Dipartimento di Ingegneria Civile, Chimica, Ambientale e dei Materiali (DICAM), Università degli Studi di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy; Civil, Architectural & Environmental Engineering Department, Drexel University, 3141 Chestnut St., Philadelphia, PA 19104, USA.
Ultrasonics. 2014 Jan;54(1):408-18. doi: 10.1016/j.ultras.2013.06.011. Epub 2013 Jul 11.
A fully coupled 2.5D formulation is proposed to compute the dispersive parameters of waveguides with arbitrary cross-section immersed in infinite inviscid fluids. The discretization of the waveguide is performed by means of a Semi-Analytical Finite Element (SAFE) approach, whereas a 2.5D BEM formulation is used to model the impedance of the surrounding infinite fluid. The kernels of the boundary integrals contain the fundamental solutions of the space Fourier-transformed Helmholtz equation, which governs the wave propagation process in the fluid domain. Numerical difficulties related to the evaluation of singular integrals are avoided by using a regularization procedure. To improve the numerical stability of the discretized boundary integral equations for the external Helmholtz problem, the so called CHIEF method is used. The discrete wave equation results in a nonlinear eigenvalue problem in the complex axial wavenumbers that is solved at the frequencies of interest by means of a contour integral algorithm. In order to separate physical from non-physical solutions and to fulfill the requirement of holomorphicity of the dynamic stiffness matrix inside the complex wavenumber contour, the phase of the radial bulk wavenumber is uniquely defined by enforcing the Snell-Descartes law at the fluid-waveguide interface. Three numerical applications are presented. The computed dispersion curves for a circular bar immersed in oil are in agreement with those extracted using the Global Matrix Method. Novel results are presented for viscoelastic steel bars of square and L-shaped cross-section immersed in water.
提出了一种完全耦合的 2.5D 公式，用于计算浸入无限无粘流体中的任意横截面波导的色散参数。通过半解析有限元（SAFE）方法对波导进行离散化，而使用 2.5D BEM 公式来模拟周围无限流体的阻抗。边界积分的核包含空间傅里叶变换的亥姆霍兹方程的基本解，该方程控制着流体域中的波传播过程。通过使用正则化过程避免了评估奇异积分的数值困难。为了提高外部亥姆霍兹问题的离散边界积分方程的数值稳定性，使用了所谓的 CHIEF 方法。离散波动方程在复轴向波数中导致非线性特征值问题，通过轮廓积分算法在感兴趣的频率处求解。为了将物理解与非物理解分离，并满足复波数轮廓内动态刚度矩阵的全纯性要求，通过在流体-波导界面上强制施努尔-笛卡尔定律，唯一地定义径向体波数的相位。给出了三个数值应用。浸入油中的圆形棒的计算色散曲线与使用全局矩阵方法提取的色散曲线一致。还提出了浸入水中的方形和 L 形横截面粘弹性钢棒的新结果。
