摘要 本文為研究四邊均為簡支邊界之薄方板，當板面上開有矩形且對稱分佈之孔洞時，受旋轉聲源聲壓外力作用時，薄板之運動情形，並探討激振後於薄板之另一面空間中聲場的變化情形。 本文利用“Ectoplasm”方法，以漢彌爾頓定理為基礎，求取四邊為簡支多孔薄方板之運動方程式，於此方法中，整片薄板包括板面上孔洞將被一層薄膜覆蓋，此法可推導得到正定且對角化的質量與勁度矩陣，使解具有唯一性，續以旋轉聲源之聲壓函數取代系統之外力項，探討多孔薄方板受外力激振後之振動與聲場分析，於文中並引入了克赫積分式與格林函數以處理空間聲場中之輻射與繞射聲壓等相關問題。 Abstract The purpose of this research is to apply the use of “Ectoplasm” for the vibration analysis and corresponding sound field analysis of the holed plate excited by a rotating sound source. This formulation allows predication of high order eigenfrequencies and mode shape of a simply supported plate with holes. Such an algorithm can avoid a non-unique problem with ill-conditioned mass and stiffness matrices. In this study, Hamilton’s principle is used to obtain the governing equations. Then, the dynamic responses due to rotating sound source are solved. The Kirchhoff-Helmholtz integral and the Green’s function are used to deal with the acoustic field of the holed plate. Radiation and diffraction of the system is discussed.
