Abstract
The dynamic response study on thermo-magneto-elastic behavior of shallow conical shell in a time-dependent magnetic field is investigated, and the dynamic responses of displacement of shallow conical shell under mechanical loads, electromagnetic fields and temperature field coupling are analyzed. Based on Maxwell’s equations, heat conduction equation and nonlinear equations of classical plates and shells, the nonlinear dynamic response governing equations are derived. The electromagnetic field and temperature field equations are solved using variable separating technique, the nonlinear elastic field equations are solved by Galerkin method. The variation of temperature, magnetic field intensity and displacement with time under the coupling effect of the applied magnetic field and the surface uniform load were obtained. The influence of frequency of the applied magnetic field on the displacement wave forms is discussed.
Highlights
Thermo-magneto-elasticity is a new subject to study the strength, stiffness and stability of elastic components under the combined action of electromagnetic, temperature and deformation
The electromagnetic field and temperature field equations are solved using variable separating technique, the nonlinear elastic field equations are solved by Galerkin method
Considering shallow conical shell with thickness h, radium a and pyramid dip φ, whose neuter plane is showed in Figure 1 Assume that shallow conical shell in alternating magnetic field works under axisymmetric state, whose outer surface is subjected to normal stable mechanical load
Summary
Thermo-magneto-elasticity is a new subject to study the strength, stiffness and stability of elastic components under the combined action of electromagnetic, temperature and deformation. The thermo-magneto-elasticity includes heat conduction theory, classical elasticity theory and electromagnetic theory These theories are applied to solve the coupling problems of temperature field, electromagnetic. The elastic elements and structures in high energy-varying magnetic field under mechanical loads can produce various stresses. In addition to mechanical stress, there are the thermal stress generated by the induced eddy current losses, and the magnetic stress generated by the Lorentz force These stresses affect each other, and to be high nonlinear. It is very difficult to study the nonlinear dynamic response of a shallow conical shell in an alternating magnetic field and subjected to mechanical loads. Based on nonlinear equations of classical plates and shells, considering the coupling effect of the Lorentz force and temperature stress, nonlinear magneto-elastic heat equations of shallow conical shell are deduced.
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