本文以考慮橫向剪力與轉動慣量效應的厚板，分別施加預力、側向平面彎矩及邊界彎矩，探討對於厚板自然頻率產生的影響。 過去的文獻中，對於薄板受預力作用的問題已有大量的研究，利用李維法或格樂肯法等數值方法來處理，在工程實務上預力構件也已經被廣泛的使用，但當平板厚度大到一定程度時，薄板所忽略的橫向剪力及轉動慣量的效應會變大，此時薄板的自然頻率與實際值會有明顯差異。 本文針對厚板在四周邊界為簡支撐的情況下，來研究受預力及彎矩等作用對於自然頻率的改變，應用二維彈性力學理論，得到受預力厚板的總勢能，利用漢彌爾頓原理求得統御方程式，並以格樂肯法來求解出自然頻率，與薄板在同樣的預力及彎矩作用情況下所求得自然頻率比較，探討不同厚度下，橫向剪力與轉動慣量對於自然頻率的影響。 In this paper, the rectangular plate considers the effects of transverse shear and rotatory inertia. Transverse free vibrations of thick plate which are subjected to in-plane force, in-plane moment and edge moment. The influence for natural frequency of thick plate subjected to in-plane loads. The problem is assumed that the thick plate is simply supported on all opposite edges and subjected to in-plane loads. The two-dimensional elastic theory and Hamilton principle are exercised to obtain the governing differential equations of thick plate subjected to in-plane loads. The natural frequency of the problem is obtained by using the Galerkin method and treat the effects of transverse shear and rotatory inertia.
