If you want to see what has already been written before starting your own simulation, the GitHub topic page is the fastest survey. It lists roughly twenty public repositories tagged chladni, sorted by stars, spanning vanilla JavaScript demos, WebGL and WebGPU solvers, Python notebooks, a C implementation limited to square unclamped plates, and a TeX repository collecting Chladni's public-domain works.
It also shows the field's edges honestly. Alongside the physics there are projects framed around healing frequencies, and several one-commit experiments with no licence. The topic is not curated, so quality varies enormously and star counts are a poor guide when half the entries are days old.
Use it as a starting index rather than a recommendation list: check the licence, check the last commit date, and check whether the maths is a real eigenvalue solve or the usual closed-form square-plate approximation before you build on anything.