Harmonic balance-boundary element and continuation methods for steady-state wave scattering by interior and surface-breaking cracks with contact acoustic nonlinearity
Harmonic balance-boundary element and continuation methods for steady-state wave scattering by interior and surface-breaking cracks with contact acoustic nonlinearity
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DOI：
10.1016/j.ijsolstr.2020.11.007
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发表时间：
2020-11
影响因子：
3.6
通讯作者：
T. Maruyama
中科院分区：
文献类型：
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作者：
T. Maruyama
本文开发了一种利用接触声学非线性 (CAN) 的裂纹引起的非线性稳态波散射的数值方法。这里解决了面内散射问题。研究的两个系统由包含内部裂纹的无界弹性固体和包含表面断裂裂纹的弹性半平面组成。时谐平面波入射，裂纹面上产生拍击和摩擦运动作为非线性现象。采用谐波平衡边界元法（HB-BEM）来解决非线性稳态问题。 HB-BEM 获得的方程组由弹静边界积分方程 (BIE) 和多个不同频率的频域弹动力 BIE 组成，它们通过非线性边界条件耦合。为了对系统进行数值求解，需要对非线性边界条件进行正则化。在正则化边界条件下，牵引力由相对于裂纹张开位移的平滑单值函数表示。使用参数连续方法跟踪稳态系统的解以研究分岔。连续方法中变化的参数是入射频率和静态场变量。为了确定稳态解的稳定性，提出了一种基于希尔无限行列式的稳定性分析方法。经过足够的时间后，该方法获得的稳定解与传统时域解一致。对于特定参数，观察到具有分岔的 1/2 阶次谐波谐振。裂纹引起的局部谐振特性与 CAN 之间的相互作用会引起次谐波谐振。
A numerical method for nonlinear steady-state wave scattering due to a crack with contact acoustic nonlinearity (CAN) is developed in this article. The in-plane scattering problem is addressed here. The two systems studied are composed of an unbounded elastic solid that includes an interior crack and an elastic half plane that includes a surface-breaking crack. A time-harmonic plane wave is incident, and clapping and rubbing motions on the crack faces are induced as nonlinear phenomena. A harmonic balance-boundary element method (HB-BEM) is utilized to solve the nonlinear steady-state problem. The system of equations obtained by the HB-BEM consists of an elastostatic boundary integral equation (BIE) and frequency-domain elastodynamic BIEs of several different frequencies, which are coupled by nonlinear boundary conditions. To solve the system numerically, the nonlinear boundary conditions are regularized. In the regularized boundary conditions, traction is expressed by a smooth single-valued function with respect to crack-opening displacement. The solution of the steady-state system is tracked with a parameter continuation method to investigate bifurcations. The parameters that vary in the continuation method are the incident frequency and static field variables. To determine the stability of the steady-state solutions, a stability analysis method based on Hill’s infinite determinant is proposed. The stable solutions obtained by the proposed method agree with the conventional time-domain solutions after enough time has elapsed. A 1/2-order subharmonic resonance is observed with bifurcations for particular parameters. The interaction between the local resonant properties due to the crack and the CAN causes subharmonic resonance.