Error estimation and adaptive meshing for vibration problems

Abstract The paper discusses selected procedures for estimating the discretization error of finite element modeling as applied to the calculation of undamped natural frequencies of vibration. One method uses improved strain energy by smoothing the element-by-element stress field. Another method uses improved kinetic energy by using alternative mass matrices. Neither method requires the introduction of additional DOF. Error estimates are also used to identify elements whose discretization error is greatest, and thus drive mesh refinement by r- and h-methods. Axial vibrations of bars and in-plane vibrations of membranes are used as example problems.