Analysis of electromechanical coupling responses of piezoelectric nanobeams under multi-physical field coupling

This study established a piezoelectric nanobeam model that considers surface effects, the action of a magnetic field, high-order electric fields, and the constraints of the Winkler–Pasternak linear elastic foundation, and then, the electromechanical behavior of this model was systematically analyzed. Based on the Hamilton variational principle, the governing equations and boundary conditions were derived. By using the Fourier series expansion method, the analytical solutions for deflection, rotation, and polarization intensity were obtained. Through numerical analysis, the influence patterns of various parameters on the nanobeam’s response were revealed. The results indicate that the Winkler parameter, Pasternak parameter, and surface elastic constant significantly enhance the structural stiffness and suppress deformation. Residual stress has a bidirectional regulatory effect on the mechanical–electrical response. The magnetic field can effectively control the structural deformation and polarization intensity via the Lorentz force. Although the surface piezoelectric coefficient has a relatively minor influence, it still holds engineering value in high-precision regulation. This research provides a theoretical basis for the design and performance optimization of micro-nano piezoelectric devices under complex physical fields.