MAGPIE: a web-based, open-source framework for plate vibration analysis

The analysis and simulation of plate vibrations are central to many branches of science and engineering, specifically acoustics and musical acoustics. Well-developed plate theories exist, along with numerous simulation software packages, but they are seldom available in open-source form and are not easily accessible to a greater audience. MAGPIE is a framework for interacting with a novel finite difference scheme for plates under general elastic boundary conditions. Free, clamped, and simply supported boundary conditions are obtainable by setting stiffness coefficients to very small or large values. Boundary conditions are parameterised which allow for intermediate possibilities. A web browser based implementation of the framework includes interactive elements. Users begin by providing parameters for an isotropic plate. These parameters are then used to generate visualisations of the mode shapes from the finite difference scheme simulation. Elastic boundary conditions can then be changed on a continuous scale to see their effect on mode shapes. Results are then available for export in common image and data formats. MAGPIE aims to make it easier to explain concepts such as mode shapes to a wider audience and also provide a tool for research that is accessible to students, scientists and musical instrument builders.