On the combination of asymptotic and direct approaches to the modeling of plates with piezoelectric actuators and sensors

摘要

We suggest a method for the mathematical modeling of the response of a thin structure with integrated piezoelectric sensors and actuators under mechanical and electrical loads. The plate with attached piezoelectric patches is considered as a two-dimensional material surface with mechanical and electrical degrees of freedom of particles. The model is complemented with an asymptotic analysis of the three-dimensional problem. For the equations of a layered piezoelectric plate, we seek those terms in the solution, which dominate as the thickness tends to zero. The results serve as a basis for the analysis of geometrically nonlinear shell structures as well as for model-based monitoring and optimal sensor and actuator placement.