Numerical modelling of polymer mounting by using fractional differential formulation
In many technical systems which are exposed to dynamic loading (oscillating excitation), it is required to reduce the reaction of the system Eigen dynamic due to durability, functionality or comfort. A widespread means of the Eigen dynamic reaction redaction is uncoupling/isolating the excitation source from the examined Eigen dynamic and damping of this reaction. For this purpose the elastomer (rubber) mounting is often used. The elastomer material shows a distinct elastic and less viscose behavior. For increasing of viscosity the elastomer is intermixed with, for example, carbon particulate matter. The system operation in viscos mode involves energy dissipation so that oscillation redaction is very efficient. An alternative to the rubber mounting with or without the additives is polymer mounting that exhibits in addition to elastic characteristic a distinctive viscos behavior. The polymer mounting is also convenient to isolating and damping of system oscillation exciting by environment or other technical systems in the neighborhood. Furthermore the viscoelastic material is the base of many smart materials. Thus smart materials mounting are often interest for active application. That is why we pursuit the investigation of mechanical properties of the viscoelastic material. We investigated viscoelastic behavior of polymer mounting at one degree of freedom oscillator in translating mode and estimated the frequency response of this dynamic system. Thereby, the stiffness-damping ratio is varied. We considered a numerical model of the one mass point oscillator with polymer mounting. Due to aperiodic damping behavior, we used to describe of this oscillator the fractional differential formulation. The fractional differential formulation is powerful to represent wide more dynamic behavior than the integer differential formulation. The amplitude and phase plot even depends on the derivative order of terms of the corresponding differential equation. In many cases the formulation by fractional differential equations is not pays off, because the accuracy achieved by ordinary differential equation is well enough. However in the cases of strong damping it seems to be a required way.