利用Ritz法分析具有裂縫之矩形薄板振動

Abstract

本研究使用Ritz法分析裂縫矩形板之自由振動，為能描述裂縫尖端之奇異性並滿足跨越裂縫之位移與轉角不連續行為，在所需之允許函數中引入本文提出之一組特殊函數。如此能確保Ritz法所得之自然頻率值由上界收斂至真解之特性。在收斂性分析中，以不同長度水平裂縫之案例，將所得結果與文獻比較，以驗證本研究所提函數之可行性與正確性。最後，應用本方法於分析各種不同邊界條件、不同裂縫長度、角度與位置之案例，探討不同裂縫長度、角度與位置對板振動行為之影響。本研究所得頻率值與振態節點圖，其中大部分均尚未見於文獻。

This study analyzes the free vibrations of rectangular plates with cracks by the famous Ritz method. To ensure the important and useful feature of the Ritz method providing the upper bonds on exact natural frequencies, the work proposes a new set of admissible functions that are able to properly describe the stress singularity behaviors near the tips of the crack and meet the discontinuities of displacement and slope crossing the crack. The validity of the proposed set of functions is confirmed through comprehensive convergence studies on the frequencies of rectangular plates with cracks having different lengths and showing the excellent agreement with published accurate resultes obtained by an integration equation technique. Finally, the present approach is applied to investigate the effects of location, length and orientation of cracks on the free vibration frquencies and mode shapes of simply supported and cantileverd rectangular plates with cracks. Most of the resultes shown are novel and first shown in literature.