An Unusual Damped Stability Property and its Remedy for an Integration Method


  • Shuenn-Yih Chang Department of Civil Engineering, National Taipei University of Technology, NTUT Box 2653, No. 1, Section 3, Jungshiau East Road, Taipei 10608, Taiwan, Republic of China



dynamic analysis, time integration, responses of building, viscous damping, structure vibrations


An unusual stability property is found for a structure-dependent integration method since it exhibits a different nonlinearity interval of unconditional stability for zero and nonzero damping. Although it is unconditionally stable for the systems of stiffness softening and invariant as well as most systems of stiffness hardening, an unstable solution that is unexpected is obtained as it is applied to solve damped stiffness hardening systems. It is found herein that a nonlinearity interval of unconditional stability for a structure-dependent method may be drastically shrunk for nonzero damping when compared to zero damping. In fact, it will become conditionally stable for any damped stiffness hardening systems. This might significantly restrict its applications. An effective scheme is proposed to surmount this difficulty by introducing a stability factor into the structure-dependent coefficients of the integration method. This factor can effectively amplify the nonlinearity intervals of unconditional stability for structure-dependent methods. A large stability factor will result in a large nonlinearity interval of unconditional stability. However, it also introduces more period distortion. Consequently, a stability factor must be appropriately selected for accurate integration. After choosing a proper stability factor, a structure-dependent method can be widely and easily applied to solve general structural dynamic problems.


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Author Biography

Shuenn-Yih Chang, Department of Civil Engineering, National Taipei University of Technology, NTUT Box 2653, No. 1, Section 3, Jungshiau East Road, Taipei 10608, Taiwan, Republic of China

Shuenn-Yih Chang received a Ph.D. degree from the University of Illinois, Urbana-Champaign in 1995. Prior to joining National Taipei University of Technology, Taipei, Taiwan, in 2002, he was an associate research fellow of National Center for Research on Earthquake Engineering (NCREE). His research focuses on the structural dynamics and earthquake engineering. His work addresses on the dynamic testing of large-scale earthquake resistant structures, including the developments of novel pseudo-dynamic techniques. He is also of great interest in the design of accurate and efficient computational methods for dynamic problems of contemporary engineering interest. He has published more than one hundred and fifty refereed journal articles since 1988.


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Dynamics of Structures and Vibrations