Viscoelastic foundation-induced vibrations: Exploring linear theory application fields through numerical simulations

Abstract

This study investigates the dynamic interaction between a massive rigid body and a viscoelastic, non-adhesive flat substrate, behaving as a moving unilateral foundation and, thus, oscillating under various kinematic conditions (stationary sinusoidal, time-varying harmonic, and stochastic excitation). Such a problem is reduced to an equivalent single-degree-of-freedom base-excited system, where the intricate contact interactions involving the oscillating viscoelastic foundation are assessed by introducing a complex dynamic contact stiffness. This model is intrinsically linear and is based on the assumption that variations in the contact area, relative to the contact length in the static equilibrium configuration, may be neglected. Special attention is given to the phenomena of tapping, that is, the contact separation: the latter is clearly related to the amplitude and frequency of the foundation oscillations. An analytical relation, derived within the linear framework, is obtained to predict the incipient tapping front. To establish the application fields of this linear approach, we implement a Boundary Element Method (BEM)-based model that calculates the contact force, iteratively coupling the contact problem with the dynamic equation of the rigid supported mass. The results confirm that the linear model provides accurate predictions for transmissibility and the separation front under low-amplitude oscillations. For higher amplitudes, a specific frequency range emerges, characterized by tapping mode, thereby verifying the model’s capacity to delineate regions of continuous contact and tapping mode. Additionally, under non-stationary excitation conditions, the linear theory effectively predicts the transitions between contact and separation phases.