New implicit time integration schemes for structural dynamics combining high frequency damping and high second order accuracy

The time integration schemes, GA-23 and GA-234, recently proposed by the authors for first order problems, are extended to solve second-order problems in structural dynamics. The resulting methods maintain unconditional stability and user-controlled high-frequency damping. They offer improved accuracy and exhibit less numerical damping in the low-frequency regime, outperforming the well-known generalised- α method. When the high-frequency damping is maximised the new schemes can be cast in the format of backward difference formulae, offering more accurate alternatives to the standard second order formula. The effectiveness of the new time integration schemes is validated through a number of numerical examples, including a linear elastic cantilever beam, a nonlinear spring pendulum, and wave propagation on a string. • New single step second order accurate time integration schemes for structural dynamics. • Unconditional stability and user-controlled high frequency damping. • Compares favourably to generalised-alpha method and to Bathe method. • For maximum high-frequency damping, can be represented as backward difference formulae.