Developing Equations for Free Vibration Parameters of Bistable Composite Plates Using Multi-Objective Genetic...

Area of Science:

• Composite Materials Science
• Structural Mechanics
• Computational Engineering

Background:

• Bistable composite laminates possess two stable shapes, offering unique structural capabilities.
• Accurate modal analysis of these structures is computationally intensive with existing methods.
• Developing efficient analytical tools for natural frequency prediction is crucial.

Purpose of the Study:

• To propose a novel methodology for analyzing bistable composite structures.
• To derive analytical relations for predicting modal parameters (natural frequencies).
• To reduce the computational cost associated with modal analysis.

Main Methods:

• Integration of the Finite Element Method (FEM) with Multi-Objective Genetic Programming (MOGP).
• Utilizing FEM-generated data (length-to-width ratio, thickness) for MOGP model training.
• Developing four predictive formulas for free vibration parameters.

Main Results:

• Four accurate analytical formulas were derived using MOGP for predicting natural frequencies.
• The proposed formulas demonstrated excellent performance and reliability when validated against test data.
• Parametric and sensitivity analyses provided insights into input parameter trends and formula sensitivity.

Conclusions:

• The developed MOGP-based methodology provides accurate and computationally efficient analytical relations for bistable laminate natural frequencies.
• These explicit mathematical expressions can be generalized for other bistable laminates based on geometric dimensions.
• The findings were validated against experimental data and FEM outcomes, confirming the methodology's robustness.