Observações sobre as respostas estática e dinâmica de uma membrana hiperelástica anelar - Xavier, Jhonatas Venancio (2019)
In this work is studied, a membrane with ring geometry and coupled with an internal rigid ring with negligible weight. The membrane is composed of hyperelastic, incompressible, homogeneous and isotropic material. The constitutive models of Mooney-Rivlin and the neo-Hookean are used. The membrane equilibrium equations are obtained using the theory of nonlinear elasticity and the variable method. The solution of the equilibrium equations is done by the iterative numerical method of Runge-Kutta and the shooting method. For a static response are done two parametric analysis, one in the transverse direction and another in the radial direction of the membrane, obtaining the answers for the radial and transverse displacements and strain. The dynamic analysis is made from the static solution. To obtain the equation of motion, it is necessary to use the numerical method of Rayleigh-Ritz for integration in the membrane domain and Urabe method for integration in time. From the equation of motion, we obtain the natural frequencies and the frequency x amplitude relation for the free vibration and for the forced vibration the resonance curves. For the static case are compared the responses of the Mooney-Rivlin and neo-Hookean models and the responses of two models are convergent and no convergent for some cases of high transversal displacements. For the dynamic case the Mooney-Rivlin and neo-Hookean responses are convergent for the natural frequencies, relation frequency x amplitude and for the resonance curves.