本文探討無限域含圓形剛性夾域受平面P波入射之動態反應,旨在決定垂直向與水平向入射勢能場之間振幅的比值關係,使之於擬靜態情況下能近似於一靜態均勻張力場。並進而探討不同入射波前入射圓形剛性夾域之暫態反應。 在求解受雙向平面P波入射場之穩態反應方面,分析方法主要是將全域之動態反應分成自由場基函數與散射場輔助函數。其中,基函數為無夾域之均質等向性材料受入射勢能場之反應;輔助函數則為由於剛體存在所造成之散射場。解題方法為波函數展開法,首先分別將自由場和散射場利用圓柱形波函數Bessel和Hankel函數展開,再透過剛體之運動方程式決定散射場波函數之待定係數,進而得到全域之動態反應。 在暫態反應方面,觀察一個單向入射之單位階梯平面P波函數,利用傅立葉級數展開以及頻譜概念將此函數展開為無限多個穩態反應的疊加。討論在不同入射波前值情況下之暫態反應。
This paper presents the stress concentration and the rigid body motion of a rigid cylindrical inclusion which embedded in elastic infinite medium. In aspect of unaxial incident P-wave, the stress field reduces to a field under a biaxial load Kirsch static solution when the frequency approaching zero. In this paper, we introduce a vertical incident P-wave to eliminate the stress contribution due to Poisson effect so that the stress field reduces to a field under a uniform tension or compression in horizontal direction when the frequency approaching zero. Then we discuss the transient response of a uniaxial Heaviside function incident P-wave in different wave front situation.