Abstract This paper investigates the wave propagation dispersion, spurious reflection and spurious bifurcation of flexural waves that occur in the numerical integration of the wave equation. To this end, the classic cubic beam finite elements of two nodes with a consistent mass matrix for integration in space and the Newmark average acceleration integration method of a single step for integration in time are considered. The resultant system of the difference equations is then analytically integrated in non-finite terms (numerical wave solution) using complex notation. Numerical results reveal that even for a refined mesh the dispersion and spurious reflections are quite high in comparison with numerical integration of the scalar wave.

中文翻译：

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弯曲波的色散、虚假反射和虚假分岔

摘要 本文研究了波动方程数值积分中出现的弯曲波的波传播色散、伪反射和伪分岔。为此，考虑了空间积分具有一致质量矩阵的两个节点的经典立方梁有限元和时间积分的单步Newmark平均加速度积分方法。然后使用复数符号以非有限项（数值波解）对差分方程的合成系统进行分析积分。数值结果表明，即使是细化的网格，与标量波的数值积分相比，色散和虚假反射也相当高。