加勁揚聲板之最佳化設計

Abstract

本文旨在以揚聲板心層厚度及面層加勁長度為設計變數，透過最佳化設計方法，獲得揚聲器最大之聲壓感度及增加聲壓曲線之平滑區域。因長形揚聲板易受彎矩模態的變形而使聲壓在中音域產生明顯落差，其中若心層厚度與面層加勁長度設計不當時，會使揚聲板的重量、剛性及板變形量發生不宜的改變，以致造成聲壓感度的高低變化加大或進一步造成對聲音品質不好的中音谷。本研究使用有限元素法建構揚聲板的數學模型，進行揚聲板的振動及聲傳分析，以得到聲壓曲線。再將揚聲板的心層厚度與面層加勁長度作為設計參數，以聲壓感度為目標函數，聲壓的平滑性為限制條件，利用最佳化設計方法改善揚聲器之聲壓曲線表現。本文探討四種不同的設計參數組合以進行最佳化設計，並根據最佳化結果，將聲壓曲線表現最平滑的設計來作實驗驗証，說明本研究使用的最佳化設計方法可有效地應用於揚聲板的聲傳分析及設計上，以獲得更完美之聲壓曲線。

The purpose is to obtain the maximum sound pressure level (SPL) and improve the smoothness of the SPL curve of a rectangular sound radiating panel using the optimization method. The design variables considered are the middle-layer thickness and the face-layer lengths of the sound radiating panel. A major drop on the SPL curve in the mid frequency range can be attributed to the bending mode shape of the long rectangular plate. The mass, stiffness and deformation of the panel can be changed by varying the middle-layer thickness and face-layer lengths, and such changed can affect the sound pressure level and the drop in the mid frequency range. For this reason, the finite element method is used to analyze the vibration and sound radiation of the panel for attaining the SPL curve. In the optimal design, the design variables composed of the middle-layer thickness and face-layer lengths are determined to improve the loudspeaker performance by maximizing the average sound pressure level and enhancing the smoothness of the SPL curve. Four design cases used to investigate the optimal results are discussed in this work. In the experimental study, the speaker of the best design is fabricated to verify the suitability of the proposed method. The optimization technique can efficiently design stiffened sound radiating panels to produce acceptable SPL curves for the panels.