Maruyama Taizo, Touhei Terumi
Department of Civil Engineering, Tokyo University of Science, 2641 Yamazaki, Noda-shi, Chiba Prefecture, 278-8510, Japan.
J Acoust Soc Am. 2018 Jun;143(6):3545. doi: 10.1121/1.5042163.
The present article describes the steady-state numerical modeling of anti-plane shear wave scattering by a crack with frictional boundary conditions. The system is composed of an unbounded elastic solid that includes a closed crack under static compressive stress. A time-harmonic anti-plane shear wave is incident, and dynamic friction between the crack faces is induced as a nonlinear phenomenon. The anti-plane wave scattering can be described in a retarded potential integral equation by taking the nonlinearity into account. The present article introduces the steady-state expression as an asymptotic vibration of crack faces after a sufficient elapsed time. In order to solve the equations describing nonlinear steady-state vibration, a harmonic balance method is integrated into a boundary element method. Fourier coefficients of crack opening displacement distributed on the crack face are treated as unknown variables. The system of nonlinear equations is solved by means of a numerical continuation method. The present numerical results show almost complete agreement with those obtained by the conventional time-domain analysis after a sufficient elapsed time. Furthermore, the robustness and effectiveness of the proposed method are demonstrated numerically.
本文描述了具有摩擦边界条件的裂纹对反平面剪切波散射的稳态数值模拟。该系统由一个无界弹性固体组成，其中包含一个处于静态压缩应力下的闭合裂纹。一个时谐反平面剪切波入射，裂纹面之间的动摩擦作为一种非线性现象被诱发。考虑到非线性，反平面波散射可以用一个延迟势积分方程来描述。本文引入稳态表达式作为经过足够长的时间后裂纹面的渐近振动。为了求解描述非线性稳态振动的方程，将谐波平衡法与边界元法相结合。分布在裂纹面上的裂纹张开位移的傅里叶系数被视为未知变量。通过数值延拓法求解非线性方程组。目前的数值结果表明，经过足够长的时间后，与传统时域分析得到的结果几乎完全一致。此外，通过数值验证了所提方法的稳健性和有效性。
