NONLINEAR VIBRATIONS OF A RADIALLY STRETCHED CIRCULAR HYPERELASTIC MEMBRANE
The paper presents a detailed analysis of the nonlinear vibration response of a pre-stretched hyperelastic membrane subjected to finite deformations under the action of a time-varying lateral pressure. The membrane material is assumed to be isotropic, homogeneous and neo-Hookean. First the exact solution of the membrane under a uniform radial stretch is obtained. Then the equations of motion of the pre-stretched membrane are derived. From the linearized equations, the natural frequencies and mode shapes of the membrane are obtained analytically. Then the natural modes are used to approximate the nonlinear deformation field using the Galerkin method. Several reduced order models are tested and the results compared with the results evaluated for the same membrane using a nonlinear finite element formulation. Excellent agreement is observed. The results show the strong influence of the stretching ratio on the linear and nonlinear oscillations of the membrane.