The comparative analysis of the fully nonlinear, the linear elastic and the consistently linearized equations of motion of the 2D elastic pendulum

The floating frame of reference approach is used for the analysis of the in-plane oscillations of the suspended rectangular plate. The deformation is interpolated by means of polynomial shape functions. The equations of motion become nonlinear in the deformation degrees of freedom both due to the geometrically nonlinear deformation model and to the inertial coupling between the rotation and the deformation of the body. Consistent linearization with respect to the deformation degrees of freedom simplifies the equations significantly and speeds up the time integration. A convergence study with respect to the maximum interpolation order is performed. The comparative analysis of different problem statements and their ranges of applicability is presented in the paper.