Structural Dynamic Analysis with Generalized Damping Models: Analysis

Chapter 3Non-Viscously Damped Single-Degree-of-Freedom Systems

Increasing use of modern composite materials and active control mechanisms in aerospace and automotive industries demands sophisticated treatment of dissipative forces for proper analysis and design. Viscous damping is the most common model for modeling of vibration damping in linear systems. This model, first introduced by Lord Rayleigh [RAY 77], assumes that the instantaneous generalized velocities are the only relevant variables that determine damping. In the previous chapter, we discussed the dynamics of viscously damped systems in some detail. Viscous damping models are used widely for their simplicity and mathematical convenience even though the energy dissipation behavior of real structural materials may not be accurately represented by simple viscous models. It is well recognized that in general, a physically realistic model of damping will not be viscous. Damping models in which the dissipative forces depend on any quantity other than the instantaneous generalized velocities are non- viscous damping models. Mathematically, any causal model that makes the energy dissipation functional non-negative is a possible candidate for a non-viscous damping model. Clearly, a wide range of choice is possible (see Table 1.1), either based on the physics of the problem, or by a priori selecting a model and fitting its parameters from experiments. Among various damping models, the “exponential damping model” is particularly ...