High-fidelity numerical simulation of the dynamic beam equation

A high-fidelity finite difference approximation of the dynamic beam equation is derived. Different types of well-posed boundary conditions are analysed. The boundary closures are based on the summation-by-parts (SBP) framework and the boundary conditions are imposed using a penalty (SAT) technique, to guarantee linear stability. The resulting SBP–SAT approximation leads to fully explicit time integration. The accuracy and stability properties of the newly derived SBP–SAT approximations are demonstrated for both 1-D and 2-D problems.