Nonlinear vibration with axisymmetric 3:1 internal resonance is investigated for an incompressible neo-Hookean hyperelastic cylindrical shell under both axial and radial harmonic excitations.A full nonlinear strain-di...Nonlinear vibration with axisymmetric 3:1 internal resonance is investigated for an incompressible neo-Hookean hyperelastic cylindrical shell under both axial and radial harmonic excitations.A full nonlinear strain-displacement relation is derived from the large deflection theory of thin-walled shells.A set of nonlinear differential equations describing the large deflection vibration are formulated by the Lagrange equation and the assumption of small strains.Steady-state responses of the system are predicted via the harmonic balance method with the arc length continuation,and their stabilities are determined via the modified sorting method.The effects of excitations on the steady-state responses are analyzed.The results reveal a crucial role played by the phase difference in the structural response,and the phase difference can effectively control the amplitude of vibration.展开更多
The nonlinear vibration problem is studied for a thin-walled rubber cylindrical shell composed of the classical incompressible Mooney-Rivlin material and subjected to a radial harmonic excitation. With the KirchhofF-L...The nonlinear vibration problem is studied for a thin-walled rubber cylindrical shell composed of the classical incompressible Mooney-Rivlin material and subjected to a radial harmonic excitation. With the KirchhofF-Love hypothesis, DonnelFs nonlinear shallow shell theory, hyperelastic constitutive relation, Lagrange equations and small strain hypothesis, a system of nonlinear differential equations describing the large-deflection vibration of the shell is derived. First, the natural frequencies of radial, circumferential and axial vibrations axe studied. Then, based on the bifurcation diagrams and the Poincare sections, the nonlinear behaviors describing the radial vibration of the shell are illustrated. Examining the influences of structural and material parameters on radial vibration of the shell shows that the vibration modes are highly sensitive to the thickness-radius ratio when the ratio is less than a certain critical value. Moreover, in terms of the results of multimodal expansion, it is found that the response of the shell to radial motion is more regular than that without considering the coupling between modes, while there are more phenomena for the uncoupled case.展开更多
Thin-walled structures are commonly utilized in aerospace and aircraft structures,which are prone to buckling under axial compression and extremely sensitive to geometric imperfections.After decades of efforts,it stil...Thin-walled structures are commonly utilized in aerospace and aircraft structures,which are prone to buckling under axial compression and extremely sensitive to geometric imperfections.After decades of efforts,it still remains a challenging issue to accurately predict the lower-bound buckling load due to the impact of geometric imperfections.Up to now,the lower-bound curve in NASA SP-8007 is still widely used as the design criterion of aerospace thin-walled structures,and this series of knockdown factors(KDF)has been proven to be overly conservative with the significant promotion of the manufacturing process.In recent years,several new numerical and experimental methods for determining KDF have been established,which are systematically reviewed in this paper.The Worst Multiple Perturbation Load Approach(WMPLA)is one of the most representative methods to reduce the conservatism of traditional methods in a rational manner.Based on an extensive collection of test data from 1990 to 2020,a new lower-bound curve is approximated to produce a series of improved KDFs.It is evident that these new KDFs have an overall improvement of 0.1-0.3 compared with NASA SP-8007,and the KDF predicted by the WMPLA is very close to the front of the new curve.This may provide some insight into future design guidelines of axially compressed cylindrical shells,which is promising for the lightweight design of large-diameter aerospace structures.展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11672069,11872145,11872159,12172086,and 12101106).
文摘Nonlinear vibration with axisymmetric 3:1 internal resonance is investigated for an incompressible neo-Hookean hyperelastic cylindrical shell under both axial and radial harmonic excitations.A full nonlinear strain-displacement relation is derived from the large deflection theory of thin-walled shells.A set of nonlinear differential equations describing the large deflection vibration are formulated by the Lagrange equation and the assumption of small strains.Steady-state responses of the system are predicted via the harmonic balance method with the arc length continuation,and their stabilities are determined via the modified sorting method.The effects of excitations on the steady-state responses are analyzed.The results reveal a crucial role played by the phase difference in the structural response,and the phase difference can effectively control the amplitude of vibration.
基金supported by the National Natural Science Foundation of China (Nos.11672069,11702059,11872145).
文摘The nonlinear vibration problem is studied for a thin-walled rubber cylindrical shell composed of the classical incompressible Mooney-Rivlin material and subjected to a radial harmonic excitation. With the KirchhofF-Love hypothesis, DonnelFs nonlinear shallow shell theory, hyperelastic constitutive relation, Lagrange equations and small strain hypothesis, a system of nonlinear differential equations describing the large-deflection vibration of the shell is derived. First, the natural frequencies of radial, circumferential and axial vibrations axe studied. Then, based on the bifurcation diagrams and the Poincare sections, the nonlinear behaviors describing the radial vibration of the shell are illustrated. Examining the influences of structural and material parameters on radial vibration of the shell shows that the vibration modes are highly sensitive to the thickness-radius ratio when the ratio is less than a certain critical value. Moreover, in terms of the results of multimodal expansion, it is found that the response of the shell to radial motion is more regular than that without considering the coupling between modes, while there are more phenomena for the uncoupled case.
基金the National Natural Science Foundation of China(Grant Nos.U21A20429,11772078,and 11825202)the National Defense Basic Research Program(Grant No.JCKY2020110).
文摘Thin-walled structures are commonly utilized in aerospace and aircraft structures,which are prone to buckling under axial compression and extremely sensitive to geometric imperfections.After decades of efforts,it still remains a challenging issue to accurately predict the lower-bound buckling load due to the impact of geometric imperfections.Up to now,the lower-bound curve in NASA SP-8007 is still widely used as the design criterion of aerospace thin-walled structures,and this series of knockdown factors(KDF)has been proven to be overly conservative with the significant promotion of the manufacturing process.In recent years,several new numerical and experimental methods for determining KDF have been established,which are systematically reviewed in this paper.The Worst Multiple Perturbation Load Approach(WMPLA)is one of the most representative methods to reduce the conservatism of traditional methods in a rational manner.Based on an extensive collection of test data from 1990 to 2020,a new lower-bound curve is approximated to produce a series of improved KDFs.It is evident that these new KDFs have an overall improvement of 0.1-0.3 compared with NASA SP-8007,and the KDF predicted by the WMPLA is very close to the front of the new curve.This may provide some insight into future design guidelines of axially compressed cylindrical shells,which is promising for the lightweight design of large-diameter aerospace structures.
