Undamped Single Degree-of-Freedom System

Abstract

The analysis and design of structures to resist the effect produced by time dependent forces or motions requires conceptual idealizations and simplifying assumptions through which the physical system is represented by an idealized system known as the analytical or mathematical model. These idealizations or simplifying assumptions may be classified in the following three groups:

• 1. Material assumptions. These assumptions or simplifications include material properties such as homogeneity or isotrophy and material behaviors such as linearity or elasticity.

• 2. Loading assumptions. Some common loading assumptions are to consider concentrated forces to be applied at a geometric point, to assume forces suddenly applied, or to assume external forces to be constant or periodic.

• 3. Geometric Assumptions. A general assumption for beams, frames and trusses is to consider these structures to be formed by unidirectional elements. Another common assumption is to assume that some structures such as plates are two-dimensional systems with relatively small thicknesses. Of greater importance is to assume that continuous structures may be analyzed as discrete systems by specifying locations (nodes) and directions for displacements (nodal coordinates) in the structures as described in the following section.