Plate Vibration Analysis

📌 Overview

This repository contains a C++ Finite Element Method (FEM) solver for performing modal analysis of plate (shell) structures.

The implementation focuses on classical plate theory and standard FEM formulations, including:

• Kirchhoff plate theory
• CTRIA3: 3-node triangular element
  • 9 DOF formulation
  • Based on Cheung, King, and Zienkiewicz (CKZ)
• CQUAD4 (MITC4): 4-node quadrilateral element

The solver computes natural frequencies and mode shapes using ARPACK, typically extracting the lowest 20 modes.

The input model format follows the NASTRAN bulk data format, and example models are provided in the repository.

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🚀 Features

• ✅ Finite element modal analysis of plate/shell structures
• ✅ Support for triangular and quadrilateral elements
• ✅ NASTRAN-style input file support
• ✅ Interactive visualization using OpenGL

🎮 Visualization Controls

• Rotate → Ctrl + Left Mouse Drag
• Pan → Ctrl + Right Mouse Drag
• Zoom → Ctrl + Mouse Scroll
• Zoom to Fit → Ctrl + F

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🖥️ Visualization

• OpenGL 3.3-based rendering
• Mode shape animation and deformation visualization
• GUI powered by ImGui

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📦 Dependencies

Make sure the following libraries are installed:

• C++17 (or higher) compatible compiler
• Eigen – Linear algebra
• GLFW – Window and input handling
• GLEW – OpenGL extension loader
• ImGui – GUI framework
• ARPACK – Eigenvalue solver

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📂 Input Format

• NASTRAN .bdf style input files
• Supports:
  • GRID (nodes)
  • CTRIA3 elements
  • CQUAD4 elements
  • Boundary conditions (constraints)

Example files are available in the repository.

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📊 Examples

Example 1: Circular Plate (Mixed Boundary)

• Half edge: Pinned support
• Half edge: Free boundary

First four mode shapes are shown below:

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Example 2: Circular Dome

• Edge: Pinned support

Selected vibration modes:

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⚙️ Build Instructions

1. Clone the repository:

git clone https://github.com/Samson-Mano/Plate_Vibration_Analysis.git
cd Plate_Vibration_Analysis