  A single-step high-order implicit time integration scheme with controllable
numerical dissipation at high frequencies is presented for the transient
analysis of structural dynamic problems. The amount of numerical dissipation is
controlled by a user-specified value of the spectral radius $\rho_\infty$ in
the high frequency limit. Using this user-specified parameter as a weight
factor, a Pad\'e expansion of the matrix exponential solution of the equation
of motion is constructed by mixing the diagonal and sub-diagonal expansions. An
efficient timestepping scheme is designed where systems of equations, similar
in complexity to the standard Newmark method, are solved recursively. It is
shown that the proposed high-order scheme achieves high-frequency dissipation,
while minimizing low-frequency dissipation and period errors. The effectiveness
of the provided dissipation control and the efficiency of the scheme are
demonstrated by numerical examples. A simple guideline for the choice of the
controlling parameter and time step size is provided. The source codes written
in MATLAB and FORTRAN are available for download at:
https://github.com/ChongminSong/HighOrderTimeIntegration.
