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Volume 20, Issue 1
A Spring–Beam System with Signorini’s Condition and the Normal Compliance Condition

Jeongho Ahn & Nicholas Tate

DOI: 10.4208/ijnam2023-1004

Int. J. Numer. Anal. Mod., 20 (2023), pp. 67-91.

Published online: 2022-11

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  • Abstract

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.

  • Keywords

Timoshenko beams, duffing equation, normal compliance, Signorini’s condition, Galerkin’s method, contraction mapping argument.

  • AMS Subject Headings

34A12, 35M33, 65J08, 74H15, 74H20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-20-67, author = {Ahn , Jeongho and Tate , Nicholas}, title = {A Spring–Beam System with Signorini’s Condition and the Normal Compliance Condition}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {20}, number = {1}, pages = {67--91}, abstract = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2023-1004}, url = {http://global-sci.org/intro/article_detail/ijnam/21205.html} }
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 -

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.

Ahn , Jeongho and Tate , Nicholas. (2022). A Spring–Beam System with Signorini’s Condition and the Normal Compliance Condition. International Journal of Numerical Analysis and Modeling. 20 (1). 67-91. doi:10.4208/ijnam2023-1004
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