NEHRP Clearinghouse
- Title
- Damping of Structures: Part 1. Theory of Complex Damping.
- File
- PB92197235.pdf
- Author(s)
- Liang, Z.; Lee, G. C.
- Source
- National Science Foundation, Washington, DC., October 10, 1991, 259 p.
- Identifying Number(s)
- NCEER-91-0004
- Abstract
- The report presents a complex energy-based damping theory and its applications. The theory is formulated by considering the dissipative and the conservative energy components of damped vibrating systems simultaneously by complex-valued quantities. It provides a theoretical foundation for the analyses of generally (non-proportionally) damped systems. At the same time the complex damping theory offers new approaches to model the dynamic responses of multiple-degree-of-freedom systems (a relatively underdeveloped area in Newtonian mechanics) and to deal with vibration control problems in structural engineering. Chapter 1 selectively reviews the basic concepts of structural dynamics and damping, as they will be needed in subsequent presentations in the report. Chapter 2 presents the theory of complex damping. The theory gives a unified representation of energy dissipation and energy transfer by means of one complex quantity. Chapter 3 is concerned with lightly damped systems. In such systems, the real part of the eigenvalue of the state matrix and the damping ratio possess a special linearity. Chapter 4 deals with evaluation methods for the damping matrices. Chapter 5 first presents the reasons that the quantitative value of the damping matrix depends not only on damping configurations, but also on the mass and stiffness matrices of the structure.
- Keywords
- ; Earthquake resistant structures; Structural vibration; Seismic waves; Matrices (Mathematics); Mathematical models; Damping; Dynamic response; Earthquake engineering; Vibration damping; Dissipation; Dynamic structural analysis