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] images

together with the initial conditions

[4.2] images

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

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