Vibration Analysis Of Magneto-electro-elasticcircular Plate

Magneto-electro-elastic material is a novel functional material with magnetic,electric,elastic field coupling performance.It is composed of piezoelectric materials and magnetic materials.Due to piezoelectric,piezomagneto,magneto-electric coupling effects and excellent magneto-electric properties,magneto-electro-elastic materials in intelligent and microelectromechanical system and other related engineering field has a good application potential.The engineering practice of magneto–electro–elasticproblems associated with vibration,therefore magneto-electro-elastic vibration problem is more and more aroused people's concern.In this paper,the transverse free vibration and in-plane free vibration of magneto-electro-elasticcircular plate was analyzed.According to the principle of simple to complex,easy and difficult,first of all,the vibration characteristics of electro-elastic circular plateunder the action ofelastic field and electric field,and the vibration characteristics of magneto-elastic circular plates under the action ofelasticfield and magnetic fieldwere studiedrespectively.Further the vibration characteristicsof magneto-electro-elastic circular plate under elastic field,electric field and magnetic fieldwas studied.The Hamilton principle of electro-elastic body,magneto-elastic body and magneto-electro-elastic body were established respectively by the variable integral method.According to therelationship between the generalized force andthe generalized displacement,the partial differential equations of circular plate of the free vibration transform into a partial differential equation about space coordinatesand differential equation about time coordinates by using the method of separation of variables.According to the different boundary conditions,circular plate Eigen solution of free vibration wasobtained,further natural vibration frequencies of circular plate was obtained.Finally,according to the Eigen solution,modal superposition method,the orthogonality of the vibration mode function and initial conditions,the free vibration response of thecircular plate was analyzed.The research on free vibration of magneto-electro-elastic circular platehas certain reference value to development of magneto–electro–elastic theory and engineering application.