A new magneto-mechanical coupling model was proposed for ferromagnetic materials under applied stress and in magnetic fields. The proposed model is based on the thermodynamic theory of ferromagnetic materials and Jiles–Atherton–Sablic (J–A–S) theory with respect to the effective magnetic field. Compared with the existing models for ferromagnetic materials, the prediction results of this model are more consistent with the existing experimental results, and the prediction accuracy has been significantly improved. This model can more accurately predict the nonlinear changes in the magnetization and magnetostriction under the applied stress and magnetic field. In addition, the effects of applied stress and magnetic field on magnetization and magnetostriction of ferromagnetic materials are analyzed on the basis of magnetic domain theory. In conclusion, the proposed model can fully describe the effect of applied stress on magnetization, magnetic permeability, and magnetostrictive strain, and the effects of applied stress and magnetic field on total magnetostrictive strain (i.e., the ΔE effect); furthermore, it sufficiently reflect the nonlinear coupling properties of the magnetic field, magnetization, and magnetostriction for ferromagnetic materials under applied stress and in magnetic fields.

In this paper, the Haar wavelet discretization method (HWDM) is proposed for the calculation of natural frequency of the laminated composite conical-cylindrical coupled shells. The displacement components of the system are set by the first order shear deformation shell theory (FSDST), and all the displacement functions of conical and cylindrical shells including boundary conditions are obtained by the Haar wavelet and its integrals. The Hamilton’s principle is applied to the constitution equation and the artificial spring technique is introduced to generalize the boundary and continuity conditions of the coupled structure. The convergence and accuracy of the proposed method are validated by comparing with the results obtained from the previous works and finite element analysis, and the proposed method shows high accuracy, reliability and good convergence in both individual structure and coupled structure. Using the proposed method, in the laminated composite conical–cylindrical coupled shell with any boundary condition, new numerical results on the natural frequency are obtained along with the parameter studies, and these results can provide the referential data for the following research in this field.