The Nonlinear Dynamic Response Analyses Of Functionally Graded Materials Circular Plates

Functionally graded materials(FGM) composed of two or more materials and thematerial parameters change continuously along a certain direction. FGMs achievedthe purpose of optimizing the structure and avoid the stress concentration,delamination and so on. FGM is widely used in aerospace, nuclear reactors, internalcombustion engines and other fields. However, these FGM structures, often undersevere conditions, would exhibit the different property within the different conditions.In this paper, as the research of the functionally graded circular plates, assumingthe material properties of FGM circular plates vary through the thickness, consideringthe effect of the temperature field, electric field and geometry nonlinear factors. Atfirstly, applying the theory of Hamilton or minmum total energy states establishedfunctionally graded circular plate’s motion control equations; Secondly, based on theFirst-order shear deformation Mindlin plate theory or Kirchhoff theory, functionallygraded circular plate’s motion control equations could be rewritten for displacement;Then utilizing the the finite difference method, the orthotropic collocation pointmethod, the Galerkin method and Newmark method to discretize the variablefunctions in space domain and time domain, respectively; Lastly, the whole problemis solved by the iterative method. Through the above method, solved the impactingnonlinear dynamic response of functionally graded material circular plates, nonlineardynamic response of the viscoelastic functionally graded circular plates, the nonlineardynamic response of functionally graded circular plates in the thermal environmentand nonlinear dynamic response of piezoelectric functionally graded circular plates.In the numerical examples, discussed the effects of the material composition, thegeometrical parameters and the outside environment on the nonlinear dynamicresponse of the functionally graded material circular plates.This paper will enrich and develop smart materials and structural mechanics,nonlinear dynamic mechanics and thermomechanical coupling, supplys the theoreticalbasis for security assessment and optimum design, and is important to engineeringapplications.