討論高頻各局部音谷成因，如何以非正六邊形蜂窩的設計改善之。

Flat-panel loudspeaker has become an attractive device for generating sound in the audio industry. The capability of producing smooth frequency response and high sound pressure level is vital to such loudspeaker. Higher bending strength can make frequency response smoother and light-weight panel improve sound pressure level. The thesis applies honeycomb core to fabricate sandwich panel for the loudspeaker. Plain papers of different weights are used to make sandwich plates which can be comparable with the light-weight balsa wood. Execute three point bending test of sandwich beams made of paper to identify the Young’s modulus of face plate and shear modulus of core material. Also execute compression test to identify the Young’s modulus of core material. Substitute the identified material constants into the 2D and 3D finite element models of the sandwich plate to construct the sound pressure level (SPL) curves in the audible frequency domain. Compare the theoretical results with the experiment results to check the correctness of the 2D and 3D models. Then discuss the suitability of two simplified 2D finite element models in predicting accurate SPL curves. The 2D models can greatly shorten the computing time when compared with the 3D model. The thesis discusses how to adjust the parameters of the sandwich plate to produce smoother frequency response and higher sound pressure level. It has been found that the thickness of core material can greatly affect the effective shear modulus Gyz of the sandwich plate. The thickness of core layer can greatly affect the bending strength per unit density and the equivalent density of the plate. An increase of the equivalent density and reduction of strength could be recovered by an increase of thickness of core layer. The thesis studies how to choose the proper design of the honeycomb sandwich panel that can improve the SPL curve of the plate via a numerical simulation approach. Finally, the cause of the local sound valley in the 3000 to 20000Hz range is investigated via the use of one equivalent layer plate model and the elimination of the sound valley is performed via the use of non-hexagonal honeycomb cells.