Analysis Of Nonlinear Vibration For Carbon Nanotube Composite Plates Based On Various Higher-order Plate Theories

Carbon nanotube reinforced composites(CNTRCs)have been regarded as one of the advanced inhomogeneous composite materials with great application potential in many fields such as physics,chemistry,information technology,power generators,aerospace vehicles and so on.Investigations on nonlinear static and dynamic characteristics of CNTRC plate structures have been,therefore,receiving considerably more attention in recent years due to their prime importance in both theoretical and practical aspects.In this paper,the nonlinear dynamic characteristics of CNTRCs are studied.Firstly,the research background,research status,research significance and development trend of CNTRCs are summarized.For the CNTRC plates,uniformly distributed(Type UD)and functionally graded(Type ?)reinforcements are considered.Intrudcing the physical properties parameters of CNTRCs,based on the continuum theory and von Karman-type geometric nonlinearity theory,a set of unified nonlinear dynamics governing equations of the CNTRC rectangular plate considering different higher-order shear deformation function forms are established by using Hamilton's principle.Then,the single-mode nonlinear ordinary differential equations of a simply supported CNTRC rectangular plate are deduced by applying Bobnov-Galerkin discretization method.With the dimensionless parameters being introduced,the dimensionless nonlinear transversal vibration governing equation is gotten and solved by using the harmonic balance method.Under several parameters,the nonlinear free vibration behaviors of CNTRC plates with various higher-order shear deformation plate theories are analyzed comparatively.Using the multiscale method,the frequency amplitude response equation under the steady state motion for CNTRC plate is derived.The nonlinear principal resonance and stability of CNTRC rectangular plates under transverse harmonic excitation are studied.The effects of the thickness of the plate,the excitation amplitude and the volume fraction of CNT on the nonlinear vibration characteristics of the CNTRC plate with various higher-order shear deformation plate theories are discussed.Finally,the analysis of this paper is summarized,and the research direction of the nonlinear dynamic characteristics of CNTRC plate is introduced.