Cantilevered, Rectangular Plate Dynamics by Finite Difference Methods

Benjamin Brown

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arXiv · 2110.03503

Cantilevered, Rectangular Plate Dynamics by Finite Difference Methods

Benjamin Brown

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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.

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BibTeX RIS

Benjamin Brown. 2021-10-07. Cantilevered, Rectangular Plate Dynamics by Finite Difference Methods. https://arxiv.org/abs/2110.03503

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