Free Vibration Analysis of a Simply Supported Square Plate: A Comprehensive Guide

Free vibration analysis of a simply supported square plate is a fundamental concept in structural mechanics. This analysis involves determining the natural frequencies and mode shapes of the plate when it vibrates freely without any external force. The plate is considered simply supported, meaning its edges are free to rotate but constrained in displacement. This analysis is crucial for understanding the dynamic behavior of structures and ensuring their stability under various loading conditions.