The unimportance of the spurious root of time integration algorithms for structural dynamics

• Published in: Communications in numerical methods in engineering Vol. 10; no. 8; pp. 591 - 597
• Main Authors: Hulbert, G. M., Chung, J.
• Format: Journal Article
• Language: English
• Published: Sussex John Wiley & Sons, Ltd 01.08.1994; Wiley
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Vibrations and mechanical waves; Time dependence; Mechanical vibrations; Numerical solution; Structural analysis; Quadratures
• ISSN: 1069-8299; 1099-0887
• DOI: 10.1002/cnm.1640100803

Most commonly used second‐order‐accurate, dissipative time integration algorithms for structural dynamics possess a spurious root. For an algorithm to be accurate, it has been suggested that the spurious root must be small and ideally be zero in the low‐frequency limit. In the paper we show that good accuracy can be achieved even if the spurious root does not tend towards zero in the low‐frequency limit. This permits more flexibility in the design of time integration algorithms. As an example, we present an algorithm that has greater accuracy than several other dissipative algorithms even though for all frequencies its spurious root is non‐zero. We also show that the degraded performance of the Bazzi‐ρ algorithm is not due to its non‐zero spurious root.