A Multi-Parameter Perturbation Solution for Functionally Graded Piezoelectric Cantilever Beams under Combined Loads.

Area of Science:

• Mechanical Engineering
• Materials Science
• Electrical Engineering

Background:

• Functionally graded piezoelectric materials offer unique electromechanical properties.
• Analyzing their behavior under combined loads presents complex challenges.
• Existing models may not fully capture the intricate interactions of piezoelectric effects.

Purpose of the Study:

• To develop a novel multi-parameter perturbation method for analyzing functionally graded piezoelectric cantilever beams.
• To investigate the influence of piezoelectric coefficients on beam behavior.
• To provide a new approach for solving related nonlinear differential equations.

Main Methods:

• Derivation of basic equations for Airy stress and electric potential functions.
• Expansion of functions with respect to three piezoelectric coefficients as perturbation parameters.
• Decoupling of equations to obtain a multi-parameter perturbation solution.

Main Results:

• The study successfully decoupled the governing equations using the perturbation method.
• Clear insights into how piezoelectric effects influence beam mechanics were obtained.
• Numerical examples demonstrated variations in stress, displacement, and electric displacement.

Conclusions:

• The functionally graded piezoelectric cantilever beam can be treated as a perturbed system.
• The multi-parameter perturbation method offers a viable approach for analyzing such systems.
• This method provides a new strategy for solving similar nonlinear differential equations.