Asynchronous Modes of Beams on Elastic Media Subjected to Varying Normal Force: Continuous and Discrete Models

Abstract

The asynchronous vibration modes of a prismatic beam on elastic media under varying normal force are addressed for both continuous and discrete models. For the latter ones, with three DOF (degrees of freedom), the classical linear analysis was used to discuss the vibration modes, whereas for the continuous model quasi-Bessel modes are proposed. In the 3-DOF model, pre-stressing is force-imposed, while in the continuous one it is applied through a displacement imposition. Even if both models are calibrated in order to lead to the “same” asynchronous vibration mode in linearised formulations, it is seen that the differently assumed boundary conditions lead to distinct non-linear behaviour: Softening for the 3-DOF and hardening for the continuous model. Classic linear modal analysis for associated finite-element models is addressed for the sake of comparison and to bring about the issue of modal accumulation, which seems to be an accompanying phenomenon to that of modal asynchronicity.