Emerging dynamic stiffness modelling of physical and chemical ageing rubber vibration isolators in the audible frequency range

The dynamic stiffness of a chemically and physically ageing, axially symmetric, homogeneously aged rubber vibration isolator, is modelled in the audible frequency range, as function of frequency, temperature, time, isolator length and radius. Physical ageing is a reversible ageing process while chemical ageing is in contrast an irreversible process, the former including elastomer polymer chain reorganizations, free volume changes, freeing and trapping of elastomer polymer chain ends, while the latter is primarily recognized as oxygen reaction with elastomer polymer network either damaging the network by scission or rebuilding of new elastomer polymer links. Physical ageing is modelled by a nonlinear, fractional time order differential equation for fractional free volume evolution with relaxation time identical to that of the stress response and connected to the fractional free volume via Doolittle equation. Chemical ageing is modelled by internal, nonlinear, fractional time order differential equations for the internal variables. Dynamic stiffness is derived by a waveguide technique while using the eigen-modes for an infinite cylinder, being stress free at its radial surface, and where the boundary conditions at the lateral surface ends of the finite vibration isolator are satisfied by eigen-mode matching. Finally, dynamic stiffness results are shown while studying various parameter dependencies including physical and chemical ageing time and temperature variations.