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
together with the initial conditions
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 ...