運用直接積分法研究複合圓板的非線性振動

Nonlinear Vibrations of Composite Circular Plate with a Rigid Central Mass-Using Direct Integration Method

10.29688/MHJ.200707.0013

呂鴻猷(Hung-Yu Lu)；張國平(Kuo-Ping Chang)

非線性振動 ； 有限元素法 ； Newmark ； 直接積分法 ； ANSYS ； nonlinear vibrations ； finite element method ； Newmark ； direct integration method ； ANSYS

明新學報

33期（2007 / 07 / 01）

227 - 238

繁體中文

本研究係探討圓心具剛性質量之複合圓板的非線性振動。文中採用有限元素法並運用漢彌頓法則(Hamilton's principle)推導系統的運動方程式，由於運動方程式具非線性性質，其複雜且具耦合性質的數學方程式，不易求取數值結果。因此，本研究運用紐馬克(Newmark)直接積分法，將運動方程式對時間積分，以取得振動週期，再換算成頻率響應。本研究以有限元素分析軟體－ANSYS，作為建構有限元素模型和求解數值之工具。為確保數值精確度，本文使用增量疊代法將總振幅分為數個振幅增量，再運用直接積分法對時間積分，以獲得非線性振型，進而再加以疊代運算，直至振型與頻率響應值收斂至預設之模數。本研究採用ANSYS之APDL程式建模並作疊代分析，此模式可有效應用於相關問題之研究。

Nonlinear vibrations of polar orthotropic circular plate with central rigid mass were investigated in this study. The finite element method and Hamilton's principle were applied to formulate the governing equation of motion for the system. Due to the complex nonlinear and coupled properties of differential equations, the numerical results are not easy to obtain. In this study, Newmark direct integration method was applied to integrate motion equations with respect to time, and the frequency responses were obtained by inverting the period of vibration after completing one full cycle of time integration. The finite element software package, ANSYS, was used as a tool to create model and obtain the numerical results. To insure the accuracy of numerical results, the increment-iteration method was applied. The total amplitude was divided into several increments of small amplitude, and then the direct integration was used to integrate with respect to time to obtain the mode shapes and frequency responses. The preceding procedure is iterated until the mode shapes and frequency responses converge to a defined norm. The programmable language APDL of ANSYS, was used to create model and execute the iterations of the analysis, and this model can be effectively applied to relative researches.

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