Wednesday, December 21, 2022 1PM
ASTC # 615
Title: A spring–beam system with dynamic frictionless contact
Abstract: Contact between bodies happens in every single day life. The motion of seesaws is motivated to build a mathematical model, where two viscoelastic (Kelvin-Voigt type) objects are employed with two contact conditions.
The normal compliance condition and a transmission condition is imposed on one end of the beam and the top of a nonlinear spring so that they can touch and vibrate together. When the top of the spring moves down to touch a rigid foundation, Signorini’s condition is applied. We prove the existence of solutions satisfying the differential equation system and all the conditions. We utilize time discretizations and finite element methods to propose the fully discrete numerical schemes. Several groups of data are selected to present numerical simulations.