Elliptic balance solution to two degree of freedom, undamped, homogeneous systems having cubic nonlinearities

The application of the elliptic balance method to the solution of undamped, two degree of freedom homogeneous nonlinear systems is described. This method uses Jacobian elliptic functions in the balance and is based on the concept of averaging with respect to complete elliptic integrals of the first kind. To assess the accuracy of the approximate solution thus obtained, we consider the motion of a linear vibration absorber attached to a rigid body that is supported symmetrically by incompressible, homogeneous and isotropic hyperelastic shear blocks. It is shown that the amplitude–time response of the model system is well predicted by the elliptic balance method solution even for relatively large parameter values.