Properties of time integration with first order filter damping

• Published in: International journal for numerical methods in engineering 2005-09, Vol.64 (4), p.547-566
• Main Authors: Krenk, S., Høgsberg, J. R.
• Format: Article
• Language: English
• Subjects: algorithmic damping; Algorithms; Computational techniques; Conservation; Damping; Energy of formation; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Linear filters; Linear systems; Mathematical methods in physics; Numerical analysis; Physics; Reduced order; Solid mechanics; Structural and continuum mechanics; structural dynamics; time integration; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.1392

Introduction of algorithmic damping by increasing the parameter values in the Newmark algorithm leads to undesirable low‐frequency damping and reduced order of accuracy. It is demonstrated, how these effects can be removed by introducing an extra damping term in the form of a first order linear filter. When the linear filter is discretized in time, the state variable associated with the filter can be eliminated, leading to a weighted average of the equations of motion at two consecutive times. The filter procedure contains the known versions of alpha weighted Newmark methods as special cases, but gives a different and improved weighting of the excitation terms. A complete analysis of the properties of the algorithm when used on linear systems is given, including the frequency response properties. It is demonstrated that the effect of ‘overshoot’ is the consequence of a conservation relation that operates on a modified form of the mechanical energy of the system, and analytic results are presented for the magnitude of the effect. Copyright © 2005 John Wiley & Sons, Ltd.