In-Plane Vibration Analysis of Rectangular Plates with Elastically Restrained Boundaries Using Differential...

Area of Science:

• Solid Mechanics
• Computational Mechanics
• Materials Science

Background:

• Analyzing the vibrational behavior of advanced materials like Functionally Graded Materials (FGM) is crucial for structural integrity.
• Existing methods for plate vibration analysis can be computationally intensive, especially with complex boundary conditions.

Purpose of the Study:

• To develop an efficient numerical approach for the in-plane free vibration analysis of rectangular FGM plates.
• To investigate the influence of material properties and boundary conditions on the vibrational characteristics of FGM plates.

Main Methods:

• Utilizing a variational weak form based on 2D elastic theory and variational principles.
• Employing the differential quadrature method (DQM) and Taylor series for discretizing differential and integral operators.
• Applying matrix elementary transformation to derive the generalized eigenvalue problem for free vibration analysis.

Main Results:

• The proposed method effectively discretizes dynamics equations from a weak formulation, avoiding complex derivative transformations.
• The study successfully derives the generalized eigenvalue problem for FGM rectangular plates.
• The impact of gradient parameter, aspect ratio, and elastic constraints on dimensionless frequencies is examined.

Conclusions:

• The developed numerical approach offers an efficient and accurate method for analyzing the in-plane vibrations of FGM rectangular plates.
• The findings provide insights into how material gradients and boundary conditions affect the modal properties of FGM plates, essential for design and application.