Physics-informed neural networks for shunted piezoelectric systems

Shunted piezoelectric systems are often used for vibration suppression in smart structures. Multiphysics modeling using finite elements leads to coupled partial differential equations reflecting the strong electromechanical interaction. In the present contribution, a multi-physics-informed neural network (multi-PINN) is proposed, to solve for the first time the direct electromechanical vibration suppression problem with the shunted circuit. The mathematical framework to convert the electromechanical problem to the appropriate PINN formulation is analytically provided. Static and dynamic analysis using PINN models for a cantilever piezoelectric beam are presented. The problem of vibration reduction by means of a resonant shunt is also studied. To facilitate the solution of the dynamic problem, Galerkin’s projections are applied to discretize the dynamic model with respect to the spatial variable. A time partitioning approach is also proposed to decrease the computational cost of the dynamic problem. The obtained system of ordinary differential equations (ODE) is solved by means of the multi-PINN to accurately predict the dynamic response to a principal mode resonance excitation. The proposed method is validated using finite element analysis and MATLAB solutions. Numerical results show the efficiency and robustness of the proposed techniques.