A unified analytic solution approach to static bending and free vibration problems of rectangular thin plates

Area of Science:

• Solid Mechanics
• Structural Analysis
• Applied Mathematics

Background:

• Analyzing static bending and free vibrations of thin plates is crucial in structural engineering.
• Existing methods often require trial solutions, limiting their applicability and accuracy.
• Corner-supported plates present unique challenges in mechanical analysis.

Purpose of the Study:

• To develop a unified analytic solution for static bending and free vibration of rectangular thin plates.
• To apply this method specifically to corner-supported plate configurations.
• To establish a novel, accurate, and widely applicable analytical approach.

Main Methods:

• A symplectic superposition method is employed to transform plate problems into a Hamiltonian system.
• The solution is derived through a rigorous step-by-step process.
• No trial solutions are required, distinguishing it from conventional techniques.

Main Results:

• Accurate analytical solutions for static bending and free vibration of rectangular thin plates were obtained.
• The method was successfully applied to corner-supported plate scenarios.
• Numerical examples validated the accuracy and effectiveness of the developed approach.

Conclusions:

• The symplectic superposition method provides a powerful and versatile tool for analyzing thin plate problems.
• This approach offers a benchmark for accuracy and applicability in structural mechanics.
• The method's independence from trial solutions enhances its utility for diverse plate analysis scenarios.