Stability and Response Bounds for Structures Under Dynamic Loads
This chapter contains a review of some previous work by the author and others. Continuous elastic structures subjected to dynamic loads are considered. Results are obtained with the use of Liapunov (Lyapunov) functionals. For cases in which the stability of an equilibrium configuration is of interest, Liapunov’s direct (second) method is applied. For cases in which the structure is in motion due to dynamic loads (e.g., transient loads), bounds on the response are presented.
The author is extremely grateful to Professor C. S. Hsu for being a wonderful Ph.D. advisor. Professor Hsu was an inspirational teacher and mentor, and has been a friend for the past 45 years. The author also acknowledges the assistance of Benjamin Z. Dymond in the preparation of this chapter.
- Akeju TAI (1985) Torsional buckling of columns by the Lyapunov method. J Ship Res 29(3):189–193Google Scholar
- Plaut RH (1967) A study of the dynamic stability of continuous elastic systems by Liapunov’s direct method. Report No AM-67-3, College of Engineering, University of California, BerkeleyGoogle Scholar
- Plaut RH (1978) Liapunov stability of shallow arches. In: Developments in theoretical and applied mechanics. Proceedings of the 9th Southeastern conference on theoretical and applied mechanics, vol 9, Vanderbilt University, pp 415–425Google Scholar