# Mathematical Modeling and Experimental Investigation of the Dynamic Response for an Annular Circular Plate Made of Glass/Polyester Composite Under Different Boundary Conditions

## TL;DR

This paper develops and validates a mathematical model for the dynamic behavior of a glass/polyester composite annular plate under different boundary conditions.

## Contribution

A new mathematical model for dynamic response of annular composite plates is derived and experimentally validated.

## Key findings

- Theoretical and experimental deflections showed good agreement, especially under built-in boundary conditions.
- Higher natural frequency was observed under built-in support due to increased shear stresses and moments.
- The experimental spectrum for built-in conditions was higher than for other boundary conditions.

## Abstract

Fiber-reinforced elastic laminated composites are extensively used in several domains owing to their high specific stiffness and strength and low specific density. Several studies were performed to ascertain the factors that affect the composite plates' dynamic properties. This study aims to derive a mathematical model for the dynamic response of the processed composite material in the form of an annular circular shape made of polyester/E-glass composite. The mathematical model was developed based on modified classical annular circular plate theory under dynamic loading, and all its formulas were solved using MATLAB 2023. The mathematical model was also verified with real experimental work involving the vibration test of the fabricated composite plate. The composite plate was processed by reinforcing the polyester matrix with E-glass fibers with a 50% volume fraction each by using the handy lay-up method. After fabrication, the composite plate was tested with a universal vibration tester, where the plate was impacted and released to free vibration, and the deflection was measured experimentally to compare it with the theoretical value calculated from the derived model. The plate was tested under two boundary conditions, namely, simply and built-in supported. The findings show good agreement between theoretical and experimental plate deflections at different angles, particularly at built-in supported boundary conditions. Also, a higher natural frequency was recorded at this condition compared to others, and this may be ascribed to the higher shear stresses involved due to large moments at the ends along with supporting. Meanwhile, the real experimental spectrum of the built-in condition was higher than others, as the sig view curve revealed.