TABLE OF CONTENTS Up until now the systems we've been examining have been composed of easily identified mass and spring elements. The masses and springs always appeared discretely, never in a distributed or continuous manner. But in the real world, such idealized structures never exist. The fact of the matter is that real-world structures are always continuous. Nobody can construct a true point mass; all real bodies have finite dimensions and so are characterized by their density or mass per unit volume. Similarly, ideal springs exist only in our minds. In the simple experiments we conducted in Chapters 1, 2, and 4, we treated the physical spring as a pure spring. But it is clear that any physical spring always has mass, a mass that we neglected in our analysis.
So, if we can never construct a system made up of just masses and springs, why did we study them? In the first place, although we can never have systems whose mass and spring elements occur in a precisely discrete manner, we can often approximate real systems as being discrete with only a negligible loss in accuracy. In addition, the mathematics associated with discrete systems is a bit easier to deal with. And finally, we'll be introducing methods that explicitly include continuous responses, yet put the overall system into a discrete framework.
The point is that we may find ourselves wanting to analyze realistic systems having continuous distributions of mass, elasticity, and damping. The problem is that except in some...
