{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/cantilevered-rectangular-plate-dynamics-by","title":"Cantilevered, Rectangular Plate Dynamics by Finite Difference Methods","arxiv_id":"2110.03503","date":"2021-10-07","proceeding":null,"authors":["Benjamin Brown"],"abstract":"In this technical note, we consider a dynamic linear, cantilevered rectangular plate. The evolutionary PDE model is given by the fourth order plate dynamics (via the spatial biharmonic operator) with clamped-free-free-free boundary conditions. We additionally consider damping/dissipation terms, as well as non-conservative lower order terms arising in various applications. Dynamical numerical simulations are achieved by way of a finite difference spatial approximation with a MATLAB time integrator. The rectangular geometry allows the use of standard 2D spatial finite differences, while the high spatial order of the problem and mixed clamped-free type boundary conditions present challenges. Dynamic energies are also computed. The relevant code is presented, with discussion of the model and context.","url_abs":"https://arxiv.org/abs/2110.03503v2","url_pdf":"https://arxiv.org/pdf/2110.03503v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"cantilevered-rectangular-plate-dynamics-by","repo_url":"https://github.com/bbrown11924/CFBoundary","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}