TY - JOUR
T1 - A Spring–Beam System with Signorini’s Condition and the Normal Compliance Condition
AU - Ahn , Jeongho
AU - Tate , Nicholas
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 67
EP - 91
PY - 2022
DA - 2022/11
SN - 20
DO - http://doi.org/10.4208/ijnam2023-1004
UR - https://global-sci.org/intro/article_detail/ijnam/21205.html
KW - Timoshenko beams, duffing equation, normal compliance, Signorini’s condition, Galerkin’s method, contraction mapping argument.
AB - <p style="text-align: justify;">This paper provides mathematical and numerical analyses for a dynamic frictionless
contact problem in which both of Signorini’s condition and the normal compliance condition
are used. The contact problem is considered by employing two viscoelastic (Kelvin-Voigt type)
objects: a linear Timoshenko beam and a nonlinear spring. In addition, a transmission condition
is imposed on one end of the beam and the top of the spring so that they can touch and vibrate
together. We prove the existence of solutions satisfying all the conditions. Time discretizations
and finite element methods are utilized to propose the fully discrete numerical schemes. We select
several groups of data to present and discuss numerical simulations.</p>