Study On Nonlinear Waves In Magnetoelectro-elastic Structures Under Multi-physical Field Coupling

With the continuous development of natural science,many scholars are very interested in nonlinear science,and many fields have conducted in-depth research on nonlinear science.Magnetoelectro-elastic structure has coupling properties of magnetic field,electric field and elastic field,which makes it widely used in aerospace,sensor and other fields.These structures usually work in complex environments where temperature changes can have a big effect on the structure.The normal operation of these devices is closely related to the propagation of nonlinear waves.Therefore,in this paper,under the action of multi-physical field coupling,solitary waves of infinite length magneto-electro-elastic round rod and bending waves of infinite length rectangular magneto electro-elastic laminated beam are studied.The main contents are as follows:In the first part,taking the infinite length magnetoelectro-elastic circular rod as the research object,the constitutive relation of the transverse isotropic magnetoelectro-elastic circular rod was established.The wave equation of the infinite length magnetoelectro-elastic circular rod was derived by using the nonlinear elastic displacement relation and the effective Poisson’s ratio,combining the Hamilton’s principle and Euler equation.The wave equation is solved by using the extended Tanh expansion method,and the exact solitary wave solution of the equation is obtained.Matlab simulation was used to obtain the magnetic field intensity of 50 KA/m,100 KA/m and 150 KA/m,electric field intensity of50 KV/m,100 KV/m and 150 KV/m,temperature difference of 20℃,60℃and 100℃and radius of 0.02 m,0.05 m and 0.08 m waveforms.The numerical results show that the wave velocity decreases with the increase of magnetic field intensity,electric field intensity and temperature difference.With the rod radius increases,the dispersion parameters and the wavelength also increase.In the second part,the nonlinear bending wave equation of an infinitely long rectangular magnetoelectro-elastic laminated beam is derived by Bernoulli-Euler beam model,some basic assumptions and finite deformation theory in the beam model,and by means of Hamilton’s principle and Euler equation.The shock wave and solitary wave solutions of the curved wave equation are obtained by using F expansion method.The numerical simulation of shock wave solution and solitary wave solution is carried out by Matlab,and the relationship between wave velocity d₀ and magnetoelectric layer thickness h_m is obtained.It is found that the relationship between wave velocity d₀ and magnetoelectric layer thickness h_m is inversely proportional.By analyzing the relationship diagram between amplitude and magnetoelectric layer thickness h_m,it can be seen that amplitude and magnetoelectric layer thickness h_m are directly proportional.The analysis of the relationship diagram between wave number and magnetoelectric layer thickness h_mshows that with the increase of magnetoelectric layer thickness h_m,wave number first decreases and then increases.For shock wave,when the wave velocity c is 400 m/s,700 m/s and 1000 m/s respectively,the amplitude and wave number will increase with the increase of wave velocity;when the temperature difference is 20℃,60℃and 100℃,the amplitude and wave number will also decrease with the increase of temperature difference.For solitary waves,when the wave velocity c is 7000 m/s,8000 m/s and 9000 m/s respectively,the amplitude and wave number will increase with the increase of wave velocity;when the temperature difference is 20℃,60℃and 100℃respectively,the amplitude will decrease and the wave number will decrease with the increase of temperature difference.By using reduced perturbation method,the bending wave equation of a rectangular section magneto electroelastic laminated beam is transformed into a standard nonlinear Schrodinger equation.Bright and dark soliton solutions are obtained by some methods.The relationship among dispersion coefficient,frequency,group velocity and magnetoelectric layer thickness under different conditions is obtained by numerical simulation with Matlab.