Chladni Plate

pyChladniPlate is a Python library for modeling and analyzing Chladni plate vibration patterns through a combination of theoretical simulation and image-based experimental matching. It provides a ChladniPlate class that computes steady-state displacement fields and normalized nodal-likelihood maps via modal superposition on a simply-supported rectangular plate, and a ChladniPredict class that extracts skeletonized nodal lines from experimental images, maps them to physical plate coordinates across a range of scales, and sweeps driving frequencies to identify the best match.

Visit the entire paper on Chladni Plates on my website: Chladni Plates Applied Report

Features

• Modal superposition simulation Compute the complex displacement field $W(x,y)$ and a normalized nodal-likelihood map $L_w(x,y)$ for a driven rectangular plate using up to mode_max modes.
• Image preprocessing & skeletonization Denoise, morphologically clean, and skeletonize experimental images using OpenCV and scikit-image.
• Physical coordinate mapping Convert pixel skeleton coordinates to physical plate coordinates centered on the plate, with adjustable scaling.
• Automated parameter sweep Sweep over user-provided frequency and scale arrays to compute error metrics (mean distance, percentage error, contour size adjustment) and identify the optimal (scale, frequency) combination.
• Visualization tools Plot adjusted error vs frequency for each scale, display the raw image, overlay skeleton points on normalized grayscale, and compare skeleton vs theoretical nodal lines in physical units.

Installation

Clone the repository and install dependencies:

git clone https://github.com/CuriousAvenger/pyChladniPlate.git
cd pyChladniPlate
pip install numpy opencv-python scikit-image scipy matplotlib

• NumPy – fundamental package for array computing
• OpenCV – image operations and morphological filtering
• scikit-image – skeletonization and contour finding
• SciPy – efficient KD-tree nearest-neighbor searches with cKDTree
• Matplotlib – plotting and visualization

Usage

A simple example using main.py:

#!/usr/bin/env python3
import numpy as np
from chladni_plate import ChladniPlate
from chladni_predict import ChladniPredict

if __name__ == "__main__":
    # Initialize plate (0.24 m × 0.24 m, 0.5 mm thick, steel properties)
    plate = ChladniPlate(a=0.24, b=0.24, h=0.0005,
                         rho=7850, E=200e9, nu=0.3, zeta=0.01)
    # Define search ranges
    freqs  = np.arange(200, 400, 100)
    scales = np.arange(0.8, 1.2, 0.2)
    img_path = "lab_dataset/data_7.jpg"

    print(f"Processing {img_path}...")
    predictor = ChladniPredict(plate, img_path, freqs, scales)
    best_scale, best_freq, best_err = predictor.run()
    print(f"Best: scale={best_scale:.2f}, freq={best_freq} Hz, err={best_err:.2f}%")
    predictor.plot_error_analysis()
    predictor.visualize()

API Reference

ChladniPlate(a, b, h, rho, E, nu, zeta)

• Parameters & Attributes

  • a, b (float): Plate width and height in meters.
  • h (float): Plate thickness in meters.
  • rho (float): Material density in kg/m³.
  • E (float): Young’s modulus in Pa.
  • nu (float): Poisson’s ratio (dimensionless).
  • zeta (float): Modal damping ratio (dimensionless).
  • D (float): Flexural rigidity $E h^3 / [12(1-\nu^2)]$.

• Methods

  compute_contours(freq, F0, x0, y0, num_points=200, mode_max=20)

  • Computes grid coordinates (X, Y), complex field W, and normalized nodal-likelihood Lw.

ChladniPredict(plate, img_path, freqs, scales, F0=1.0)

• Parameters

  • plate (ChladniPlate): Initialized plate instance.
  • img_path (str): Path to experimental image.
  • freqs, scales (np.ndarray): Arrays of frequencies (Hz) and scale factors to test.
  • F0 (float): Driving force amplitude (default 1.0 N).

• Key Methods

  run() -> (best_scale, best_freq, best_error)
  plot_error_analysis()
  visualize()

  • Executes the full pipeline (skeleton extraction, frequency/scale sweep, error adjustment) and returns the optimal parameters.
  • Plots adjusted error vs frequency for each tested scale.
  • Displays: (1) raw RGB image, (2) normalized grayscale + skeleton overlay, (3) physical overlay of skeleton vs theoretical contours at best frequency.

Contributing

Feel free to open issues or submit pull requests to add features, fix bugs, or improve documentation. This project is licensed under GPL-3.0.