Research On Dynamic Buckling And Chaos Behavior Of Functionally Graded Materials Plate

Plates are important original engineering structure and widely used in civil engineering,mechanical engineering,aerospace,and biomedical engineering.It has significant research significance.Therefore,the research on the dynamic buckling of plates has attracted the attention of researchers.Functionally graded material is a new type of composite material composed of a variety of materials,with smooth and continuous characteristics between different materials,which can effectively avoid the stress concentration and delamination,cracking and other phenomena caused by the microscopic heterogeneity of the material properties of traditional composite materials.Because of its superior mechanical properties,it can meet the normal work of the structural unit under the extreme environment and has attracted much attention.Therefore,the study of dynamic buckling of functionally graded material plates has important application prospects in many industrial sectors.Based on this,this article does the following work:1.The research status of dynamic buckling of functionally graded material plates at home and abroad is briefly described.The research methods for dynamic buckling of functionally graded material plates are summarized.2.Based on the characteristics of continuous gradients of physical properties of functionally graded materials,according to the power law distribution,equal strain assumptions,and classical elastic theory and first-order shearing theory,the Hamiltonian principle is used to obtain the functional equations of the functionally graded material plate considering rotational inertia.Analytic methods are used to obtain analytical solution and buckling modal solutions for dynamic buckling critical loads.Programming calculations are performed to discuss the influence of material properties,gradient index,geometric dimensions,and dynamic buckling mode order on critical buckling loads of functionally graded material plates.3.According to the spatial gradient properties of the functionally graded materials and the laws of thermodynamics,the expression of the non-uniform temperature field of the functionally graded material plate when the temperature changes in the upper and lower surface layers is derived.Matrix expression is used to give the internal force and internal torque expression of the functionally graded material plate under the influence of non-uniform temperature field.Using Hamilton principle,the control equation of functionally graded material plate under non-uniform temperature field is obtained.The equation was solved using the De Moivre formula and the Ritz method,and compared with the result of the separation variable method.Programmatic calculations discuss the effects of non-uniform temperature field,dynamic buckling mode order,gradient index,and geometric dimensions on the critical dynamic buckling loads of functionally graded material plates.4.According to von-karman plate deflection stress and strain,apply periodic loads.The expression of the nonlinear internal force and internal torque of the functionally graded material plate is given by matrix expression.Using Hamilton principle and Galertkin's principle,the Duffing equations of functionally graded material circular arc plates are derived from vertical and horizontal excitations and converted into spatial autonomous equations.Solve homoclinic orbits and heteroclinic orbits of phase planes,and obtain homoclinic and heteroclinic orbital thresholds based on the Melnikov principle.The chaotic behavior is further described and determined by the system's bifurcation diagram,displacement history curve,phase plan,Poincaré map,and power spectrum.