Nonlinear Vibrations Of Incompressible Hyperelastic Cylindrical Shells

Cylindrical shells are widely applied in the fields of pipeline transportation,mechanical manufacture,ship production and aerospace industry.With the continuous development of material science,more and more materials(such as the rubber,rubber-like material,hydrogel and shape memory alloy)in engineering begin to employ hyperelastic models to describe their nonlinear mechanical properties.Those cylindrical shells made of this kind of materials can combine the advantages of materials and structures,and have a broad application prospect in engineering.Moreover,shells used in engineering bear various types of dynamic loads inevitably,it leads to the complex vibration response which is one of the important factors of structural failures.In order to improve the safety of hyperelastic cylindrical shells,undoubtedly,an in-depth understanding on their nonlinear vibration characteristics are essential and necessary to the design and manufacture.This dissertation mainly focuses on the continuum modelling and analyses of nonlinear dynamics of incompressible hyperelastic cylindrical shells subjected to several types of loads.The influences of structure,load and temperature parameters on the responses of shells are researched systematically.The main contents of this dissertation are divided into the following three parts:1)The axisymmetric nonlinear low-frequency vibrations of incompressible hyperelastic thin-walled cylindrical shells subjected to axial harmonic excitations are investigated.Based on the variational method and the displacement approximate expansion method,the nonlinear governing differential equations are obtained.The natural frequency of the cylindrical shell is analyzed,and the conditions of internal resonances are determined.The harmonic balance method and the arc length method with two-point prediction are adopted to calculate the complicated steady-state solutions effectively.Significantly,numerical results manifest that the length-diameter ratio serves a critical role in the nonlinear low-frequency vibrations,and its variation should give rise to abundant nonlinear phenomena,such as the typical softening and hardening,the resonance peak shift and the isolated bubble shaped response.2)The nonlinear dynamics behaviors of incompressible hyperelastic cylindrical shells subjected to axial excitation and time-varying temperature with 3:1 internal resonance are investigated.Through the analysis of the influences of temperature on material parameters,the hyperelastic strain energy density function in the unsteady temperature field is presented.Based on the nonlinear thin shell theory,the variational method,the harmonic balance method and the arc length method,the steady state solutions of shells are detected.The influences of the discrete mode number,structural and temperature parameter on the nonlinear behaviors of shells are examined.The role of parameter variation in evolution behaviors of isolated bubble responses is revealed for the 3:1 internal resonance.The results manifest that both structure and temperature parameters can affect the resonance range of the response curve,and the perturbed temperature has a more significant effect on the stable region of the solution.3)The nonlinear dynamics behaviors of incompressible hyperelastic moderately thick cylindrical shells subjected to radial excitation and steady-state temperature with 2:1 internal resonance are investigated.Based on Reddy’s third-order shear deformation theory and the higher order approximation of the curvature-related expansion,the displacements and the strain-displacement relations with more accurate coefficients are formulated.With the degreeof-freedom condensation method and the multiscale method,the approximate analytical solutions of the 2:1 internal resonance of shells are obtained.The influences of loads,structural parameters and temperature parameters on the internal resonance are analyzed with numerical methods.The results manifest that the temperature gradient has a marked impact on the doublejumping of the shell.Additionally,the splitting of resonance peak is found.