Nonlinear Combined Resonance of Thermo-Magneto-Electro-Elastic Cylindrical Shells

This study investigates the combined resonance phenomenon in magneto-electro-elastic (MEE) cylindrical shells under longitudinal and lateral excitations with thermal factors, addressing the complex interaction between mechanical, electrical, and magnetic fields in smart structures. The research aims to establish a theoretical framework for predicting resonance behaviors in energy harvesting and sensing applications. Using Maxwell’s equations and Hamilton’s principle, the governing equations for combined resonance are derived. The method of varying amplitude (MVA) is employed to acquire the combined resonance response across varying parameters. Furthermore, the Runge–Kutta method is applied to investigate the bifurcation and chaotic motion characteristics under different longitudinal and lateral excitation conditions. Key findings reveal the coupling effects of multi-physical fields on resonance frequencies, demonstrating quantitative agreement with prior studies. The results provide fundamental insights into the dynamic characteristics of MEE materials, offering theoretical support for optimizing their performance in adaptive engineering systems.