ABSTRACT
There are several possible starting points for the consideration of the dynamic behaviour. However, in the ultimate analysis, all approaches are simply a mathematical representation of an energy balance. In the present instance we will start with Newton's second law of motion:
F = Md2x dt2 (3.3)
For the analysis, we need to sum all the components, i.e. all the forces that create an acceleration of the mass of the structure. These forces comprise an external force ((t), an elastic spring force fs and a damping force fe' Thus
(3.4)
ts = -Kx (3.5) where K is the spring constant and the force opposes the motion. The damping force is often described as
tc = -CX (3.6) where the damping force is assumed to be proportional to velocity and is termed 'viscous damping'. There is a full discussion about this assumption in Chapter 7.
