Three-Dimensional Vibration Analysis of Laminated Composite Rectangular Plate with Cutouts.

Area of Science:

• Solid Mechanics
• Composite Materials
• Structural Analysis

Background:

• Laminated composite plates are crucial in engineering applications.
• Analyzing plates with cutouts presents significant challenges.
• Existing methods may lack the precision for complex geometries.

Purpose of the Study:

• To develop an exact three-dimensional (3D) analysis model for laminated composite rectangular plates with and without cutouts.
• To provide a reliable analytical solution based on three-dimensional elasticity theory.
• To investigate the vibration characteristics of these plates.

Main Methods:

• Utilizing three-dimensional elasticity theory.
• Employing Hamilton's principle and the Rayleigh-Ritz procedure.
• Using standard 3D trigonometric cosine Fourier series and auxiliary Fourier series as admissible functions.
• Incorporating cutout effects by subtracting their energies from the total plate energy.

Main Results:

• An exact 3D analytical solution for laminated composite plates with cutouts was established.
• Numerical results demonstrated good agreement with existing literature and finite element analysis, validating the method's effectiveness.
• The influence of key parameters on vibration characteristics was analyzed, yielding non-dimensional frequency parameters.

Conclusions:

• The proposed method provides an accurate and reliable approach for analyzing laminated composite plates with cutouts.
• The obtained non-dimensional frequency parameters serve as valuable benchmark data for future research in composite structure analysis.
• This work contributes to a deeper understanding of the vibrational behavior of composite plates with complex features.