The Nonlinear Vibration Analysis Of Magneto-electro-elastic Thin Plate

Now, the magneto-electro-elastic materials have been applied in engineeringwidely, which are often used in the production of sensors, converters, actuators,electro-magnetic storage elements and other equipments. In engineering practice, weall know the thin plate is one of the most common elements in engineeringstructures, usually work in mechanic field, electro-magneticfield and other field. Thedynamic properties of the system have important influence on the structural safety inengineering.Therefore, the study of dynamics problem of magneto-electro-elastic thinplate in multifield coupling field has been important theory significance and practicalapplication value.We consider a magneto-electro-elastic rectangular thin plate. The nonlinearprincipal resonance, bifurcation characteristics and chaotic characteristics are studiedwhen the system is in the action of the force-electric-magnetic coupling field. Themain research contents are as follows:This paper introduces the characteristics of magneto-electro-elastic materialsfirstly. The research status at home and abroad, the mechanics theory knowledge andthe expression of electromagnetic forces, and the research methods in this paper areintroduced.Then，according to magneto-electro-elastic thin plates, considering the largedeflection plate theory and the geometric nonlinearity, the mathematical model of thenonlinear undamped principal resonance is established. Making use of the improvedL-P method, the nonlinear undamped principal resonance problem is solved, theamplitude-frequency response equation of steady state is obtained. Furthermore, theinfluence of the material property, plate thickness, and the mechanical excitation onthe nonlinear principal resonance behaviour of the magnetoelastic thin plates is analyzed.Finally, the transversely isotropic magneto-electro-elastic rectangular simplysupported thin plate as the research object, from the theory of constitutive equationand the large deflection magneto-electro-elastic materials, combined with the dynamicbalance equation, the damped Duffing equation is obtained. Then we can get thenondimensional governing equation of the plate system. Using the Melnikovmethod, the criterion of the Smale horseshoe chaos is also acquired. Furthermore, thechaos and bifurcation diagram is numerically simulated with Matlab.The results show that the materials of magneto-electro-elastic thin plate effect tothe system nonlinear principal resonance, nonlinear bifurcation and chaos when it isin the force-electric-magnetic coupling field. The article research results can guide themagneto-electro-elastic materials in the engineering application better.