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.
Published Version
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