In-plane P-SV waves from a piezoelectric strip actuator: exact versus effective boundary condition solutions

Area of Science:

• Solid Mechanics
• Materials Science
• Acoustics

Background:

• Piezoelectric actuators are crucial for various applications, often interacting with elastic substrates.
• Modeling these interactions accurately is essential for predicting device performance.
• Simplifying complex models can enhance computational efficiency.

Purpose of the Study:

• To develop and validate an effective boundary condition for a piezoelectric strip actuator on an elastic half-space.
• To compare the exact solution with the simplified effective boundary condition model.
• To assess the applicability of the effective boundary condition at low frequencies.

Main Methods:

• Exact analytical solution using Fourier series expansions for the piezoelectric strip and elastic half-space.
• Derivation of an effective boundary condition through series expansions in the piezoelectric strip's thickness.
• Numerical comparison of the exact and effective boundary condition models.

Main Results:

• The effective boundary condition provides a highly accurate approximation of the piezoelectric actuator's behavior at low frequencies.
• Excellent agreement was observed between the exact solution and the effective boundary condition model under low-frequency conditions.
• The effective boundary condition significantly simplifies the analysis, particularly for computational implementations.

Conclusions:

• The derived effective boundary condition is a valid and computationally efficient alternative to exact solutions for piezoelectric actuators on elastic half-spaces.
• This simplification is particularly beneficial for practical engineering applications and finite element method (FEM) analyses.
• The study validates a method for reducing model complexity while maintaining high accuracy in relevant scenarios.