Bonnin A, Huchon R, Deschamps M
Laboratoire Mécanique Physique, UMR 5469 CNRS, Université Bordeaux 1, Talence, France.
Ultrasonics. 2000 Jan;37(8):555-63. doi: 10.1016/s0041-624x(99)00106-7.
Guided wave theory is applied to a thin orthotropic and absorbing plate for low frequency propagation of ultrasonic waves. The aim of this paper is to give some physical interpretations of the non-destructive characterization of paper materials, which are cellulosic fibrous networks. It is shown that the propagation problem reduces to two normal modes of propagation in the plane of the plate. Each of them depends on four complex and independent stiffnesses that are combinations of elementary complex stiffnesses of the media. The imaginary part of these stiffnesses corresponds to a possible mechanism of energy dissipation during the wave propagation for this kind of material. The reverse problem, which gives four complex values, is then numerically solved using a small attenuation assumption. The specially designed experimental set-up has led to the first measurements of tracing paper damping factors. The phase velocity measurements of the plate waves agree with the results already found by several paper researchers. As a particular and new result, the shear wave velocities are found to present a quasi-isotropic repartition in the plane of the paper sheet. It was found that the absorbing phenomenon can occur for each propagation mode in such a material. The attenuation values are small, except for one of them that corresponds to a coupling term in the propagation model. The anisotropy of their repartition is also shown in the case of quasi-longitudinal waves.
导波理论应用于薄的正交各向异性吸声板，用于超声波的低频传播。本文的目的是对纸材料（纤维素纤维网络）的无损表征给出一些物理解释。结果表明，传播问题简化为板平面内的两种正常传播模式。每种模式取决于四种复独立刚度，它们是介质基本复刚度的组合。这些刚度的虚部对应于此类材料在波传播过程中能量耗散的一种可能机制。然后，利用小衰减假设对给出四个复值的反问题进行数值求解。专门设计的实验装置首次测量了描图纸的阻尼因子。板波的相速度测量结果与几位纸张研究人员已得到的结果一致。作为一个特殊的新结果，发现剪切波速度在纸张平面内呈现准各向同性分布。研究发现，这种材料的每种传播模式都可能出现吸收现象。除了与传播模型中的一个耦合项对应的衰减值外，其他衰减值都很小。在准纵波情况下，也显示出它们分布的各向异性。
