Acoustic boundary conditions
Acoustic boundary conditions
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DOI：
10.1090/s0002-9904-1974-13714-6
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发表时间：
1974-11
影响因子：
1.3
通讯作者：
S. Rosencrans;fdG mn
中科院分区：
文献类型：
--
作者：
S. Rosencrans;fdG mn
受我们所说的声学边界条件的影响。产生这些条件的物理模型是气体在具有光滑致密边界的域 G 中从静止状态经历小的无旋扰动的物理模型。我们假设表面 bG 的每个点都像弹簧一样响应气体中的过压，并且 bG 的相邻点之间不存在横向张力，即“弹簧”彼此独立。 （这样的表面称为局部反应；参见 [2，第 259-264 页]。）如果边界具有单位面积质量 m、电阻率 d 和弹簧常数 k（bG 上的所有非负函数），则在时间 t 进入点 x G bG 域的位移 8(x, i) 必须满足弹簧方程
subject to what we call acoustic boundary conditions. The physical model giving rise to these conditions is that of a gas undergoing small irrotational perturbations from rest in a domain G with smooth compact boundary. We assume that each point of the surface bG acts like a spring in response to the excess pressure in the gas, and that there is no transverse tension between neighboring points of bG, i.e., the "springs" are independent of each other. (Such a surface is called locally reacting; see [2, pp. 259-264].) If the boundary has mass per unit area m, resistivity d, and spring constant k (all nonnegative functions on bG), then the displacement 8(x, i) into the domain of a point x G bG at time t must satisfy the spring equation