Equivalent loads for two-dimensional distributed anisotropic piezoelectric transducers with arbitrary shapes attached...

Area of Science:

• Solid Mechanics
• Materials Science
• Electrical Engineering

Background:

• Piezoelectric transducers are used in various applications, converting electrical energy to mechanical energy and vice versa.
• When attached to structures, these transducers exert forces, acting as equivalent loads.
• Understanding these loads is critical for accurate structural analysis and design.

Purpose of the Study:

• To derive general analytical expressions for equivalent loads generated by orthotropic piezoelectric actuators on thin plate structures.
• To provide a rigorous mathematical framework for analyzing transducer-structure interactions.
• To demonstrate the application of these expressions to simple geometric shapes.

Main Methods:

• Utilized Hamilton's principle for deriving the governing equations.
• Employed two distinct mathematical approaches: Green's theorem and the theory of distributions.
• Ensured consistency of results between the two mathematical methods.

Main Results:

• Developed general analytical expressions for the equivalent loads.
• Demonstrated that these loads depend on material properties and transducer contour.
• Provided specific examples for triangular, rectangular, and circular transducer shapes.

Conclusions:

• The derived analytical expressions offer a precise method for calculating equivalent loads from piezoelectric transducers.
• The findings are applicable to a wide range of orthotropic piezoelectric actuator and plate configurations.
• This work enhances the predictive capability for systems integrating piezoelectric transducers with host structures.