Nonlinear Waves In One-dimensional Magnetostrictive Material Structures Based On Temperature Effects

With the development of science and technology,science has also entered the field of nonlinear science.Solitary waves,chaos,and fractal reveal nature's nonlinearity.Magnetostrictive materials are widely used in aerospace,smart structures,precision sensors and other fields due to their excellent properties.Due to the influence of complex environmental conditions,it is easy to cause its incomprehensible function failure phenomenon,which is inseparable from the transmission of nonlinear waves.Therefore,this paper studies the longitudinal wave and bending wave in the next-dimensional magnetostrictive material structure based on the multiphysics coupling effect.The main research work is as follows:The first part constructs a nonlinear model to study nonlinear longitudinal wave in an infinite circular magnetostrictive rod.Based on the constitutive equation of temperature effect,geometric nonlinearity and Poisson's ratio effect are introduced,combined with Hamilton's principle and Euler equation,the nonlinear longitudinal wave equation is obtained.Solitary wave solution,non-topological bell-type soliton and singular periodic solutions of the longitudinal wave equation are obtained by the F-expansion method.Numerical analysis results show that the increase of the magnetic field intensity or temperature will reduce the solitary wave's propagation velocity.As the wave velocity ratio increases,the wave amplitude gradually increases;when the coupled physics parameter and the wave velocity ratio are constant,the increase of the dispersion parameter will make the wavelength longer.The reduced perturbation method is used to deal with the nonlinear longitudinal wave motion equation in an infinite circular magnetostrictive rod.The standard Kd V equation is obtained,and the solitary wave solution and the two-soliton solution are constructed.The 3D graphics of the solitary wave solution and the two-soliton solution are given by numerical simulation.The change graphics of solitary wave solution with slow variable time and the dynamic process graphics of double soliton solution with slow variable time are given.The dynamic behavior of the two-soliton solution in the magnetostrictive rod shows nonlinear superposition and elastic collision characteristics.Therefore,the phenomenon of functional failure of solid materials caused by nonlinear waves is better explained.The second part studies bending waves in infinite rectangular magnetostrictive laminated beam.Based on the basic assumptions in elastic mechanics,finite deformation theory,and Bernoulli-Euler beam theory,the influence of rotational inertia under the coupling effect of temperature field and the magnetic field is considered,by using Hamilton's principle and Euler equation,the nonlinear bending wave equations of the infinite rectangular magnetostrictive laminated beam is derived.Using the Jacobi elliptic function method to solve the bending wave equation,the solitary wave and shock wave solutions of the wave equation are obtained and numerically simulated.The results show: whether it is a shock wave or a solitary wave,the maximum amplitude is negatively correlated with the thickness of the magnetostrictive layer.Both shock waves and solitary waves decrease in amplitude with increasing temperature or increasing wave velocity.For shock waves,the wavenumber decreases with the increase of the thickness of the magnetostrictive layer and then increases with the increase of the thickness of the magnetostrictive layer.The solitary wave increases with the thickness of the magnetostrictive layer.The nonlinear bending wave motion equation in the infinite rectangular magnetostrictive laminated beam is processed by the reduction perturbation method,and the standard nonlinear Schr(?)dinger equation is obtained,and the strange wave solution of the equation is constructed by the exponential function method.The three-dimensional image of the strange wave solution is obtained through numerical analysis,which theoretically proves that there may be strange waves in the infinite magnetostrictive laminated beam;numerical simulations also show that the increase of temperature leads to the increase of the pointed crest and the rounded trough.Because of the characteristics of energy time and space focusing,strange waves occupy an important role in the dynamic design of laminated beams.