Nonlinear Vibration Of Nanotube-reinforced Composite Conical Shells

With the development of science and technology in modern society,people give more requests on materials,research and development of new composite materials research and development has become more and more important.Carbon nanotube reinforced composite material is the most vigorous research object in the research field of composite new materials has a very important effect for the future economic and social development.And in practice,vibration is a common working state when the structure starts to work.Put a research on free vibration and forced vibration of carbon nanotube reinforced composite to explore the basic principles of structural vibration can provide a reference for the problems related to vibration,and it have very important application value of carbon nanotube reinforced composite.First,considering the inhomogeneity of nanotube-reinforced composites conical shells as functionally graded materials,the nonlinear dynamic partial differential control equations expressed by stress function and deflection of nanotube-reinforced composite opening conical shells are established based on the continuum theory,classical shell theory and knowledge of the composite in curvilinear coordinates.Applying the Galerkin integration procedure,the nonlinear dynamic partial equations are transferred into a series of nonlinear dynamic ordinary equations.Furthermore,the harmonic balance method is used to solve the free vibration of nanotube-reinforced composite opening conical shells.Finally,the ratio of the nonlinear free vibration frequency and the corresponding linear frequency of nanotube-reinforced composites conical shells is obtained,and the effects of geometric parameters of conical shells and nanotube materials parameters for the conical shallow shell on the nonlinear free vibration are discussed.Secondly,based on classical theory of plate and shell and Hamilton variational principle,the nonlinear dynamic partial differential control equations of nanotube-reinforced composite opening conical shells are established.Applying the Galerkin integration procedure,the nonlinear dynamic partial equations are transferred into a series of nonlinear dynamic ordinary equations.The modal eigen functions of the beam are determined in accordance with the boundary conditions.The variable separation method and the multi-scale method are adopted to solve the nonlinear ordinary differential equations,and the response characters of forced vibration of single freedom system are discussed.The approximate stationary solution of the primary resonance,ultra-harmonic and sub-harmonic resonance are obtained,also the effects of length-thickness ratios,cone angle of conical shells and nanotube materials parameters on the primary resonance frequency of the shells is explored and discussed.