Structural Dynamic Analysis with Generalized Damping Models: Analysis

Chapter 4Non-viscously Damped Multiple-Degree-of-Freedom Systems

The previous chapter gave qualitative ideas on the dynamics of non-viscously damped single-degree-of-freedom systems. Several properties of the eigensolutions and dynamic response function have been explained. In this chapter, we devote our attention to lumped parameter linear systems with N degrees-of-freedom and non-viscous damping properties. We mainly focus on the quantitative aspects here. The system we will study can be described by an equation of motion in the form

[4.1]

together with the initial conditions

[4.2]

In this formulation, is the vector of displacements for the N degrees-of-freedom, is the vector of applied forcing, is the mass matrix, is the stiffness matrix, is the viscous damping matrix and is the matrix ...