熱效應下混合複合板之振動與穩定性

Vibration and Stability of Hybrid Composite Plates with Thermal Effects

張育群(Yu-Chiun Jang)

指導教授 ： 蔡定江

國立臺北科技大學/機電學院/機電整合研究所/碩士(2011年)

摘要

在應用複合材料的結構元件過程中，元件壽命會受提升溫度狀態的影響。元件在升溫的環境下，因為高溫而產生的壓縮應力，將局限複材平板的功能，並導致平板的挫屈。因此疊層板的受熱挫屈與穩定性，在疊層複合平板的設計與使用上，扮演著重要角色，所以要充分利用疊層板的功能，精確了解疊層板的挫屈行為是相當需要的。
本文應用Hamilton能量原理，並基於Mindlin的位移場假設，推導受熱環境下，含非均勻預力混合複合平板的偏微分統制方程式。運用Galerkin method將偏微分統制方程式簡化為常微分統御方程式。並探討受熱及含任意預力下混合疊層板的熱挫屈現象。考慮均溫與溫度沿厚度方向線性變化之兩種熱負荷。經由求解線性統制方程式的特徵值，可求得混合疊層平板的臨界熱挫屈溫度、挫屈力和振動頻率。並探討各種參數對於混合複合板的影響。由分析結果顯示厚度比 和預力 的變化對混合複合板的熱挫屈影響很大， 比值的變化對挫屈力和振動有明顯地影響，且挫屈力也受厚度比的影響。

關鍵字

Hamilton ； Mindlin ； 統制方程式 ； 特徵值

並列摘要

The structural components of composite materials are often subjected to elevated temperatures during their service life. In such circumstances, high thermally induced compressive stresses will be developed in the constrained composite plates and consequently will lead to buckling; and thus significantly degrade their performance. So, thermal buckling and stability characteristics are one of the major design criteria for composite laminated plates for their optimal usage. In order to fully exploit their strength, an accurate prediction of their buckling load carrying capacity is essential.
In the present work, the Hamilton’s energy principle is used to governing partial differential equations of hybrid composite plate in a general state of non-uniform initial stresses includes thermal effects are formulated from Mindlin plate theory. The Galerkin method is used to reduce the governing partial differential equations to ordinary differential equations. Thermal buckling is presented for hybrid composite plates under thermal loading and arbitrary initial stresses. Two types of thermal loadings, namely; uniform temperature rise and linear temperature rise are considered. The critical buckling temperatures, vibration frequency and buckling load are obtained from the linear eigenvalue problems. The effects of various parameters for hybrid composite plates will be studied. The analysis results show that the thickness ratio and initial stress has a great impact to the critical temperature parameter of the hybrid composite plates. The ratio of has an apparent influence on natural frequency and buckling load. And buckling load is also affected by thickness ratio.

並列關鍵字

Hamilton ； Mindlin ； governing equations ； eigenvalue

參考文獻

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