Shape control of moderately thick piezoelectric beams

Area of Science:

• Mechanical Engineering
• Materials Science
• Control Systems

Background:

• Piezoelectric materials enable active shape control in structures.
• Controlling thick beams presents unique challenges compared to thin beams.
• Existing models often simplify beam behavior, limiting accuracy for thicker structures.

Purpose of the Study:

• To develop and validate a shape control method for thick, multi-layered piezoelectric beam structures.
• To investigate the influence of Timoshenko beam theory on piezoelectric shape control.
• To compare the proposed method's effectiveness against existing models and numerical simulations.

Main Methods:

• Derivation of governing equations for multi-layered beams using Timoshenko assumptions and piezoelectric constitutive relations.
• Explicit calculation of deflection curves for a piezoelectric cantilever under combined mechanical and electrical loading.
• Minimization of an objective function based on quadratic deflection to determine optimal control voltage distribution.

Main Results:

• The proposed shape control method for thick beams shows improved agreement with finite element analysis compared to thin beam theories (Bernoulli-Euler).
• Optimal voltage distributions for thick beams are similar but not identical to those for thin beams.
• Piezoelectric bimorphs may be harder to control than three-layer beams due to higher-order effects not included in the current theory.

Conclusions:

• The Timoshenko-based approach offers a more accurate model for thick piezoelectric beam shape control.
• The study highlights the importance of considering beam thickness and higher-order effects for precise control.
• Further research is needed to incorporate higher-order piezoelectric effects for enhanced control accuracy.