Bifurcation And Chaos Of BNNT/FG-CNT Reinforced Plate And Shell Under Electro-Thermo-Mechanical Loading

The development of industry promotes the research and development of materials,and reinforced materials are also one of them.There are reinforcement materials in various industries.Such as aerospace,aviation,navigation,transportation,construction and other large industries,as well as precision industries such as medical and nano-biomaterials.Development creates demand,and in certain areas of special conditions,more stringent requirements are placed on the properties of materials.Both Boron nitrogen nanotubes(BNNTs)/carbon nanotubes(CNTs)have good mechanical properties,piezoelectric properties,and mechanical properties,and both have good thermal conductivity and semiconductor properties.Therefore,BNNT/FG-CNT reinforced materials have more extensive application prospects than other traditional materials in the fields of physics,chemistry and machinery.In this regard,this article will study the bifurcation and chaos of the BNNT/FG-CNT reinforced plate and shell under the electric-thermal-mechanical coupled load.In the second chapter,the basic concepts of bifurcation and chaos are briefly introduced,the conditions for the system enters into bifurcation and chaos conditions,and the basic method of analyzing chaos is introduced.In the third chapter,By employing piezoelectric theory with thermal effects and von Kármán nonlinear plate theory,the constitutive equations of the boron nitride nanotube(BNNT)-reinforced piezoelectric plate under complex load are set up.The material constants are calculated by using the "xy" rectangle model.Referring to the Reissner variational principle,the nonlinear motion governing equations of the structure are deduced and resolved by the fourth-order Runge-Kutta method.The numerical results show that decreasing voltage and temperature and increasing volume ratio can delay the chaotic or multiple periodic motions of BNNT-reinforced piezoelectric plates.In the fourth chapter,Governing equations of FG-CNTRC shells were derived according to the theory of von-Kármán nonlinear shell and PL with thermal.the material constants are calculated by mixture rule.Next,the governing equations were transformed into second order nonlinear ordinary differential equations(SNODE)with cubic terms through Galerkin procedure and further into first order nonlinear ordinary differential equations(FNODE)through introducing additional state variables.Complex system dynamic behavior was qualitatively examined using fourth order Runge-Kutta method.The numerical results show that decreasing voltage and temperature and increasing volume ratio can delay the chaotic or multiple periodic motions of FG-CNTRC shells with PL,thus improving the dynamic stability of the structure.