3 Nonlinear and Variable Stiffness Systems; Preloading

Since stiffness is the ratio of the force to the displacement caused by this force, the load-deflection plot (characteristic) allows to determine stiffness as a function of force or displacement. It is much easier to analyze both static and dynamic structural problems if the displacements are proportional to the forces that caused them, i.e., if the load-deflection characteristic is linear. However, most of the load-deflection characteristics of real-life mechanical systems are nonlinear. In many cases, the degree of nonlinearity is not very significant, and the system is considered as linear for the sake of simplicity. While a significant nonlinearity must be always considered in the analysis, even a weak nonlinearity may noticeably change behavior of the system, especially for analysis of dynamic processes in which nonlinearity may cause very specific important, and frequently undesirable, effects, e.g., see [1]. At the same time, there are many cases when the nonlinearity may play a useful role by allowing adjustment of stiffness parameters of mechanical systems.