论文标题
通过边界对声波的最佳吸收
Optimal absorption of acoustical waves by a boundary
论文作者
论文摘要
为了找到吸收噪声壁的最简单，最有效的形状以消散声波的声学能量，我们考虑了由Helmholtz方程描述的频率模型，并在边界上具有阻尼。模型的适合度显示在具有D-Set边界的一类域（n-1 $ \ le $ d <n）。我们介绍了一类可接受的Lipschitz边界，在下面的意义上存在最佳的墙壁形状：我们证明存在这种形状上的ra尺寸的存在，大于或等于通常的lebesgue措施，为此，Helmholtz问题的相应解决方案实现了与Lebesgue On Maresebesgue On Maresebesgue On Maresebesgue定义的Ocoustict Energy的亲密。如果该ra量与Lebesgue度量重合，则相应的解决方案实现了能量的最小值。对于被视为声学吸收剂的固定多孔材料，我们从阻尼波方程（体积减弱）描述的相应时间依赖性问题中得出其边界的阻尼参数。
In the aim to find the simplest and most efficient shape of a noise absorbing wall to dissipate the acoustical energy of a sound wave, we consider a frequency model described by the Helmholtz equation with a damping on the boundary. The well-posedness of the model is shown in a class of domains with d-set boundaries (N -- 1 $\le$ d < N). We introduce a class of admissible Lipschitz boundaries, in which an optimal shape of the wall exists in the following sense: We prove the existence of a Radon measure on this shape, greater than or equal to the usual Lebesgue measure, for which the corresponding solution of the Helmholtz problem realizes the infimum of the acoustic energy defined with the Lebesgue measure on the boundary. If this Radon measure coincides with the Lebesgue measure, the corresponding solution realizes the minimum of the energy. For a fixed porous material, considered as an acoustic absorbent, we derive the damping parameters of its boundary from the corresponding time-dependent problem described by the damped wave equation (damping in volume).
