Study On Dynamic Snap-Through And Nonlinear Dynamics Of Bi-Stable Asymmetric Composite Laminated Panels

Bi-stable asymmetric composite laminated plate and shell structure is a kind of composite laminated structure with two different stable state characteristics.Bi-stable asymmetric composite laminated plate and shell structure is usually composed of carbon fiber/resin composite preparation.Due to the different thermal expansion coefficients of carbon fiber and resin and the asymmetric laying way,the residual stress will appear in the process of high temperature and cooling,which lead to the upper and lower surface residual stress cannot be offset and the composite laminated plate and shell structure of two different curvature steady state.The bi-stable plate and shell structures are stable in both natural equilibrium position without external force.Moreover,the specific jumping phenomenon of the structure makes it require very little energy to obtain relatively large deflection.As a kind of energy saving deformable structure,bi-stable asymmetric composite plate and shell structures have a wide application prospect in deformable aircraft,aerospace,energy harvester,absorber and many other engineering fields.Moreover,the bi-stable structure will inevitably produce nonlinear vibration in the complex environment of engineering application.Therefore,in order to make full use of the advantages of bi-stable plate structure and make it play the greatest role in aerospace engineering applications,it is of great theoretical significance and application value to study the dynamic snap-through phenomena and nonlinear dynamics of bi-stable composite laminated plate and shell structure.In this paper,the dynamic snap-through phenomena and nonlinear dynamics of bi-stable asymmetric composite laminated shells are studied.In the case of considering geometric nonlinearity,Hamilton principle is used to establish the nonlinear motion governing equation of bistable composite laminated shell.The dynamic snap-through and nonlinear dynamics are analyzed.The experimental study is carried out.The specific research contents are as follows:(1)Based on the third order shear deformation theory and Hamilton principle,the governing equation of the bi-stable asymmetric composite laminated shell under the action of transverse foundation excitation is obtained by considering the geometric nonlinearity and shear deformation.The natural frequency and mode functions are obtained by using the Language multiplier method and Rayleigh-Ritz method,considering the boundary conditions of clamped at the center and four free edges.The intrinsic properties of bi-stable asymmetric composite laminated shells are studied,and the effects of different lay layers and different geometry dimensions on the nonlinear vibration of the structure are compared.Galerkin method is used to discretize partial differential equation into ordinary differential equation,and Hamilton function of undisturbed system is obtained.The influence of different solidified temperature on system equilibrium point and potential well was studied.The Runge-Kutta method is used for the numerical simulation of the ordinary differential equation and the critical dynamic snap-through load of the structures are obtained.The influence of the number of layers and the geometric size on the dynamic snap-through penomena of the sturcture under the transverse foundation excitation was studied.(2)The perturbation analysis of the ordinary differential governing equation of the bistable asymmetric composite laminated shell was carried out by using the multi-scale method,and the average equation of the system at 1:1 internal resonance was obtained.The influence of the transverse foundation excitation and damping coefficient on the nonlinear dynamic resonance of the bi-stable asymmetric composite laminated shell is studied.Runge-Kutta method is used to simulate the average equation and the effect of transverse basic excitation on the nonlinear dynamic behavior of the system is studied.(3)The second order perturbation analysis of the ordinary differential governing equation of the bistable asymmetric composite laminated shell is carried out by using the multi-scale method,and the average equation of the system at 1:2 internal resonance is obtained.The influence of the transverse foundation excitation and damping coefficient on the nonlinear dynamic resonance of the bi-stable composite laminated shell is studied.Runge-Kutta method is used to simulate the average equation and the effect of transverse basic excitation on the nonlinear dynamic behavior of the system is studied.(4)The vibration experiments of the bi-stable asymmetric composite laminated shell are carried out,and the boundary conditions are clamped at the center of the panel and four edges are free.The nonlinear vibration and dynamic snap-through of the bi-stable composite laminated shell under the transverse foundation excitation were measured and photographed by the electromagnetic shaker,Laser Displacement Sensor and Phantom v641 High Speed Camera,and the results are compared with the theoretical results for verification and analysis.(5)Using Abaqus software,simulation experiments are conducted on the productive process and the dynamic snap-through phenomena of bi-stable graphene-reinforced composite laminates.The boundary conditions of are clamped at the center of the panel and free on four edges,and basic excitation was applied at the center point.The relationship among the transverse displacement of the bi-stable shell and the two directions in-plane displacements of the shell is studied.Based on the third-order shear deformation theory,the dynamic governing equation of the three-degree-of-freedom bi-stable graphene reinforced composite laminates are established.The Runge-Kutta method is used to numerically simulate the motion control equation under the transverse foundation excitation,and the critical dynamic snap-through loads of the structure are obtained.The effect of the mass fraction of graphene on the dynamic snap-through phenomena is studied.