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| 1 | Nonlinear Vibration Analyses of Cylindrical Shells Composed of Hyperelastic Materials显示文摘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. | Jing Zhang Jie Xu Xuegang Yuan Hu Ding Datian Niu Wenzheng Zhang | 2019 | Acta Mechanica Solida Sinica2019，32，4： | 2 |
| 2 | DYNAMIC CHARACTERISTICS IN INCOMPRESSIBLE HYPERELASTIC CYLINDRICAL MEMBRANES显示文摘In this paper,the dynamic characteristics are examined for a cylindrical membrane composed of a transversely isotropic incompressible hyperelastic material under an applied uniform radial constant pressure at its inner surface.A second-order nonlinear ordinary differential equation that approximately describes the radial oscillation of the inner surface of the membrane with respect to time is obtained.Some interesting conclusions are proposed for different materials,such as the neo-Hookean material,the Mooney-Rivlin material and the Rivlin-Saunders material.Firstly,the bifurcation conditions depending on the material parameters and the pressure loads are determined.Secondly,the conditions of periodic motion are presented in detail for membranes composed of different materials.Meanwhile,numerical simulations are also provided. | Datian Niu Xuegang Yuan Changjun Cheng Jiusheng Ren | 2010 | Acta Mechanica Solida Sinica2010，23，5： | 2 |
| 3 | Ana- lytic Solutions of Parametric Type and Numerical Simula- tions of a Class of Nonlinear Ordinary Differential Equa- tions 显示文摘 | NIU Datian ZHANG You YUAN Xuegang | 2010 | Applied Mathematical Sciences2010，4，30： | 1 |
| 4 | Large-Amplitude Oscillations of Hyperelastic Cylindrical Membrane Under Thermal-Mechanical Fields显示文摘In this paper,the nonlinear dynamic behaviors of a hyperelastic cylindrical membrane composed of the incompressible Ogden material are examined,where the membrane is subjected to uniformly distributed radial periodic loads at the internal surface and surrounded by a thermal field.A second-order nonlinear differential equation describing the radially symmetric motion of the membrane is obtained.Then,the dynamic characteristics of the system are qualitatively analyzed in terms of different material parameter spaces and ambient tem-peratures.Particularly,for a given constant load,the bifurcation phenomenon of equilibrium points is examined.It is shown that there exists a critical load,and the phase orbits may be the asymmetrie homoclinic orbits of the“oo”type.Moreover,for the system with two centers and one saddle point,the dynamic behaviors of the system show softening phenomena at both centers,but the temperature has opposite effects on the stiffness of the structure.For a given periodically perturbed load superposed on the constant term,some complex dynamic behaviors such as quasiperiodic and chaotic oscillations are analyzed.With the Poincare section and the maximum Lyapunov characteristic exponent,it is found that the ambient temperature could lead to the irregularity and unpredictability of the nonlinear system,and also changes the threshold of chaos. | Wenzheng Zhang Datian Niu Fengxia Zhao | 2022 | Acta Mechanica Solida Sinica2022，35，2： | 0 |
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