Wavelet-based electromechanical computational model for the analysis of composite beams with piezoelectric actuators and sensors

Abstract In this work, a new numerical model is presented, addressing the challenge of accurately modeling high-frequency transient responses in composite beams with piezoelectric sensors and actuators. Simulations like these are a key aspect of the effective design of wave-based structural health monitoring and impact detection systems. Specifically, Daubechies scaling functions are utilized as basis functions for the spatial approximation of both mechanical and electric variables, extended by the integration of piezoelectric kinematic assumptions, enabling the consistent prediction of electromechanical coupling and the exact modeling of structures with physically modeled actuators and sensors. The beam’s mechanical behavior is described using first-order shear deformation theory, while the electric potential through the thickness is captured via a linear layerwise approximation. The developed model is validated and compared with finite element models under static and dynamic simulations. Interestingly, the presented method exhibits remarkably high convergence rates and requires substantially fewer grid points for convergence compared to finite element models. The findings demonstrate the potential of the proposed wavelet-based approach to enable the development of efficient and accurate models for high-frequency wave propagation simulations, which can enhance the transient dynamic analysis of smart electromechanical systems.