Nonlinear Resonance Analysis Of Thin Plate And Corrugated Sandwich Structure Under Thermal-Electro-Magneto-Elastic Coupling

With the progress of society and the development of science and technology,more and more new materials have appeared.These materials have the ability to convert energy in various physical fields,such as the piezoelectric effect,which converts force and electricity into each other,the magnetostrictive effect,which converts magnetic field into elastic force,and the Joule effect,which converts electric energy into heat.New materials need to work in a variety of complex working conditions,including thermal field,electric field,magnetic field and elastic field,etc.,and materials will be subjected to coupling effects of various fields,resulting in failure.Therefore,the research on multi-field coupling is becoming more and more important.In this paper,the nonlinear vibration of rectangular thin plate under thermal-electro-magneto-elastic coupling is studied,and the theory is extended to study the nonlinear superharmonic subharmonic resonance and resonance of corrugated sandwich structure under thermal-electro-magneto-elastic coupling.Firstly,the nonlinear primary resonance of a rectangular thin plate under the coupling of thermal field,electric field,magnetic field and force physical fields is studied.The nonlinear governing equations of the model are obtained according to von Karman’s large deflection theory and Hamiltonian principle.The first order approximate response and amplitude-frequency function of the system are obtained by harmonic balance method.The analysis shows that the model shows hard nonlinearity and jumping.The influence of different temperature differences,damping,plate thickness,magnetic field,mode and length-width ratio on the main resonance was discussed,and the amplitude-frequency response curve was obtained,which was numerically verified by MATLAB’s Runge-Kutta method.The rusults show that the temperature difference is the biggest factor affecting the main resonance of rectangular thin plate,and the magnetic field is the least factor affecting the main resonance of rectangular thin plate,which is caused by the difference of the material’s piezomagnetic coefficient and thermal-elastic coupling coefficient.Secondly,the mechanical constitutive of corrugated sandwich structure is analyzed,which is combined with the constitutive constitutive under the action of four fields of thin plate thermoelectric elastic magnetic field.The equivalent constitutive constitutive of wavy plate sandwich structure under the action of multiple physical fields of thermal-electromagnetic elastic field is obtained,and the nonlinear vibration equation of corrugated sandwich structure is derived.Lastly,the nonlinear vibration equation is dimensionless processed,and the multi-scale method is used to solve it,and the first-order approximate solution of superharmonic and subharmonic resonance and amplitude-frequency characteristic curve are obtained.The sufficient conditions for the existence of subharmonic resonance are obtained by analyzing its stability.The vibration characteristics of the corrugated sandwich structure system are numerically simulated by matlab.