Dynamic Characteristics Of Piezoelectric/Piezomagnetic And Carbon-based Reinforced Composite Circular Cylindrical Shells

Piezoelectric/piezomagnetic materials are widely used in smart material systems due to their unique thermo-electro-mechanical-magnetic coupling characteristics.Compared with macro materials,piezoelectric/piezomagnetic nanomaterials have unique advantages such as smaller size,larger specific surface area,and more significant thermo-electro-magnetic coupling.They have been gained more and more attention and application in micro/nano electromechanical systems,aviation industry and automobile industry.Carbon-based reinforced composite materials are composed of new carbon-based nanofillers and metal,ceramic or polymer matrices.As a new type of nanofillers,carbon-based nanofillers are used to improve the mechanical properties of the matrix structure and maintain its functional applications.Therefore,carbon-based reinforced composite materials are considered to be one of the most promising reinforcing materials and have a wide range of applications in the fields of electronic engineering,aeronautical engineering,biomedical engineering,automotive and civil engineering.In engineering applications,the shell structure is a more commonly used structural element.Therefore,it is of great theoretical significance and application value to further study the dynamic characteristics of piezoelectric/piezomagnetic and carbonbased reinforced cylindrical shells.In this paper,piezoelectric/piezomagnetic and carbon-based reinforced cylindrical shells are considered.Considering the geometric nonlinearity,temperature,external electric/magnetic fields and other factors,the linear/nonlinear vibration of piezoelectric/piezomagnetic nanoshells in a thermo-electric-magnetic environment and the vibration and low-velocity impact response of carbon-based reinforced composite cylindrical shells are studied.It provides a theoretical basis for their application in practical engineering.The main work of this paper includes:(1)In the thermo-electro-mechanical environment,considering the size effect,based on the Love thin-shell theory and the Hamilton principle,the dynamic equations of porous functionally graded nanoshells and functionally graded sandwich piezoelectric nanoshells are established.Using the Navier method and Galerkin method,the eigenvalue equations of the system are obtained.The effects of scale parameters,temperature,voltage,porosity volume fraction,core thickness,and geometric parameters of nanoshells on natural frequencies are discussed.The results show that the application of a positive voltage reduces the stiffness of the functionally graded cylindrical shell,and the application of a negative voltage increases its stiffness.In addition,an increase in temperature change causes a decrease in its stiffness.Core thickness also has significantly different effects on the vibration characteristics of sandwich functionally graded nanoshells with different distributions.(2)In the thermo-electro-magnetic environment,considering the size effect,based on Donnell’s nonlinear shell theory and Hamilton’s principle,the dynamic equations of functionally graded piezoelectric and magneto-electro-elastic cylinderical nanoshell are established.The Galerkin method is used to solve the nonlinear Duffing equation,and the approximate analytical solution is obtained by the multiple scales method.The effects of scale parameters,temperature,voltage,magnetic potential,elastic foundation,and geometric parameters of nanoshells on the nonlinear frequency ratio and frequency ratio are discussed.The results show that both the external voltage and the temperature change have a significant effect on the nonlinear vibration of the functionally graded nanoshell.The Winkler-Pasternak foundation can attenuate the nonlocal effects of nonlinear vibration characteristics of piezoelectric/piezomagnetic nanoshells.(3)Based on Love’s thin shell theory and Hamilton principle,the dynamic equations of carbon-based reinforced composite cylindrical shells are established.Using the Navier method and Galerkin method,the eigenvalue equations of the system are obtained.The effects of graphene platelets distribution type,weight fraction and geometric parameters/three-dimensional graphene foam coefficient,skeleton type,and skeleton weight fraction on natural frequency,axial buckling and resonance frequency are discussed.The results show that the distribution of more graphene platelets/threedimensional graphene foam on the inner and outer surfaces of the graphene platelets/three-dimensional graphene foam reinforced composite cylindrical shell is the most reasonable and effective method to enhance the rigidity of cylindrical shells.(4)Based on the first-order shear deformation shell theory and Hamilton principle,the dynamic equations of carbon-based reinforced composite cylindrical shells are established.The spring mass model and energy balance model are used to simulate the contact force between the impactor and the cylindrical shell.Using Duhamel integrals,time-dependent displacements are obtained.The effects of velocity,geometric parameters of the impactor,three-dimensional graphene foam coefficient,skeleton type,and skeleton weight fraction on the contact force and the peak transverse central displacement of the cylindrical shell are discussed.The results show that the foam coefficient can reduce the peak transverse central displacement of the threedimensional graphene foam reinforced composite cylindrical shell.However,contact force and contact time are not sensitive to the foam coefficient.Increasing the weight fraction of the three-dimensional graphene foam skeleton results in greater contact force and shorter contact time,and reduces peak transverse central displacement.