Force induced by vibration

本篇論文探討彈性體在流體中受到複合震盪的受力情況。所謂複合震盪指彈性體一方面作剛體來回震盪，一方面以某個形變模態振動，兩者頻率相同但有相位差。主要探討圓柱殼與球殼兩種情況。假設彈性體的形變模態不受流體的影響，經由聲波方程式可以求出流體內部因為彈性體振動而產生的壓力場。將壓力場在變形後的物體表面積分即可得到彈性體的受力。考慮兩種相角，其一為兩種振動模態間振動在時域上的相角，另一為形變模態對稱軸與來回震盪方向間的相角。針對不同頻率，詳細探討不同形變模態下相角變化對極值受力、受力方向的影響。In this thesis we investigate the net pressure load on an elastic body that is immersed in an inviscid fluid and undergoes compound vibration motion. The compound vibration motion consists of a rigid-body translational mode and a deformed vibrational mode. These two modes have the same frequency but different phase angles. Two simple kinds of elastic bodies, cylindrical and spherical shells, are considered in this thesis. Assuming the motion of the elastic body is not affected by the surrounding fluid, the pressure field in the fluid induced by the vibration of the elastic body can be determined by solving the acoustic equation subjected to suitable boundary conditions. After integrating the pressure on the deformed surface, we can obtain the net force exerted on the elastic body. Besides the phase angle in the time domain between the translational and deformed modes, we also consider the effect of the angle between the direction of the axis of symmetry of the deformed mode and that of the translational mode. The effects of various parameters, such as the vibration frequency, shape of the deformed mode, and phase angles, on the net force exerted on the elastic body are studied in detail.目錄 第一章 緒論…………………………………1 1.1 研究動機………………………………1 1.2 文獻回顧………………………………1 1.3 研究方法………………………………2 第二章 物體在非黏液體中的物理現象……………3 2.1 液體中的波動方程式……………………3 2.2無限長薄圓柱殼之振動模態……………4 2.3圓球殼之振動模態………………………10 第三章 理論分析…………………………………15 3.1無限長圓柱殼在液下受雙模態激振之現象……………15 3.1.1速度位能……………………………………………15 3.1.2壓力與力……………………………………………19 3.2球殼在液下受雙模態激振之現象………………………21 3.2.1速度位能……………………………………………21 3.2.2壓力與力……………………………………25 第四章 結果分析………………………………………………31 4.1推導過程與結果之概述…………………………………31 4.2圓柱殼之頻率與極值受力係數的探討…………………34 4.3圓球殼之頻率與極值受力係數的探討…………………42 4.4受力係數與 的探討……………………………………49 4.5圓柱殼受力與 的探討…………………………………51 4.6球殼受力與 的探討……………………………………51 第五章 結果討論…………………………………………… 61 參考文獻………………………………………………… 6