Influence of the Internal State of a Maxwell Damper on Free Critically Damped Vibrations

A Maxwell damper with a damper spring in series with a viscous dashpot is a more physical model than a viscous dashpot because the Maxwell damper models the elasticity of the connecting links of the viscous dashpot. The system of a main spring in parallel with a Maxwell damper is known as the standard linear solid (SLS) in viscoelasticity. The response of this SLS attached to a mass for standard initial value problems: displacement (nonzero displacement with zero velocity) and velocity (zero displacement with nonzero velocity) have been analyzed a few times in the literature. However, different authors present different conclusions about the importance of modeling the damper spring. None of these authors have explored the influence of the initial internal state of the damper spring. Here it is shown that the initial internal state of the damper spring can significantly influence the response for both displacement and velocity initial value problems.